texts: Estimating Darcy Friction Factors for Critical Flow

texts:
The Darcy-Weisbach equation is used to calculate the frictional pressure losses in pipes transporting incompressible fluids. This equation uses a dimensionless Darcy friction factor, also known as the Moody factor, to account for the relative roughness of the pipe surface.

This empirical factor was experimentally determined by Moody and is normally read off of the Moody Chart. However I am implementing the pressure drop calculation in software, so I need a non-graphical way to find the Darcy friction factor.

Equations for calculating the Darcy friction factor under laminar (Re < 2320) and turbulent (Re > 4000) flow are readily available. But I haven't been able to find one that is valid for the transitional region which exists between laminar and turbulent flow (2320 < Re < 4000), also known as the 'critical zone'.

I understand that fluid flow is complex and difficult to predict in this region. However, is there a commonly used method that provides reasonable estimates for the friction factor in this critical zone?

I have found a method described in a student paper, but it hasn't been peer reviewed and is limited to smooth pipes only. I'm looking for something more tried and tested.

If no formula is available, what approach do other engineers usually take to mitigate or solve this problem?


texts:
I'm wondering if there is any difference between Gibbs Free Energy and Exergy because their definition seems to me the same $\Delta H - Tenv*\Delta S $

Exergy represents the maximum amount of work that can be extracted from a system going in equilibrium with its environment, while the Gibbs Free Energy is evaluated at T,P of the system in equilibrium with the environment.

Practically what is the difference, if any?


texts: How thick does an aluminium vacuum cylinder have to be?

texts: Take a hollow aluminium cylinder with outer radius $r$ and length $h$, capped with two circular endcaps.  How thick does the aluminium have to be, that is what is the inner diameter of the cylinder, to withstand 1 atm on the outside and 0 mbar on the inside, without crumpling?


texts: Is there well known equation (formula) to calculate maximum practical current which copper wire of fixed diameter can handle

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I found many online calculators or tables which can give maximum current for the wire. Like 1 mm diameter can handle up to 10 Amperes, 2 mm diameter wire can handle up to 30 Amperes, etc.

Is there any practical equation (formula) for this which will work in a wide range of currents $10^{-3}-10^2$ Amperes (1 milliampere - 100 Amperes) and 0.01-100 mm wire diameter?

Is it linear? If yes, I can make up the formula from all these tables.

I need a simplified case, like a single bare copper cylindrical (round) wire without insulation, in the air with 20-25 Celcius room temperature, etc.

It does not matter for me if the formula will be depending on wire diameter or wire area. I can change it if needed.

UPDATE 1

I tried the answer from Peter Green $$I=15.774 A^{0.6077}$$
and I got this graph

The horizontal axis is wire cross-section (A) in $mm^2$ and vertical axis is current in Amperes.
Orange is a calculated graph. Blue is from one of the tables from the internet, here for example https://www.powerstream.com/Wire_Size.htm.

As I see the shape is matching, but values are not. For the current less than 10A, the calculated value is higher, for current less than 10A, calculated value is smaller.

If I put it like this
$$I=22 A^{0.6077}$$
then it works much better for the current more than 15A, but still not very good for small currents.

Looks like using these tables is the only way :( I will try to get an equation from the table with the assumptions that true equations should be

$$I=y A^{x}$$

I will try to find y and x and post it here if I will be successful.


texts: Can I use a threaded bolt to support a ball bearing?

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I'm working on a design where I need a ball bearing with an inner diameter of 8mm. The ball bearings will support small 3D printed wheels, looking kind of like a skateboard wheels. In order to fasten these wheels, I'm planning to use 8mm screws. The screws that I have found are threaded all the way, and I'm wondering if it is possible/recommended to use threaded screws to support ball bearings? Ideally I would use screws that are not threaded all the way, so the ball bearing can sit on the part that is not threaded. However, I couldn't find such screws. So what if I would use threaded screws? Would it work at all? Is there some workaround I can do using washers/extra bolts?

Edit:

Here is the design, plus a new design I came up with...

https://www.dropbox.com/s/c86cxw1wyc9zi7v/IMG_3628.JPG

What I have learned so far... There is such a thing as a shaft collar, and that's what I should be using in this case. Here is one that is 3D printed:

https://www.thingiverse.com/thing:400921

And on there there is also an example of how it is used together with ball bearings. That's what I should be inspired by...


texts: I have a question about gas valve selection and working out the CV. The equation I have needs the mass flow in kg/hr, but I have been given the volumetric flow rate in litres/minute. How do I go about converting this? Thanks


texts: Economical difference with high-pressure vessel design pressures for fixed volume

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Suppose space is not an issue and I need a fixed volume of compressed air (for storage), say 1m³. Is it more economical to manufacture a thick-walled vessel but with a smaller volume or a thin-walled vessel but with a larger volume? Take into consideration that there will be a valve for filling and releasing too.
Is there some proportional relationship or is it a "it depends" situation with "best of both world" solutions?


texts: Slab Stiffness Modifiers applied in Vertical Elements design but not in Slab design?

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Why in the design of vertical elements (columns and walls) for a structure against lateral loads (such as seismic and wind) we use a slab (or shell) with a stiffness modifiers (such as 0.25 according to ACI Code) to reduce the moment of inertia (example when we design vertical elements in ETABs and Robot), but in the simple design of the slab we do not use these modifiers (and a side question is: why don;t we include the lateral load of seismic and wind in the design of the slab)??

Thank you in Advance.


texts: Why don't modern warships still use cannons?

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This question is about a technical aspect of naval warfare, and I think that this site is the closest fit. History would have been my next guess.

In the TV show “The Last Ship” the protagonists have an Arleigh-Burke class guided missile destroyer. It seems to engage targets mainly with rockets of different sizes. Incoming rockets are shot down either with the point defense turrets or with other rockets. It is probably skewed for the plot of the show, but they seem to be able to shoot down most incoming missiles, making the ship appear near invincible.

In the fifth season they are up against a battleship and are struck with incoming shells from canons in two different episodes. The first time the destroyer gets rendered disabled, the second time it starts to sink.

Reading up on this I noticed that modern fleets do not have battleships with huge cannons any more, guided missile destroyers are the largest warships that are built now. Given that in the show the rockets appear somewhat ineffective and the shells seem to be unblockable, I wonder why modern ships use mostly rockets.

Judging by their presentation of cyber warfare, the military accuracy is probably not good enough to extrapolate this. But if guided missiles are supposed to be so much better, did the destroyer have a serious problem with the battleship just for plot reasons or is that somewhat realistic?


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I'm currently stuck on obtaining a description of the robot base velocities (xdot, ydot, thetadot) based on data obtained from 4 IMU sensors located, with an offset, on 4 pivot points. See picture below:

And a closeup of 1 of the pivot wheels:

The IMU is located at the red dot and since this is a 2d problem, I'll only consider acceleration in the X,Y direction of the IMU frame and rotation around the Z axis of the IMU frame.

Now, since I'm looking to obtain a description for the velocities xdot, ydot en thetadot, this all would result in something like the following:

[dx dy dtheta]' = [3x12 matrix] * [ax_1 ay_1 gz_1 .. .. .. etc.]'

I think that if a description of how the accelerations of the individual IMU's influence the robots odometry is known, I can average the individual components to come to the 'true' odometry. So what's first (I think) is obtaining a description of either dx or dy or dtheta as a function of the angle delta and the velocities of the IMU.

If we want to know the location of the IMU in the robot's frame, we would need translation matrices which look like the following:

H_imu_p = [1 0 -d_s; 0 1 0; 0 0 1];
H_p_r = [cos(d) -sin(d) -d_px; sin(d) cos(d) -d_py; 0 0 1];

Where d_s is the distance in X between the IMU and the pivot point and d_px and d_py are the distance between Robot Origin and pivot point expressed in the Robot's frame.

Multiplying these matrices would result in a matrix that is able to give the location of the IMU in the Robot's frame. Since the IMU is located wrt the IMU frame at:

p_imu = [0 0 1]'

We can obtain the location of the IMU wrt the global frame by taking the last column of the multiplied translation matrices.

Differentiating this information twice obtains how the accelerations of the IMU are expressed in the Robot's frame.

Here is where the question part begins:

Assuming all this information above is correct, how do I go from an expression that expresses xddot_IMU yddot_IMU and thetaddot_IMU in the robot's frame to that of determining the velocities of the robot's frame?

Would integrating the measurement results (so obtain velocities of the IMU) and then having the expression of location of the IMU wrt the robot's frame differentiated once? deltadot could then be obtained from the gyroscopic data around the Z-axis. I'm having doubts about this method due to the complex kinematic relationships between the IMU and the robot. Essentially all the four pivot points could rotate without the robot ever moving (while still measuring values at [ax_1 ay_1 gz_1 .. .. .. etc.]

I'm not asking for a worked out solution but I'm quite stuck here and couldn't find the required literature to find a way out. If someone could point me towards the solution (or towards some examples in literature), that would be very much appreciated.


texts: What is the name of this particular mechanical linear position switch made of perforated spring strip?

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I'm writing a few elementary paragraphs about switches and switch technology, and I cannot for the life of me remember what a particular kind is called, to give it an honorable mention.
Here is a sketch of the switch in question:

It is constructed of at least one roller, past which a strip of spring is pulled or pushed. The spring has cut-outs of various shapes, which can be regular or irregular, making the spring strip "prefer" some positions over others, requiring a certain force to overcome them. Various combinations of perforations and rollers could be used to create very complex "preference" patterns. You can see the usefulness: you can put the switch in any one of it's "stop points" and it just stays there until you move it away; and it gives wonderful oportunity (from a design standpoint) for what is now called "haptic feedback".
I learned about them in grade school, studying simple and complex machines, but now I can't remember any sort of name for them. I've combed the LEXICON encyclopedia, where I seem to remember having seen the thing in the first place, and all the switches I come up with are electrical switches. In Google, ditto, along with a great number of maddening diagrams of gamers mechanical keyboard switches and their various merits.
I'm not a well-formed engineer, so I beg you have patience if this isn't the right place to ask; or tell me what other information I should give and I will try.
I'm looking generally for example uses, but I'll be quite happy if someone kindly just gives the name, as I will probably be able to do the rest of footwork myself. Cheers!
EDIT1: 27-JUL-2020:
Kevin gave the right name, and now I see that my recollection went astray: the rollers actually roll on each other with only the band between them, and they have (in many cases, at least) mobile axes, constrained by the transversal rigidity of the band.


texts: What is the type of nut and tool to be used to unscrew?

texts: Please see the two images. I marked a nut and locking part. what type of nut and lock mechanism it is? and what is the tool I have to use to open it?


texts:
I.e. when you wait at a traffic light, without stopping your combustion engine.

( My long term curiosity is about some empirical raw approximation of the consumption in liters/minute. Easy to measure at road speed, but not at rest - or very slow speed. Ultimately I'ld like to get orders of magnitudes, for main factors isolated, but here for a start a global number at rest is all I seek for. ).

To settle numbers if needed, I can give the setup for my (French) car: gasoil, electronic injection, 130 ch din, 2.0 liters. But I'm curious for other setups as well.


texts: Why is this simulation not working in multisim?

texts:
I am trying to simulate this circuit, difference amplifier op amp circuit,  which uses a 741 opamp and set the gain (i.e R2/R1) to be 1000. Assume that the maximum difference input (V2-
V1) is ±5mV and that the common-mode voltage is 2.5V.
My problem is i don`t know if my input voltages are correct, also if i have to set Vcc and Vdd. And my voltage output is not changing when i change my resistor values, so  i know my circuit is not working properly.
Can you help me fix this?


texts: Easy model to calculate water flow rate over trough ledge?

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Trough is 1.87 meters long and 0.5 meter wide and 0.22 meter deep.  Water only flows over the 1.87 meter long side and from both sides (so x2).  The water overflow is 0.012 meters tall (ruler positioned on edge of trough and water hits 1.2 cm up ruler, this is similar to depth of a waterfall at the ledge).  It is consistent across trough length.

What is the flow rate of water over the edge?

I modeled water molecules like balls thrown upward and being decelerated by gravity.

$$\frac{2 \cdot 0.012}{t^2} = 9.81$$

Assuming final velocity of rising water molecule is zero, then initial velocity of 0.485 m/s can be calculated (as it leaves trough edge traveling upward). [sqrt (2*gravity*height)]

The average is therefore half of that at 0.243 m/s, since we are averaging with zero.

The cross sectional area over which water flows is 1.87 m * 0.012 m and multiplying that by 0.243 m/s gives 0.00545 m^3/s which converts to 86.4 gpm.  There are two sides of the trough so multiply by 2 to get 172.8 gpm.

I derived this naively based on physics knowledge, so please tell me where I'm wrong regarding a simple model of the system.


texts: How does measurement uncertainty combine with tolerances?

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Given a tolerance within which your workpiece should be manufactured, say some length should be $10\pm1$mm. If you determine that your uncertainty in measuring this length is $0.2$mm (at 95%). How should a measurement of $9.1$mm be treated?

Clearly there is a significant probability that this value will actually be outside of tolerance. Do you need to decrease you tolerance range based on the uncertainty in your measurement?


texts:
If so, what would it be its official name? it might have another name than Torsion test because I googled it and nothing was found.
pdta: I know there is a torsion test for metals , but that is not what I am looking for. thank you.


texts:
Disclaimer: amateur mechanic, not an engineer of any kind.
I just bought a spring compressor for my car. It's the factory recommended type so I'm assuming it's strong enough, but I'm wondering exactly how strong - since it looks (to my untrained eye) like there's a clear weakest link. The spring gets sandwiched between cast iron plates. The bottom plate rests on a threaded handle that looks really thick and sturdy. The top plate however is held in place by a hemispherical piece ('Upper Ball' in Figure 1), which is in turn held onto the main shaft by a small dowel pin ('Pin' in Figure 1). The upper ball fills a tapered hole in the upper plate, which presses down onto the coil. Everything seems like a well-machined fit - the pin slides in easily with no play.

Here's an image of the actual pieces:

The pin is 7.75mm in diameter and 56.0mm in length. The upper ball has an ID of 18.6mm and an OD of 44.3mm, so during use the pin sticks out both sides as per the image. I can't tell what it's made of, but I'm assuming either grade 5 or grade 8 steel or the equivalent metric grade.
Two questions:
(a) am I correct in assuming that this is the weakest part of the assembly?
(b) is it possible to calculate an approximate yielding/breaking strength of this part of the assembly, assuming either grade 5 of grade 8 steel?
For reference, the total force I would routinely put on this compressor is 1000 lbs (~4500 N).


texts: How do these thread-holder mechanisms work?

texts:
In old scientific apparatus for electrical experiments, and more particularly in instruments such as galvanometers and torsion balances, we often need to hold one end of a thread in place. Examples include the following (particularly large photos are given as links):

https://upload.wikimedia.org/wikipedia/commons/4/4a/Galvanometer-MHS_229-IMG_3875-gradient.jpg (Very large)
https://catalogue.museogalileo.it/images/cat/oggetti_944/1560_3283_1933-011_944.jpg
https://catalogue.museogalileo.it/gallery/DemonstrationModelAstaticGalvanometer.html

Galvanometer (courtesy of museo galileo, here):

In one description, from museo galileo, here:

  A pair of astatic needles is suspended from the fine silk wire attached to a torsion mechanism at the top of the pillar. The needles can be raised or lowered by means of a complex screw-operated scissors-type mechanism.

In Coulomb's torsion balance, we get the following drawing, and description:

  The top, n° 1, bears a knob b, the pointer io, and the clasp of
  suspension, q ... The clasp q (figure 2, n° 1) has approximately the shape of
  the extremity of a solid mechanical pencil clamp [porte-crayon], which can be
  tightened by means of the annulus q. The clasp of this porte-crayon holds the end of a filament of very thin silver. The other end of the filament of silver is fixed (fig. 3) at P, by the clasp of a cylinder Po of copper or of iron, whose diameter is but a [ligne], and whose end P is split and forms a clasp which is tightened by means of the collar Φ.

I've been reviewing these sorts of mechanisms for a while, and Coulomb's description (the clasp of a mechanical pencil) is the closest I've found to a proper description. But with mechanical pencils, as I know them, the clasp (e.g.a two-part split piece of plastic in a modern one) supports a fixed diameter of lead, typically much thicker than the width of a silk thread. As well, it's not clear from my (limited) research what mechanisms were used for "porte-crayons" in that time period.

I'm looking to recreate some of these instruments in some way, e.g. with modern methods of fabrication and using modern mechanisms available. But these thread-holders are giving me a fair bit of trouble. Is there any resource available where I can get mechanical drawings of such mechanisms, or is there a common "household item" which uses these sorts of clasps that I could look at? Does anyone have any ideas about how these would have worked?


texts: How to keep a tray horizontal when moving around a closed, vertical track?

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I have seen this somewhere in the wild, perhaps a space-efficient storage system in lieu of two shelving units. I'm trying to reproduce, and failing.

Imagine two stacks of trays which hold things that must not fall out, so the trays must remain horizontal. The trays are all connected to the same track, which loops around, so that the first stack is on "the way down" for the track, and the second stack on "the way up".

Q: how are the trays connected to the track, so that they can move along the track eternally without ever tipping over?

I sort of remember that there is a wheel on each tray that counteracts the rotation coming from the track, but I don't remember how.


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Are there any fabrics available in today’s time which can stretch in one direction only and behave completely rigid in the perpendicular direction ?

Or does any Materials Science expert know about any on-going research in this area ?

I particularly wanted to know the way in which one might go about manufacturing something like this.

So, if such a fabric is imagined to be made up of perpendicularly intersecting fibres, one of which is stretchable while the other is not, like criss-crossing rubber & fibreglass fibres, for instance, what would be the way to make something like this ?


texts:
I asked a previous question about pipe t-junctions with pipes of varying diameters, and it got me wondering...

How are losses handled and calculated in pipes with holes drilled directly into them? Flow runs perpendicular to the hole and most of the theory I can see for flow through a pipe exit assumes the pipe and orifice are coaxial. Or for an orifice plate directly in the pipe flow, neither of which seem appropriate.

I'm guessing some theory must exist since common objects like lawn sprinklers contain these pipes with many holes drilled into them. I have been thinking about a pipe with one hole drilled in it of small diameter. Essentially we have a free jet exiting perpendicular to the main pipe flow.


texts: Would a Flettner rotor make sense for an ocean cruising trawler?

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A Flettner rotor can be used to provide propulsion for ship from the wind.

Would it make sense to fit a Flettner rotor to a full displacement expedition trawler in the 55-70 foot class like a Nordhavn or Bering? These vessels are deep draft ships that move slow, about 8 knots typically, and are designed for stable ocean travel over long distances. The idea is that the rotor would augment the diesel propulsion to make the ship faster and more fuel efficient.

Below is a photo of a 65-foot Bering with a rectangle showing the imaginary location of a Flettner rotor. A 4 inch drive shaft would go through the decks to the engine room and be coupled to the engine or main drive shaft via a gear box.

The drawbacks I can see are that it could potentially decrease the stability of the ship and would be added weight. Also there would be a 6 inch column going through the center of the lounge and a loss of space on the top deck.

The question would be how much benefit would the rotor bring?

For example, if the rotor could increase cruising speed by 20% and decrease fuel usage by 30% on a transoceanic crossing, that would be significant benefit.

Another question would be how would the rotor affect the roll stability of the ship? Would it tend to dampen roll or increase it?


texts:
I am setting up a simulation in fluent to estimate the UV radiation dosage of an air stream passing through a cylindrical duct with the UV source in line with its main axis. It is a very simple system, one inlet and one outlet.

I've done simple simulations involving convection heat transfer but never one with radiation. As you can see the duct behaves as a mirror and reflects the radiation internally which makes solving this example by hand rather complicated.
Can anyone suggest the best way to go about setting the simulation specially the radiation boundary conditions? I know the total UV radiation of the lamp as well as the W/cm^2 output, i also have an estimation of the lamp's surface temperature.
In the end my simulation should provide a similar result to this:

Any tips would be very useful, Thank you very much in advance


texts: Relation between burgers vector and direction of motion for dislocations?

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I am  bit confused. The slip direction is the direction of movement of a dislocation which is denoted by the burgers vector.

This makes sense in an edge dislocation, because the stress is applied perpendicular to the dislocation line and the movement of the line is in the direction of the applied stress. The burger vector is also perpendicular to the dislocation line for edge dislocation. So it makes sense that the direction of motion corresponds to the direction denoted by the burgers vector.

But for screw dislocation, the motion of the dislocation is perpendicular to the applied stress and since the burger vector points in the direction of the dislocation line; the burger vector cannot point in same direction as the direction of movement?

The professor even said that the direction of motion for a screw dislocation is perpendicular to the burgers vector. So how can a burger vector then correspond to the direction of slip when this direction of slip is the direction of movement?

So the points that confuse me:

slip direction: specific direction along which dislocation motion occurs
burger vector: direction corresponds to a dislocation's slip direction
screw dislocation: direction of motion is perpendicular to applied stress and the motion is perpendicular to the burger vector

So these 3 things conflict with each other:
the motion of the dislocation is here perpendicular to the burger vector (and i have heard is always perpendicular for screw dislocations), so how can a burger vector denote the slip direction if the slip direction is the direction of the motion of the dislocation? For it to denote the motion of the dislocation shouldn't it align/be parrallel?
Or is that the mistake I am making, that a burger vector tells about  direction of the dislocation motion, but that it doesn't mean that the motion is in the same direction?
That there is just always a fixed relation between the two depending on the type of dislocation, but that the relation isn't always parrallel.
It is 90 degrees for screw and 0 degrees for edge related to the dislocation motion. So that indeed the burger vector says something about the direction of the motion but just that it doesn't say that they always in same direction?

Because again clearly here the dislocation motion is not in the same direction as the direction of the burger vector;
The motion is from front to back, while the burger vector points in direction of the shear stress in this picture


texts: Parameter effects on kinetics of esterification for bio-diesel production

texts:
I want to discuss the effect of parameters on the kinetics of esterification for bio-diesel production. In esterification process, temperature effect and molar ration are two important parameters. During conversion of oliec acid with methanol to bio-diesel, temperature contributes more than molar ratio ( happen before 70 to 80 % conversion to bio-diesel). But after 70 to 80% conversion molar ratio contribute more than temperature.

My question is why this happens. Why the contribution of temperature and molar ratio reverse after 70 to 80% conversion to bio-diesel?


texts: Deflection of a stack of disks under applied force/pressure

texts:
I'm trying to calculate the deflection of a stack of metallic disks, when subjected to a force.

In the case of the figure below, representing a valve for a shock absorber, the force is due to a pressure differential. The stack of disks (also called "shim") is represented in orange.

I found a couple of papers that delve in this theme, but they all seem to be a direct citation of the following paper: "An Experimentally Validated Physical Model of a High-Performance Mono-Tube Damper", by Michael S. Talbott and John Starkey.

They briefly exemplify for a 3 disk stack, but actually explain very little of the method of computing the deflection of the stack as a function of force.

Using Roark's formulas for disk plates and the superposition method, one can obtain a system of equations to be solved, akin to:

$$\begin{gather}
y_1 = z_{2,R12} + z_{2,R23} \\
y_2 = z_{3,R23} + z_{3,R34} \\
\vdots
\end{gather}$$

where $y_i$ is the deflection at the outer radius of disk $i$, and $z_{i,Rkj}$ is the deflection of disk $i$ due to the reaction force between disks $k$ and $j$ (this is better explained in the papers).

I'm having trouble however in determining how the disks transfer forces between each others. It is assumed that two different disks only touch at the tip of the smallest one, the pressure difference is known and by using Roark's formulas one can calculate the reaction force at the base of one isolated disk.

I'm however unsure on what amount of force is transferred between disk 1 and disk 2, disk 2 and disk 3, etc.

Are there any papers or books that described this problem or a similar one (stacked disks, stacked beams, stacked plates, etc.) and that illustrate the solution method in greater detail?


texts:
for this question: "What is the difference between strength, hardness and toughness in materials?" i have searched and have found these following definitions

  Strength refers to resistance to deformation, and also to a large
  elastic range. In the Elastic region of the stress-strain
  relationship, the relationship is described by a linear function, such
  that σ = E ϵ, where σ is the stress, E is the Elastic modulus, and ϵ
  is the strain.

  Toughness is the resistance to failure or crack propagation. It is
  somewhat related to strength. Very strong materials will have low
  toughness, i.e. low tolerance for flaws or defects, i.e. incipient
  cracks.

  Reference
  https://www.physicsforums.com/threads/difference-between-toughness-and-strength.67220/

i don't understand those definitions. Aren't deformation and failure one? Are toughness, strength and hardness both the ability to resist external forces?


texts: Effect of bypass valve on flow rate and pressure

texts:
I have no background in thermodynamics or fluid dynamics, so please bear with me. Refer to the following figure:

A working fluid with a flow rate of $1~kg/s$ enters a heater at a pressure of $1~MPa$ and temperature $150~^\circ C$, which raises its temperatures to $300~^\circ C$. It then enters a turbine, does work, loses pressure and temperature, and exits at $0.5~MPa$ and $200~^\circ C$ at the same flow rate. The bypass valve's purpose is to control the work output of the turbine by bypassing some of the working fluid from the inlet stream directly to the outlet stream. Suppose that we're free to make all the "simplifying assumptions" for this problem. Suppose also that initially the opening fraction of the bypass valve is $0\%$ i.e., the valve is fully closed. My questions are:

How would the pressure and flow rate change as the bypass valve opening fraction is varied ($0\%$ means fully closed, $100\%$ means fully opened)? In particular, I'm interested to know them at points A, B, X, Y and E.
Would a high pressure stream at Y intercepting the low pressure stream at E raise the pressure and flow rate of the latter? How could that be quantified?
Could the valve's opening fraction be linearly related to flow rate and pressure? Meaning, could it be assumed that flow rate and pressure at point B would be halved if the valve was half-open ($50\%$ opening fraction)?
What would be the simplest way to model this valve?

Some questions might seem redundant, but I listed them to get a thorough response, for clarity and understanding. Also, all the numbers are arbitrary and any unreported quantities could be assumed. Thank you.


texts: What is the purpose of the isolated subpanel terminal of a solar inverter?

texts:
In a grid-connected (utility-interactive) battery-based PV system, what is the purpose of the 'Isolated Subpanel' terminal of the inverter?

EDIT: Found this descriptive image and hence answered the question myelf.


texts: Why is the moment of forces on a rigid body in static equilibrium must be zero about any point, even if the position of that point is not on the body

texts: Why is it necessary for the moment of the forces on a rigid body in static equilibrium to be zero about any point, even if the position of that point is not on the body itself.


texts: How to consider the dimension of a cylinder when computing its radiative budget?

texts:
I am trying to derive a heat budget model to estimate the temprature of very small a stationary vertical cylinder (1mm) under environmental conditions. Imagine a wooden stick. Simply put, I have

R = H
InSW * albedo + sigma * emissivity * Tcylinder^4 = rho_air * cp * (Tcylinder - Tair)/rH.

Where,

R = sum of radiative components
H = convective components (latent heat and conduction ignore)
InSW = Incident solar radiation observed by a pyranometer
albedo = albedo of the cylinder
sigma = ste-boltz constant
emissivity = emissivity of the cylinder to longwave IR
Tcylinder = temperature cylinder
rho_air = density of the air
cp = heat capacity of the air
rH = resistance to convection

This is the basis of a heat budget model, but how do I incorporate the fact that its a cylinder? I've managed to find information about how to deal with rH with the forced and natural convections, so what I'm more concerned about is the radiative components. Is it alright for me to leave them like this or do I need to start accounting for the geometry and its potential impact on the intercepted light and resistance to radiative transfer?

Thanks


texts: What is a method to detect thermal oxide layer after steel is painted?

texts:
Is there a method to test for thermal oxide on a painted steel part after the paint has cured?  I'd rather the method be nondestructive but it only being destructive in the presence of thermal oxide is also acceptable.

I am specifically looking for laser oxide under 3mils of polyurethane, if that helps.


texts: Why are combination load factors necessary?

texts:
According to Eurocodes, we multiply designed loads by safety factors to account for non idealities and uncertainties. When multiple load types affect a structure, the corrected loads are summed and the sum is multiplied again by a load combination specific factor. Why do we need to correct the sum as well?

For example, we may have a live load and a snow load on a structure. Both have their own safety factors, but why does their combination have one as well? Aren't the uncertainties included already in the individual factors for each load?


texts:
My friend and I are working on building a valveless pulsejet out of sheet metal. We initially built a small one (a few feet in length) using the below dimensions:

The issue was that we were unable to get it running without compressed air. When we had a nice stream of compressed air running in the intake, it would fire right up, but it would die when the air was removed. We hypothesized that our tolerances on the engine weren't very accurate, and so decided to make a bigger one where the tolerances wouldn't matter as much. We scaled all the dimensions by two. With the new engine, we were able to get it running with compressed air just fine like the first engine. However, we had the same issue. When the compressed air was removed the engine would die. We now had a different theory. We wondered if the fuel wasn't mixing well when it was injected, and what the compressed air was doing was mixing the fuel really well. To remedy this, we took the fuel line and crimped it at one end and drilled small holes in it along its length to try to create more of an even distribution of fuel. This also didn't work, and the engine died when the compressed air was removed.

So, I am wondering if anyone here has suggestions for what we can do to get this engine running without needing to hold a compressor to it the whole time! Below is a link to a bunch of pictures of the engine:
https://imgur.com/a/iCIfnIq

Any ideas are appreciated!

EDIT: We are using propane as fuel

EDIT 2: With compressed air, we are able to get it to pulse correctly. It is not just a continuous whoosh. We watched some videos of pulsejets, and we know the correct sound.


texts:
Around where I live there's these soapbox/gravity kart races (google "carros de rolamentos") in which the wheels are built simply from ball bearings. As I was building my own, I began wondering how I could easily mount my large bearings onto my kart, and it occurred to me that an easy way to do it would be to get some smaller bearings inside the ones previously mentioned and mount the resulting pair onto the frame, like this:

More importantly, I was under the impression that this would improve the performance of the kart in terms of speed. I am not completely sure though, hence why I am asking this question.

On one hand,  I find that my older kart reaches some sort of terminal velocity when the inner and outer races of the bearings can only move so fast in relation to each other. So, the inner bearing would sort of take some load out of the larger one by rotating in the same direction, allowing the outer-outer race to rotate faster in relation to the inner-inner race (or, in the worst case scenario, I would get no gain but also no loss, unless the smaller bearing spins backwards).
On the other hand, I asked this to a student of mechanical engineering and he said he doubted I would get any gain, because there would be more overall friction, which does make some sense, but does not convince me much.

Also:

We can assume that they will be well coupled together (I can file them if needed and will probably weld them afterwards).
I can't run any practical tests at the moment because I haven't bought the smaller bearings yet (I don't know if it's worth it)
From my research, this kind of configuration has only been mentioned in some videos about fidget spinners, and sure enough, it seems to rotate fairly well.


texts: How to calculate change in pressure from LN2 state change (constant volume)

texts: I am trying to calculate the increase in pressure caused by liquid nitrogen at the moment it changes from liquid to vapor within a closed, constant volume at atmospheric pressure. Do I need to include the heat of vaporization? How can this be done?


texts: Which materials we can use for storing liquid nitrogen?

texts:
What are the materials we can use for the long-term storage of 30~liters of liquid nitrogen with composition and grade, along with the thickness of the sheet and storage capacity? Can we use any composites for the same? And which is the best among all?

The nitrogen is for rocket cooling, but the device doesn't need to be a thermo-flask.

Please provide references also.


texts: Why do binary cycle geothermal power plants have so low efficiency?

texts:
Well, a binary cycle geothermal power plant utilizes the low temperature of the primary liquid to generate heat. I found out that they are only 10% to 15% efficient.
Is the continuous flow of the primary fluid a major cause for such inefficiency? From what I understand due to the continuous flow of the primary fluid the secondary fluid is only able to capture a portion of that heat due to continuous flow of primary fluid.
Or is the inefficiency is due to the use of a low boiling point secondary fluid?
Please guide me if I am wrong in my assumptions. I researched a bit but was not able to clear my doubt so though to seek some expert advice.


texts:
I intend to build a kiln in my free time over the next few months and am trying to avoid my past mistakes (heated too quickly, the kiln started cracking, the kanthal element melted and it was just plain terrible). So I'm thinking of using element holders. I have two ideas in mind. Either I use a ceramic tube around which the heating element is wound or I use ceramic grooves.

The second idea (Fig. 1) increases the usable space which is why I prefer it. However the price being prohibitively high (almost tripling the price of the kiln), I am considering using refractory cement to make them. It's cheap and also does not require firing the holders which is a huge advantage.
The question is three fold:

Should I use inset element holders such as in Fig. 1 or do offset tubes offer some advantage such as possibly quicker temperature increase due to the walls heating slower.
Will refractory cement survive hundreds of cycles in such close proximity/contact with the heating elements?
Can ceramics be used above the temperature at which they were fired without sustaining damage? Meaning, can I use the local pottery to make element holders (they can fire up to about 1350°C and I intend to be able to go to 1400°C (the bricks are supposed to be able to go to 1440°C).

If you need more specific information, I will answer the best I can. Thank you.
Best regards


texts:
I built/assembled a small drill press recently and used a part from a Junk Drill because I couldn't figure out what a particular component I needed was called.

What I was looking for was a way to step up in chuck size so I could accommodate a bigger bit on a rod that was a smaller size (see: 3.17mm motor shaft driving 1/4"+ bits).

I now know the function of what I was looking for, it's a chamber of gears driven by a central D shaft gear the motor shaft can be inserted into. It's the internal component used to drive keyless chucks available in most retail drills.

Does anyone know what this would be called so I could look for it properly next time? I resorted to stripping an existing finished product for a part just because I couldn't figure it out, I was originally wanting to mount a keyed chuck


texts: Failure of N.R.T.L method to model Phenol / Methylcyclohexane / Toluene system in AspenPlus. Why?

texts:
I have an extractive distillation column set up in AspenPlus. Methylcyclohexane (MCH) is expected to come out from the top (in the distillate stream) and the bottoms stream is mostly Toluene/Phenol, with a bit of MCH. The feeds are MCH+Toluene (at stage 8 out of 25) and Phenol (at stage 18 out of 25).

Temperature - 100 C. Pressure - 1 atm.

When I use the N.R.T.L (non-random two-liquid) model for the simulation, I get weird results. However, when I use UNIFAC, I get what I expect.

I thought NRTL was supposed to take into account deviations from ideality (caused by the phenol group?), so I don't know what's throwing it off.

Any suggestions?


texts: Error propagation in reciprocal of a measurement

texts:
I have a measure of a quantity, x, and I know the standard deviation of the measure, STDx.
I want to compute the inverse of x, which is y= 1/x, but then what would happen to the standard deviation?
How can I compute STDy?
Many thanks in advance.


texts: Is it possible to calculate torque using strain gauges on a rotating shaft?

texts:
I am currently designing a torque sensor and am looking into the ability to use strain gauges as a instrument to measure strain and calculate torque.

The current setup is two motors connected via a shaft. One of these motors will provide a torque and spin, while the other opposes and acts as a resistance.

The strain gauges will be placed at opposing 45° angles to each other, one will measure the positive strain while the other will measure the negative (as shown in the image above).

The gauges will be wired using a Wheatstone bridge, this will provide a voltage output and seems to be the recommended method of getting an output.

How is this Vout translated to a strain and/or is a torque value calculated?
The end goal is to calculate a torque from the strain gauges.


texts:
First post so bear with me:
I am designing a frame for a press, which needs to be able to withstand 250 N. I am planning to make the frame an L-shaped beam, turned around. With a side view, it will look something like this (the press will be attached on the right side of the vertical beam, which will push downwards):
__________
l
l
l
l
The height of the vertical beam will probably be 160 mm and the length of the vertical beam will probably be 50 mm. The lower end of the vertical beam will be screwed on top of a table, so this will be a clamping.
For me, the question seemed simple at first, but I just can't seem to figure it out. I am almost sure I would need to use the E-modulus of the material (probably steel), but I can't find the correct formula. I have tried using the formula:
$$\sigma = \frac{M * y}{I}   $$
then I drew a cross-section of the beams, and made the assumption of using an 80 by 80mm beam.
Using this, I got M=12.5 Nmm, y= 40 mm and $I={1\over 12} * b * h^3$ (not sure how it is in English, probably 1/12wh^3). I could not figure this out further.
I am trying to find a suitable length and width for the horizontal and vertical beams, but this seems to be way harder than I thought... can anyone help me into the right direction?


texts:
I'm trying to conduct a thermo-mechanical analysis in ansys workbench, I've been able to obtain some results using the transient thermal and static structural modules, however, I would like to perform a more accurate simulation.

Until this moment I just have reach a linear solution for the static structural module, as shown in the next images,

Once I get the solution from the thermal module I import it to the static structural module and solve, but there are some elements that cross each other, for example, inside the leaf of the door there are some stiffeners that cross the frontal door plate. Also the leaf interferes with the frame of the door in various locations.

How can I fix this?

I've been trying to use the static structural module with the large deflection set "on", but I'm new to this kind of analysis and I'm not been able to solve the problem.

I can send the files if it's needed.


texts: Boundary conditions in a heat transfer problem

texts:
One end of a small insulated rod is attached to a support which is maintained at a constant temperature of 473 K,and once the rod has reached a uniform temperature in its entire length the insulation is removed. Now the surrounding air is at 298 K with convective heat transfer coefficient h.

I am required to find the time elasped when the temperatures at some length of rod reaches a given temperature.The radius,thermal conductivity and thermal diffusivity are all given

This is a unsteady state heat conduction and convection problem.I got the following pde $$k \frac{\partial^2 T }{\partial z^2} - \frac k\alpha \frac{\partial T}{\partial t}=\frac{2h}{R} (T-T_0)$$

where $k$ is thermal conductivity $\alpha$ is thermal diffusivity and $T_0$ is surrounding ambient temperature.I am facing trouble finding out the two boundary conditions.The initial condition is that at $t=0$ the rod is at a uniform temperature of 473K.The first boundary condition is at $z=0$ the temperature is 473K.However i am unable to find out the second boundary condition.The tip of the fin is not insulated and is neither maintained at a constant temperature.


texts: Why do hairdryers use line power and beard trimmers use adapters?

texts:
Hairdryers are capable of electrocuting people and are used in generally wetter conditions and run on mains power. Trimmers are used on dry bodies and use safe DC power from an adapter. Why are hairdryers not using adapters, especially when they are used in more dangerous conditions?

I can guess these reasons:

Trimmer cables are detachable from the body and harder to insulate
Trimmers have chargeable variants, so they are designed to run on DC
Trimmers will be unpleasantly heavy with integrated chargers


texts: Can you channel more air into a nozzle by creating a vortex inside of it?

texts:
There are designs for ducting in wind turbines to channel a wider cross section of wind into the rotor area. This is unpractical for structural and economical reasons but does actually increase power output. I was thinking if it would be possible to gather even more air from a nozzle the same size by creating a vortex inside this nozzle. Imagine imparting a spin on the entering air by rifling similar to a gun barrel. Would this vortex extend outwards of the nozzle and thus effectively increase the inlet area (A0 in the sketch)? Could the obtainable mass flow be increased? See the attached draft for a better illustration.

I tried to find some publications and similar ideas to this concept. I only found this relating sounding publication (https://www.jstor.org/stable/43749083?seq=1). But as I can't access it, I can't tell if it even goes into the right direction. Do you happen to know any similar ideas?


texts: Structural steel standard S235, is it average yield strength or some fractile?

texts: Question is in the title. There are many structural steels like S235 and S355, but are these values average values or 5 % fractiles for example (assuming some distribution of values found in tests), as usually assumed for characteristic values for resistance in standards like Eurocode? I could not find any information anywhere, these values are usually stated as "nominal" values, but what does this mean?


texts:
I am trying to identify the section designation so I can determine it's properties.

I have looked under "C 150 x 100 x 40" but I can't find its properties or what it's correct designation.

What is this section called? It's not just a "channel" is it?


texts: 2D Solid - Axisimmetric - Missing properties and material

texts:
Goodmorning,

I'm trying to understand how 2D solid elements work. I want to study the local buckling of a simple aluminium pipe with thin walls.
From what I understood, I can use 2D solid elements and model just a section of this pipe .

I've drawn a surface on the XZ plane (Z axis of simmetry). This surface is just a long but very thin rectangle that rapresents the pipe's wall. The pipe is open so no caps etc.
I applied the property 2d solid axisimmetric, my costrains and my loads. I then created my mesh with quadx elements.
In analysis, I selected SOL105 for bucking analysis.

When I run Nastran, I get some errors, the first one being:

USER FATAL MESSAGE 2011 (TA1)
NO PROPERTY ENTRY FOR ELEMENT TYPE QUADX

Indeed, checking the bdf file, there's no property to be found, nor the material definition!

I tried to group elements with no properties in Patran, but it found none.

What am I doing wrong?

Thank you for helping me out.


texts: Thermography - objects appear hotter than they are

texts:
recently I started working with IR thermal camera (Hikvision DS-2TD1217-3/V1) and I have a slight problem. The camera works fine when there are only people in the image, however if I place a hot coffee mug in the image, suddenly everybody has 80 degrees Celsius... why is that? Normally, you would expect that the regions with faces would become darker in the image (because of automatic temperature scaling) when another, much hotter body enters the scene.
Any tips are appreciated.
Also, not sure if it's the right place to post it ¯_(ツ)_/¯


texts: Is it possible to find heat flux without emissivity value?

texts: In this question there is a value given for absorptivity of infrared radiation however in order to work out a value for heat flux emitted from the solar panel in order to answer part (a) surely I'd need a value of emissivity? I have been stuck on this and have no clue how to work part (a) out without a value for emissivity.


texts: Why Nusselt number for laminar flow in a pipe is independent of reynolds number

texts:
I understand that for fully developed flow inside a tube (with constant properties), Nusselt number doesn’t change in axial direction but it is surprising that it is also independent of Reynolds number which means that the rate of heat transfer (for constant pipe diameter and fluid properties) doesn’t change with mass flow rate (and velocity).
So could someone please  give an explanation for this.


texts:
Does anybody know where to find statistics on the energy mix in Europe (preferred by country)? I can only find the share of renewables.
I'd like to see the whole mix with a split into energy sources (Wind (best case: offshore, onshore), Solar, Oil, ...) for 2020 (or the latest data available) and, if possible, also the target for, e.g., 2030.
Please point me in a direction.
Thank you!


texts:
In a heating circuit, there's two (known to me) ways to decouple primary flow (through heat source) and the secondary flows (to consumers):

a hydraulic switch in the heating manifold
complete hydraulic separation with a heat exchanger

When is which solution more appropriate?


texts: Curved Slider Mechanism With Two Different Radii

texts: I'm trying to make a slider mechanism that is guided around a curved rail that consists of two different radii. As you can see in the image, the section of the rail with a diameter of 120 mm requires the 3 circles to be spaced 9.615 mm apart, and the section of the rail with a diameter of 196.615 mm requires the 3 circles to be spaced 9.686 mm apart. This difference of .071 mm causes too much play between the slider and the rail, and I really need the slider remain as stable as possible. Any suggestions of how to design the slider in order for the slider mechanism to slide along the rail smoothly with the least amount of play?


texts: 90 degree pivot steering system to allow vehicles to move sideways

texts: Are there any restrictions that would not allow a steering system to cause a vehicle to be able to move sideways - at 90 degrees from the convention direction of travel?


texts: Time to change temperature inside the box

texts:
I have an interesting problem here.
I have a box of certain dimensions. Inside of the box is some insulation and another box, from the same material as the outer box. I know everything possible about the materials possible.
Is there an equation to calculate that if there are for example -4 degrees Celsius outside, it will take XY minutes to cool the inside of the inner box by 1 degree?
I really don’t know where to start. Thanks for any help.


texts: 2 mm accuracy in an affordable water level sensor (pressure transducer) - Does one exist?

texts:
I'm looking to conduct water level monitoring in streams and rivers for water resource engineering purposes. My plan is to use Arduinos and Raspberry Pis in conjunction with a pressure transducer, as Pis and Arduinos work with the telemetry system and water quality sensors that I have chosen for the project.

However, the standards in British Columbia, Canada (where I work) require that the sensor must have a 2 mm accuracy to collect "Grade A" data. Grade B data requires 5 mm accuracy, and as it turns out a pressure transducer with these accuracies are hard to find unless you spend >$500 per pressure transducer.

Does anyone know if a low cost ($300 max, but preferably $50 to $150) pressure transducer designed for measuring water with 2 mm or 5 mm accuracy exist? I'm also open to other technologies as well.

Thanks!

Page 4 in the attached in BC's standards doccument is attached if anyone is interested in checking it out.


texts:
From the first law of thermodynamics:

$$\Delta U = Q_{12} - W_{12}$$

where $\Delta U = m(u_2-u_1)$, $W = p(V_2 - V_1)$ with constant pressure, and $Q = m(h_2-h_1)$.

In the energy rate form of the first law simplification for a turbine (or compressor): $\left(\dfrac{\partial E}{\partial t}=0=-W'+m'[h_1-h_2]\right)$

$W' = m'(h_1-h_2)$ while assuming that there's no heat transfer $\left(Q'\right)$ and change in potential and kinetic energy is zero.  ($W'$ is power, or $\dfrac{\partial W}{\partial t}$)

I think I must be missing something obvious here, but it seems inconsistent that $Q' = 0 = m'(h_1-h_2)$ while using $(h_2-h_1)$ in the equation.  Shouldn't $h_2 = h_1$ in both equations?


texts:
The Reynolds Number is defined as $Re = \frac{\rho v L}{\mu}$, where $\rho$ is the density, $v$ is the fluid velocity, $L$ is the characteristic length, and $\mu$ is the dynamic viscosity.  By definition, inviscid flow implies that $\mu=0$.  By this formula, this would make the reynolds number infinite and thus turbulent.

Is it possible to have laminar inviscid flow?  Must inviscid flow always (necessarily) be turbulent?


texts: I have two different UDLs for 6.5m and 3m spaced side by side on a primary beam. If I were to calculate the FEM of this beam, how should I proceed as there're no formulas for situation particularly like this (unsymmetrical UDL on beam) on the FEM Formula sheet. Kindly advice me on this matter ,tq.


texts: Rotational Motion Kinematics - Not sure how to fix axis of rotation

texts:
Hi I am trying to make a CAD model of something like the scoop sampler shown below.

http://www.rolls-royce.com/~/media/Files/R/Rolls-Royce/documents/customers/nuclear/scoop-sampling-tcm92-50918.pdf

This is for a university coursework that requires design of bespoke machines. I am trying to design a machine that can literally scoop out a 1 mm thick sample from any aerospace component. My intention is to use a motor to rotate the shaft which is connected to the cutter (with abrasive particles to cut through metal).

See this would initiate the cutting and only cut at the controlled depth (based on the dimension of the cutter) but how can I possibly make the cutter to eventually go up? (lets say after 35 - 40mm length I want the cutter to make a vertical movement so that it scoops out). To clarify I want the final metal scoop to be roughly 40mm long, 20mm wide and max thickness of 1mm. So once it reaches around 35mm how can I make it go up vertically while the shaft and cutter is rotating in the horizontal axis?

Finally what if I don't have a flat surface. Imagine if I have a concave surface. I have some ideas but I can't seem to get through these initial problems.


texts: Is there any formula to model the effective Young's Modulus of a fluid-filled spherical shell?

texts:
I am creating composites of a host epoxy and filler particles which are thin-walled fluid-filled shells. Using the Halpin-Tsai equations, for example, I can predict the bulk composite Young's modulus by knowing the particle volume fraction, modulus, geometry, etc, and this seems to work well for both Solid and Liquid particles (using a negligible modulus to approximate liquid)
However, I am having difficulty determining the effective modulus of a liquid-core shell particle for use in these equations. I have found this paper Bulk Modulus of a fluid-filled spherical shell which provides a formula to predict the Bulk Modulus of such a shell, but without also knowing the Shear Modulus or Poisson's Ratio of these fluid-filled shells I cannot determine a Young's Modulus.
This seems like something that should have a well-documented formula, but I can't seem to find anything. Any ideas on how to calculate the Young's Modulus?


texts: Recently I have been trying to find out more about the process that is used to coat glasses lenses with gold. I asked about it in another forum last night and I was directed here. I initially thought that I could use the same process that NASA used to coat astronaut's helmet visors in gold, but now that is too expensive of a process. I want a thin transparent layer of gold on my glasses (lenses) basically. I have access to jewelry equipment.


texts: Are there solutions for coupling a spline shaft to a round diameter shaft

texts:
I only have basic metal fabrication tools and do not own a mill or a lathe, but would like one. I took apart my cheap drill press to study whether or not I can convert it into a milling machine. The spindle features a 4 tooth 9mm x 9mm tooth male splined section that mates with a female splined bushing press fit into the pulley's bore (see parts numbers 62 and 71 in diagram). The entire spindle fits inside the quill tube (see part 68) creating the quill assembly (see photo below).  The spline allows the spindle to extend downwards and upwards in the head casting while also allowing the spindle to rotate with maximum torque.

Currently, I am considering replacing the entire spindle with an 16mm O.D.  ER20 tool holder. This will give me a more ridgit hold on the cutting tool as Jacobs Taper cannot handle axial forces required for milling. I am also planning on replacing the existing bearings with either angular contact bearings or tapered bearings.

I would like to maintain the quill's retract and extend mechanism. To do this, I will have to somehow jointhe end of the ER toolholder to a splined shaft that will fit in the female end. Currently, I can't seem to find any off the shelf spline to 16mm coupling. I am not even sure what they are called.

Are there any solutions for coupling or attaching a spline shaft to a plain old shaft? What is it called and do they exist?  Finally, I am not completely married to using a spline drive mechanism in order to extend and retract the quill, so I welcome any suitable alternative mechanisms. I saw a ball spline, but wasn't sure if it works the same way as the existing mechanism.

Here's a photo of a similar quill:


texts: State space representation of a product of transfer functions?

texts:
In short, I suppose the question boils down to: If we are asked to find the state space representation of $C(s) \cdot G(s)$, where C(s) and G(s) are both transfer functions, then do we treat them as two state space models in series or not? If series/not in series, then why?
Example:
If we are given that $C(s) = \frac{s - 1}{s + 1}$ and $G(s) = \frac{1}{s - 1} $, then let us try two methods I have seen:
1. Just multiplying the two transfer functions
Thus, $C(s)G(s) = \frac{s - 1}{s^2 - 1} $ and this can be written as:
$ \dot x(t) = Ax(t) + Bu(t) = \begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix}x(t) + \begin{pmatrix} 1 \\ 0 \end{pmatrix} u(t)$
and $ y(t) = Cx(t) = \begin{pmatrix} 1 & -1 \end{pmatrix}x(t) $
This representation will eventually lead to the fact that there is an unobservable state.
Method 2: Treating the state spaces as in series
High level: find state space representation for both and then treat them in series. Therefore, output $y_1 $ is the input $u_2$
If we take $C(s)$ as appearing before $G(s)$, then we can find the following state space representation for $C(s) = \frac{s - 1}{s + 1} = 1 - \frac{2}{s + 1}$ (functions of $t$ have been dropped for simplicity)
$ \dot x_1 = - x_1 + u_1 $ and $ y_1 = -2x_1 + u_1 $
Then for $G(s)$, we get:
$ \dot x_2 = x_2 + u_2 $ and $ y_2 = x_2 $
Then, because they are in series, we let $ u_2 = y_1 = -2x_1 + u_1 $. By stacking them together we can get:
$ \begin{pmatrix} \dot x_1 \\ \dot x_2 \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ -2 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} +  \begin{pmatrix} 1 \\ 1 \end{pmatrix} u_1 $
and
$ y_2 = \begin{pmatrix} 0 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} $
However, this leads to the fact that there is an uncontrollable state.
Which method is correct?
Any help would be greatly appreciated.


texts: Are gas distribution networks tree-like?

texts:
I was wondering, if it is justified to say, that gas distribution network graphs (primarily in Europe) are typically tree-like. By gas distribution networks I mean municipal and regional distribution networks, not the long-range transport networks.
To me, it would seem reasonable, since alternation of flow direction makes little sense, given that there are few sources and mostly sinks in the network and establishing circular flows would be a waste of energy. Does anyone have experience with that?
Cheers,
Tobi


texts: Tuning Feedforward + PID Controller just with Feedforward Data

texts:
Hello there, hope you are all doing well.
Right now I am trying to design a Feedforward + PID Controller for KUKA youBot on simulation. Since I do not have the equation of the system, I am trying to tune my gains manually and it is a bit struggling for me. Is using MATLAB's System Identification Toolbox  is a good approach to solve the situation. If so, where can I find good tutorials for that? I thought about setting the gains to 0 initially and evaluate the system just with Feed-forward control and then examine the new gains from the Feed-forward data. Does that make sense to you? I am kind of new to Control Theory, so I cannot think of many possible ways. Can you help me with that?
Hope you all have a great day.


texts: What is the purpose and cause of disposable syringes being single use only?

texts:
What's the mechanism behind disposable syringes jamming? How do you prevent this from happening or reverse the effect? They are a lot cheaper.

The problem is that once the syringe is pressed all the way in, the plunger sticks and can not be pulled back out.


texts:
Assume you have a solid walled sphere with an opening of diameter x. The sphere has volume  0.02 litres and has air at 1.4 bars.

What general equation would be appropriate to correctly size the diameter of the sphere's opening such that pressurized air in sphere would be released in exactly 40 seconds? End pressure should be 1 bar


texts: Hydrostatic force on inclined immersed surface

texts:
Help me to find out the hydrostatic force acting on an inclined immersed surface that is actually the diagonal of a 4mx3m rectangular tank filled with water. Given that the tank is 2m deep.

I know, F = Specific weight x Area x Depth of the center of gravity of the immersed surface from the free water surface.

But the problem is that I have no idea how to calculate that depth of the center of gravity of the immersed surface from the free water surface. Any help will be appreciated.


texts: How to calculate the required thickness of a steel stiffener plate in a corbel/bracket

texts:
I am dealing with a setup similar to the image below.  The horizontal plate is bolted to a horizontal concrete surface (Bridge Abutment). And a horizontal force is being applied to the the vertical.  My question is how do you determine how thick the stiffener plate needs to be.  I am looking to understand the general process and then I will turn around and try to apply my code (CHBDC).

My thoughts are you need to check to see if it will buckle.  Treat it like a column and performa k*L/r check.  k=2 for fixed fixed connection due to welds.  not sure about section properties as they vary.  Also not how to convert a horizontal point load in the middle of the plate into axial load? in the plate.

Was looking to stay out of FEA. Wondering if there was some basic first principles formula or something along those lines.

I am actually trying to size the green peices:


texts: Motor needed for large scale disco ball!

texts:
I am working on fabricating a large scale revolving disco ball for an event in Cincinnati. The scale is 10'diameter and the frame is flat bar steel. the exterior is cardboard, duct tape, and adhesive "mirror stickers." I am looking to have the ball rotate at 1 RPM. Total weight is 350 lbs. What type of motor should I research to purchase? The motor will be hard mounted at the top of the structure that is to be suspended.

Thank you advance.

Joe


texts: Sizing an AC Servo Motor for lifting pallets

texts:
I am trying to size a servo motor and my basic physics and math is so rusted that I can't figure out how to go about it?
The scenario is as follows:
I need to lift an object in the vertical direction against gravity. The object has a mass of 30kg. It is lifted to a height of 1m. It takes 5 sec to lift the object. I want to select a servo motor which is capable of doing this task. I have two options for the mechanism, rack and pinion (R&P) or lead screw (LS).
I want the lifting to be done in three sections

Acceleration of 250 mm/s^2 for 1 sec. distance covered is 125mm
Constant velocity of 250 mm/s for 3 sec. distance covered is 750mm.
Deceleration of 250 mm/s^2 for 1 sec. distance covered is 125mm.

First thing is the power of the motor. From basic physics I know that

Weight (force) = mass x g = 30 x 10 = 300N
Work = Force x Distance = 30 x 1 = 300Nm
Power = Work/time = 300/5 = 60W

This is the base Power if I add in some friction and a safety factor I would say that 100W-120W should be enough. But I have serious doubts about this calculation.

  Is the power calculation same when I have a Rack and Pinion or a Lead
  Screw?
  The downwards force due to gravity in case of Lead screw is acting at
  an angle on the screw threads so should I be resolving that weight
  component?
  What happens to the equations in case of downward motion?

I was doing some online research and many factors came up in sizing of servos. For example the Inertia ratio, velocity profile, max torque, RMS torque [1].
I found a forum post which suggested calculating motor RPM based on linear distance and pitch of the lead screw [2].
Then calculating the motor torque using this relationship Torque = 30 x Power / pi x RPM [3].

But this formula is not accounting for the required velocity and acceleration

  Also how can I find the inertia ratio for a vertical moving load? Do I
  need to calculate the inertia of my payload when the payload is moving
  in linear direction only?

I want to understand the basic principles to the sizing so I can size the motor for a belt or a rack and pinion or any other mechanism. Any help or guidance is appreciated.

Edit: [1] I was trying to follow this two part video tutorial https://www.youtube.com/watch?v=4MaGqSQfYOk&t=210s
[2] https://www.physicsforums.com/threads/calculate-torque-power-needed-to-lift-a-4-kg-load.661367/#post-4211630
[3] http://wentec.com/unipower/calculators/power_torque.asp

and some other sources
https://www.orientalmotor.com/technology/motor-sizing-calculations.html
https://www.motioncontroltips.com/tips-for-sizing-a-servo-motor/
https://www.motioncontroltips.com/faq-how-do-i-calculate-the-inertia-of-a-servo-driven-system/


texts: Percentage error in calculated Forces during simple structural analysis for a truss pin-jointed strucures

texts:
I am currently trying to design a simple truss (pin-jointed) structure able to withstand a 1.2 kN load.

I carried all the analysis and found the forces, stresses and strains in the members. My question now is how good and accurate are those forces I calculated.

Say I found that in a particular member the force was 10000N (tensile) and the proof stress of the alloy I'm using = 100 MPa. Theoretically, using any bar with area > 100mm^2 should be fine, right? However, in the analysis I made several assumptions (massless bars, no firction, loaded through centroid...) and the calculated Force might not be exactly the real-life one. As a rule of thumb, what margins should I take to account for these assumptions? Should I systematically allow for 10% error for example?

Secondly, how safe is it (with regards to failure of the member) to go close to the proof stress? Should I there again allow for a margin for error?

Thank you very much for your answers!!

Best wishes,

NB1: I do not have access to a Finte Elements Sotware to run it computationally and check!

NB2: The structure is statically determinate.


texts: Diffusion Pump Copper Cooling Coil Repair

texts:
I bought a Varian VHS-4 oil diffusion pump off of ebay about a year ago. The pump was stored outside by the people I bought it from so it suffered mostly cosmetic issues. Recently I have acquired all the necessary components for my UHV (Ultra-High Vacuum) system and began to test the pump. After about 30 minutes of warmup the pump is only able to acheive a chamber pressure of about 1.6 mTorr (this seems to be the max where the water temperature exceeds the rated value). I suspect the issues lies in the fact that the cooling coil (meant to chill the chamber wall to about 60F) has lots of dents which heavily restricts the water flow rate. The water isn't able to remove the heat quick enough which results in decreased performance. Here are some photos of a couple of the worst indents in the coil.

[

[

What I want to know is if you guys have any ideas as to how I can repair these dents to increase flow rate. The copper pipe is very small (maybe 1/8" OD) which makes it difficult to replace. The piping has some compound between the piping and pump body but I dont know what it is made of. I thought about TIG brazing or soldering copper pipe to bypass the kinks but Im not sure I would be able to get a water tight seal easily. The pipes are made of copper and the pump body is made of stainless steel so welding is not an option either. There is a powder coating on the pipe presumably for corrosion resistance but I'm not apposed to removing some as it would only be for a few small sections of tubing.

Here is some information from the pump manual regarding cooling coil requirements

"Connect the inlet water fitting (near the inlet flange at the top of the pump) to a continuously running water supply at 0.15 gpm (VHS-4) and at a temperature of 60 to 80 °F".


texts: Will deodorant flamethrower ever explode?

texts:
Yes, the one where you put lighter close to nozzle of deodorant, light it up and start to spray out the deodorant. I suppose that this is simillar to how gas stoves work, so it shouldn't explode. Even when I stop pushing on spray button, flame gets closer to deodorant and it feels like its your last moment, flame can't get back into the can and cause a fireshow, becasue there's no air in the can. Worst thing that can happen is nozzle meltig down over time and flame getting bigger but not out of control. Right?

Also, when things can go bad? I know that i shouldn't throw deodorant can into flame, but can it overheat just from being used as a flamethrower and boom?


texts: FEA: What boundary conditions am I missing?

texts:
I'm working on a 2D-model (in the xy-plane) in NASTRAN and am getting convergence problems. The main cause of these convergence problems is a "high or negative matrix factor diagonal ratio."

I've attached a picture of a setup similar to the one I'm working on. The elements in white are rod elements; the elements in pink are bar elements.

The loads and BCs are:

Angular velocity of 60 rad/sec about the y-axis
Gravitational acceleration of 9.8 m/s$^2$ in the -y-direction
$123456$ constraints on the top and bottom nodes to prevent them from moving or rotating
$123$ constraints on the inner-most node to prevent it from moving

Here is some text from the f06 file:

Nodes 13 and 27 are where the rods connect to the bars, and Nodes 20 and 24 are just two random nodes on the right-hand side of the pink section.

Under the bar properties, there is an option called "Pinned DOF @ Node 1," which may or may not be helpful here. The options are UX, UY, UZ, RX, RY, RZ.

I've tried experimenting with various boundary conditions, but I can't get convergence in either the linear static case or the nonlinear static case.

Generally high matrix factor diagonal ratios imply that I have a very stiff element connected to a not-very-stiff element, but Nodes 20 and 24 aren't where the rod/bar intersection happens.

Does anyone know how I might go about diagnosing the problem? I think I'm missing boundary conditions somewhere, but I'm not entirely sure where that is.

UPDATE

Whoops, I forgot to explain what behavior I expect from this contraption.

Since I have a really high angular velocity (and perfectly normal gravity), I would expect the pink nodes to move rightward and downward due to the loads. The only thing stopping them from moving indefinitely are the white rods. Since these aren't beams and don't transmit moment stiffness, all these rods can really do is extend in length and change angle, since they're required to be a straight line.

This will result in a shape that looks similar to the pink curve, but probably shifted rightward a bit.

I ran the case with PARAM,BAILOUT,-1 (linear static), and I got the following clearly incorrect deflection ($10^7$ m deflection): image removed since it didn't provide any useful information and it took up too much space.

UPDATE #$2$

I've pinpointed the problem, I believe.

Blue elements are rods, pink elements are bars. The first case converged (nonlinear static) and gave results pretty close to what I expected (deflections were slightly high, but my angular velocity is slightly high, too).

The second case failed to converge, and it had a problem with my new node - it told me that it's having diagonal ratio problems in the T2 direction.

There's something NASTRAN is doing wrong with how these two bar elements are connected at this node. Any ideas?


texts: Looking for a current multiplier circuit - if possible

texts:
I used a very inexpensive circuit based on the TP4056 chip and built a Lithium Ion battery charger for 18650 batteries.

The problem is, the batteries I use have so much capacity that the circuit, which is limited to only charging at 1 amp, takes many hours to charge my batteries.

What I would like to do, is build a circuit that I can add to the one I purchased. This new circuit would (ideally) sample the current flow from the charger circuit to the battery, and multiply it by two.  My batteries can handle a charge current of 3 amps safely. All I want to do is charge them at 2 amps.

I have attached a diagram that I made hopefully clearly illustrating what I am looking for. Obviously any and all of it is subject to modification based on new information, knowledge etc.


texts: How can I choose a motor for my project?

texts:
I'm working in a project that consists of something similar to a motorized skate. I know how to do it, but I don't know what motor to use. I need that the skate to be able to move 90 Kg to 20 Kph (12 miles per hour) or more if it's possible. I also need the motor as cheap as possible.

I have read things about motors but we can say that I don't know anything about them.

What kind of motor and what facts do I need? What transmission ratio should I use between the motor and the wheels? What size and type of wheels? Any special type of transmission?

I know the basic mechanics, but I don't know what motor should I use, my requirements are:

Move 90 Kg to 20 Kph (if the motor for that is very expensive only 15 kph)
I don't mind the acceleration
I think that it should work with battery (I'm not sure)
The skate is thought for city, but may have to go up small slopes
As cheaper as possible

I don't have the budget to buy numerous motors and try them all, so I need to be sure that it will work before I purchase one.


texts:
For the connection above, I think that once the beam  is loaded, their is no room for rotation of the beam.

But as per British Standard this is a pinned connection. So I have been trying to determine how a connection is defined as Pinned or fixed. After reviewing American and British codes, I have come to the conclusion that steel structure designers need to follow their Standard connections for design (for which they have done experiments) or conduct experiments on connections to determine to evaluate whether its a pinned or connections based on certain criteria. Is my understanding correct?


texts: Does the length of a beam change upon deflection?

texts:
I have made a Python program in which I have computed the deflection of a beam.

I am plotting the deflected beam and am now asked to show the length of the beam.

If the beam is not deflected, it is easy to show the length of the beam but when the beam is deflected, I guess the length of the beam is longer than the undeflected beam. How can I compute the length of the deflected beam? Is it correct to distinguish between the length of the deflected and undeflected beam?


texts: Is it normal to get different solutions with different ODE methods in MATLAB simulink?

texts:
I made a block diagram using simulink. When I solve it with ode45 and ode23 it gives me different graphs. Is it normal? Should I use the proper one?

m1=1.3608;
m2=0.096;
r=0.0592;
I2=0.0002175;
k1=186.3;
g=9.81;

Here is what the model looks like:

and the ode45 solution:

I can't post the ode23 solution but it is very different.


texts: Why we need to consider only 3 cases when we want to find the max positive shear ? IMO , We know that the max shear will only occur when the 67.5kN act on B , am i right ? There is no need to consider 3 different cases .....Or my concept is incorrect ? If so , can anyone show me the example where the max shear will occur at B although the max concentrated load doesn't act on the particular point ?


texts: MIMO (multi input - multi output) system decoupling method

texts:
A MIMO system with 2 input and 2 output decoupling method to a SISO system is described in many articles and books. How about m*n size transfer functions systems? How can we generalize the method for example to 3*3 or 3*7 MIMO systems?

Here is a 2*2 MIMO system description:

  with $\mathrm{D_{11}(s)=D_{22}(s)=1}$ to the form

  $$\mathrm{D(s)}=\begin{bmatrix} D_{11}(s) & D_{12}(s) \\ D_{21}(s) &
> D_{22}(s) \\ \end{bmatrix}$$

  Here we specify a decoupled response and the decoupler with the
  structure in Equation

  $$G_p(s)D(s)=\begin{bmatrix} G_{11}(s) & 0 \\0 & G_{22}(s)
> \end{bmatrix} \\ \begin{bmatrix} G_{11}(s) & G_{12}(s) \\ G_{21}(s) &
> G_{22}(s) \end{bmatrix} \begin{bmatrix} 1 & D_{12}(s) \\ D_{21}(s) & 1
> \end{bmatrix}
> = \begin{bmatrix} G^*_{11}(s) & 0 \\ 0 & G^*_{22}(s) \end{bmatrix}$$

  And we can solve four equations in four unknowns to find

  $$D_{12}(s) = -\frac{G_{12}(s)}{G_{11}(s)} \\ D_{21}(s) =
> -\frac{G_{21}(s)}{G_{22}(s)} \\ G_{l1}(s) = G_{11}(s) = -\frac{G_{12}(s)G_{21}(s)}{G_{22}(s)} \\ G_{l2}(s) = G_{22}(s) = -\frac{G_{21}(s)G_{12}(s)}{G_{11}(s)} $$


texts: Identifying Compression and Tension as well as Hogging

texts:
Im looking for clarification on how the solution identified the moment to be hogging, as well as the axial stress to be in compression?

Also I'm confused as to how the solution came to a conclusion that the bottom of the cross section is compressive stress, whilst the top of the cross section is tensile stress.

Please reference the photo below with the red box's

Thankyou!


texts: Why do we neglect the radial stress in case of a thin pressure vessel?

texts:
A cylindrical or a spherical pressure vessel, having inner diameter $d$ & thickness of wall $t$, is called thin if $\large \frac{t}{d}<\frac{1}{20}$.

$\bullet$ Thin cylindrical pressure vessel

hoop or circumferential stress $ \sigma_h=\large\frac{pd}{2t}$  & longitudinal stress $ \sigma_l=\large\frac{pd}{4t}$

$\bullet$ Thin spherical pressure vessel

hoop or circumferential stress $ \sigma_h=\large\frac{pd}{4t}$  & longitudinal stress $ \sigma_l=\large\frac{pd}{4t}$

In both the cases we consider only two stresses i.e. the system of plane stresses neglecting the radial stress $(\sigma_r)$.

The question is why do we neglect the radial stress for thin pressure vessels?
Can it be explained by Lame's equation used for thick pressure vessels:

$$\sigma_h, \sigma_r=\frac{B}{x^2}\pm A\ \text{?}$$


texts: How does one activate viscosity change, in gap flow, as the dependency (field variable) is specified at a particular node in Abaqus Standard?

texts:
I have a question regarding fluid flow and the change in viscosity of the fluid flow as the field parameter changes from one step to another.

I am modelling fluid flow, followed by fluid and proppant flow inside a cohesive fracture. In step 2, I just pump in normal fluid (that has low viscosity of 1 cP) and at the beginning of step 3, I am assigning to a particular node a field variable number so that the viscosity of the fluid will change from 1 cP to 3cP at the start of step 3. Thus, what I am doing is the following:

Under *Gap Flow keyword,

I am entering the following lines:

  *Gap Flow, dependencies=1

  0.001, ,   0.

  0.00122408, , 0.05

  0.00153288, ,  0.1

  0.00558678, ,  0.3

  0.0187778, ,  0.4

Under *Step keyword (when it is step 3),

I am entering the following line:

  *FIELD, VARIABLE=1

  Part-1-1.inlet_Node, 0.273

"Part-1-1.inlet_Node" is the node where I am injecting the fluid, using the command *cflow at the beginning of step 2.

When step 3 will start, I want Abaqus to change the fluid viscosity because I am introducing the field variable at this node. Basically, I am trying to tell Abaqus that I am injecting fluid with proppants mixed with them at the beginning of Step 3, which will result in the higher pressure gradient accross the fracture length!!!

But when I do this, for some reason, this change is not taking place! The pressure change, due to injecting viscous fluid, is not taking place!

Could you please help me with this? Maybe I am doing this wrong!


texts: Modeling of a Wireless Channel with known BER

texts:
I have to model through software a wireless (my choice: 3g,4g, 802.11...) channel with given Bit Error Rate. I'm searching some distributions, I'm reading tons of papers but I can't find how to simulate in realistic way the Channel.

The model should take as input a bit sequence and BER and produce the bit sequence as it could be received with noise.


texts: Are there different Gauge standards out there?

texts:
It is my understanding that a mil is a one thousandth of an inch (1mil = 0.001”). Also, a mil is 25.4 microns, aka micrometers. Then, it is my understanding that Gauge is 100x mil (1mil-100Ga).

I am looking for some copper sheets for a project, and I am confused. This Amazon listing:

Lists 0.0216" (inch) as a 24Ga (Gauge). How does that work? Am I reading the units wrong?
0.0216" = 21.6Mil = 2160Ga ? Is that right?


texts: I am looking for a way to focus the vibration of a metal sheet at a specific point on that sheet so that other points vibrate less. Just like light and lens. Is there any way to focus the mechanical vibration or stress of an object?


texts: Interference fit problem in ANSYS Workbench 16.1 - how do I get rid of pressure/displacement raisers?

texts:
I have an interference fit problem of two perfect cylinders modelled in 2D using symmetry. The overall interface pressure is around 20MPa lower than the hand calculations and I get non-uniform displacement / pressure near the edges of the model. Any suggestions on how to remove these raisers would be greatly appreciated!

I've attached the pressure results.
[


texts: How does electricity flow through this kind of vacuum tube?

texts: Does the current flow from the bottom left pin to the bottom right pin, or from the bottom pins to the cap on top?


texts: J2 orbit propagation problem in MATLAB (solver instability)

texts:
The problem is that when I try to solve the following equations of J2 perturbed gravity:

function xdot = Gravity( ~ , x )

Re  = 6378.137;
J2  = 1.08262668e-3;
mu  = 398600.4418;

r   = norm(x(1:3));

% xdot = [x(4:6)
%         -mu/r^3*x(1:3)];

xdot    = [ x(4);
            x(5);
            x(6);
            -mu*x(1)/r^3*(1+1.5*J2*(Re/r)^2*(1-5*(x(3)/r)^2));
            -mu*x(2)/r^3*(1+1.5*J2*(Re/r)^2*(1-5*(x(3)/r)^2));
            -mu*x(3)/r^3*(1+1.5*J2*(Re/r)^2*(3-5*(x(3)/r)^2))];
end

using any of the solvers (ode45, ode113, etc.), the propagated position and velocity has a considerable error compared to a trusted commercial software (STK), and the error keeps growing. I've tried various settings of tolerances, initial steps, and max steps, but the problem persists!

It might be surprising, but when I wrote a fixed step 4th order Runge-Kutta code as below, it didn't get much better.

function [t,x] = RK4( fn,tspan,x0 )
% An implementation of fixed step 4th order Runge-Kutta method

f = str2func(fn);
t = tspan;
h = tspan(2)-tspan(1);
x(:,1) = x0;

for i = 1:size(t,2)-1
    k1 = f(t(i),x(:,i));
    k2 = f(t(i)+h/2,x(:,i)+k1*h/2);
    k3 = f(t(i)+h/2,x(:,i)+k2*h/2);
    k4 = f(t(i)+h,x(:,i)+k3*h);
    x(:,i+1) = x(:,i) + (k1 + 2*k2 + 2*k3 + k4)*h/6;
end

end

any idea of what the problem might be? I also have to mention that to a great surprise, I did get a result using RK4, but the same code with the same conditions misbehaved later!!

A sample result:


texts: Oil refinery pipeline direct to gas stations

texts:
I know major oil pipelines do exists either underground or under the seabed. However, these usually move crude/unrefined oil from refinery to refinery.  Yet we don't have refined petroleum or gas directly piped from refinery to the gas station? I mean we have done it with electricity, water, sewage, stormwater and piped LPG gas (for cooking), why do we still see petrol takers plying the roads to top up gas stations that you go to top up your car?

NOTE: I understand this is easier to achieve in big cities and Urban areas rather than laying pipework for rural areas. But I so not yet have concrete info this is implemented in long term gas stations located in the cities.


texts: Determining Pump Dead Head Pressure and Pump Curve

texts:
I want to verify the pump curve of a regenerative turbine pump. The manufacturer doesn't supply any pump curve of it.
This is the test setup.

With the discharge valve shut off (plugged) and water line opened. I measured the following discharge pressure of 28 psi.

This is the inlet or suction pressure of 14.3 psi.

Is it correct to deduct the discharge pressure from the suction pressure to arrive at the head dead pressure? It is 28 psi - 14.3 psi = 13.7 psi.
So 13.7 psi is the pump dead pressure right?
I made a lot of measurements with pressure gauges and water flow rates to get some idea of the pump curve which the pump doesn't have
This is the pump specs. 8 is the meter in heads or about 11.7 psi.

This is my bathroom minipump connected to a heater and shower with 2 gauges label by A and B. The green arrow is the water pipe entry to the bathroom with 1/2 diameter hole. It can produce 10 liter per minute (2.64 gallon per minute) when directly measured with a container without all the hoses which are 1/4" in diameter (note all tankless heaters use the same 1/4" flexible hoses).
Without the pump turn on. I'm getting 4 liters per minute (about 1 gallon per minute) of water in the shower. With pump turn on. I'm getting 6 liters per minute (about 1.6 gallon per minute of water in the shower).
With and without the pump turned on. The gauge in the bathroom pipe entry labeled in A read 13 psi.
Without the pump turned on. The pressure gauge at B (after pump) reads 10 psi. With the pump turned on. The pressure gauge (after pump) reads 20 psi.
Do the actual test data above support the pump specs shown above?
From my existing water of 6 liter/minute (1.5 gallon per minute). I want it to be at least 2.5 gallon per minute (or 9.4 liter per minute). So i need to understand pump curve to be sure i got the right one.


texts: What if the paper of my drawing changes at the last moment?

texts:
I have a full set of about 500 drawings sheets, in Autodesk AutoCAD 2018, with layouts, paper sizes and scales set up for an A0 paper, meant to be printed in A0 at the project beginning.
At the very end of the project, at the moment of the final deliverables, the client requested us to print everything in A1 paper. Now, printing in A0 is not as option.
Which should be the optimal resource and political way for solving this dispute?

Should we change ALL but not EVERYTHING in the drawings, keeping the A0 Layouts, keeping all the viewport scales, and changing the scales texts, e.g. 1:5000, multipling them by $\sqrt 2$ (A0/A1 ratio), and having awful scales like 1:7070, or better looking and somehow approximate figures such as 1:7000 in this case (among other figures), and changing the revision of ALL the drawings?
Should we absolutely change ALL and COMPLETELY the viewports, for fitting the new scales, in this case, 1:7000, changing the Layout to A0, changing the scale texts, and changing the revision of ALL the drawings?
Should we tie a clean template note "All Scales for A0 Paper" in ALL the drawings, leaving everything untouched, indicating the scales are for A0 paper, and changing the revision of ALL the drawings? Or leaving all revision as is, excusing the change is only in the template?
Should we leave ALL the drawings untouched, not requiring any additional approvals, nor revision upgrades, and changing only the Global Index Sheets of the overall set, with a clear note "All Scales for A0 Paper"?

Whatever the automation of annotations indicating the scale, passing from A0 to A1 will lead to nasty scales, e.g. from 1:5000 to 1:7070 (!), hence this do not seems to be an automation problem... Unless there could be a way to "round" scales at a viewport, which is a completely different topic...
Note. Please keep the discussion technical; how, when and why to charge the client is a discussion out of the question.


texts: I want to build a pod. I am thinking to put a linear actuator on its lid. but my problem is, since linear actuators have this self locking mechanism, if it will be brown out, I cant open or close the lead manually. How can I deal with this scenario?


texts: What is meant by soaking time in heat treatment?

texts: After heating at 950°C and holding the temperature for 3 hours there is a soaking time that is provided for 12 hours. What is the soaking time being referred to here? A detailed reply to this will be very welcome.


texts: how many power stroke in 3 cylinders, 4 stroke at 3000 rpm?

texts: According to some answers, in 3 cylinder , 4 stroke we have power stroke each 240°, as we have 1500 rev. Of 720° in this rpm, so we will have  this: 1500 x 1.5 = 2250 power stroke at 3000 rpm, is it right?


texts: Effect of step pulse shape on stepper motor function

texts:
I am using Nema17 12 v motors with A4988 drivers for a project that drives an XY stage. I am programming the pulses to the STEP pin of the drivers in C and I can control the frequency and the shape of each pulse. I was wondering if anyone can tell me (or point me to a reference about) what is the relationship between pulse SHAPE and performance of the motor (as distinct from pulse FREQUENCY). By 'performance' I mean any effect on torque or the reliability of converting the step signal into a rotor step. For example, what would be the difference (for the same frequency) of applying these pulse shapes to the STEP pin of the driver:

a) -_____-_____-_____-_____ etc. (most of the cycle the signal is 'off'/'logical zero')
b) ---___---___---___---___ etc. (equal time for 'on' and 'off')
c) -----_-----_-----_-----_ etc. (for most of each cycle the signal is 'on'/'1')

I am currently using form (b) for my pulses (as most examples I have seen do this) but I was wondering what advantage/disadvantage there may be for changing this. Many thanks in advance.


texts:
Looking for advice or suggestions for high articulation joints (>57°) for an automotive halfshaft.  Peak operating conditions are in the ballpark of ~1000RPM, ~300ft-lb torque.
I've considered u-joints, double cardan joints and rzeppa CVs, but double cardan joints are the only type that appear to be able to hit this target (albeit with some geometry caveats).


texts: How to design a 915 MHz waveguide circulator?

texts:
I would like to design a waveguide circulator.  I tried to design one but, my attempt was not successful.  My design used a cylindrical cavity with ferrite as region. I then connected 3 waveguides in 0,120 and -120 directions. Upon applying the excitation, I got a pathetic result.  I have referred to some more resources but can not resolve this problem.  Has anybody tried this before?

My design and its parameters are shown below

Frequency of operation: 915 MHz
Dielectric permittivity of material(ferrite): 14.2
The height of cylinder: 5.5 mm
Radius of cylinder 30 mm
The waveguide cross section a = 20 mm
The waveguide cross section b = 2.5 mm
The length of waveguide l = 50 mm


texts:
The optical encoder has a code wheel with a single track of slots and two photodetectors. The photodetectors are positioned so that they produce signals with a 90 degree phase difference.

I want to calculate how many slots there has to be in the code wheel in each of the following cases in order to measure the position of the linearly moving object with a resolution of 0.02 mm.

Case 1:
motor + gear + ball screw ($p=8 \text{mm}$)

Case 2: motor + gear + conveyor belt ($d = 38 \text{mm} $)

in both cases the gear ratio is 6.5.

Is it simple as this:

$$\frac{8}{0.02\cdot 6.5}=62$$

and

$$\frac{19}{0.02\cdot6.5}= 146$$

so needed slot are 62 and 146.

Is this wrong and if it is how do I calculate this?


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I'm trying to find PSIG from other variables that I have values for. I'll try my best to explain.

I have Helium flowing through a 1" copper pipe at 65 psig and at 40 deg F to a 1" ball valve and power control valve. There is a flow meter connected after the power control valve, with the ball valve throttled to achieve 40 CFM. I need to find the PSIG after the throttled ball valve.

I'm looking for the formula or a web calculator to solve this equation. I don't need a precise answer, just a rounded.

Any help will be appreciated.
Thanks, Steve.


texts: Most efficient way to build a toothpick bridge

texts:
In my stem class we are going to have a competition where we have to build a toothpick bridge that can support as must weight as possible, while using only toothpicks and glue. These are the rules:

Each toothpick costs \$10,000.
Each end of a toothpick glued to another end of a toothpick costs \$10,000.
The bridge must span at least 1 foot.
We can't build beams down to the floor for support.
The base of the bridge, the part cars would drive on if it were a real bridge, can't have any large gaps in it, although I'm not entirely how much this matters.
We will have a time limit when building it, but I don't know what it will be. We can bring a hairdryer to help the glue dry faster.
It must hold a lot of weight, and be cheap. I don't know how much each of those factors matter, but I'd imagine the weight it can hold is much more important.

My teacher wants  us to do lots of research before the project and have a clear plan, so I have been looking into what kind of bridge to build. It seems like the obvious choice is a beam bridge, but I could be wrong. I found this site talking about how a truss can help a beam bridge hold more weight, but I don't quite understand how it helps.

If a beam bridge is my best option, would a truss significantly help at this scale? And if so, which kind of truss? The warren looks more efficient as far as costs are concerned, but I don't know if the pratt or any other kind has a major advantage. Any advice on this would be greatly appreciated, thanks!