texts: Can I combine two shear-stresses acting on one plane?

texts:
For example, I have an axial force and a torsion force applied on a rock socket installed in bedrock. If I am considering the side friction between socket and rock as a resistance, the socket surface will have two shear stress generated, one in axial direction, and the other in radial direction. If I want to design this, what is the maximum I should use?

Can I combine the two stresses by triangle rule, or simply adding them up, or only take the larger one?

Here is a conceptual sketch:


texts:
I am trying to control a real inverted pendulum by means of a DC motor, for this I must model the torque of the motor, the work I've done in this direction is the following (which I believe is right):

Something I don't get is, both the motor back-emf constant ($k_e$) and the torque constant ($k_t$) are supposed to be the same, at least as far as I've read on several places. Is it safe to assume both are the same ($k_e = k_t = K$), in which case, I can obtain the constant by measuring the angular speed and the voltage applied to the motor, and dividing both, right?


texts: simulation of an attitude optimal Backstepping controller based quaternion for a UAV in MATLAB


texts: Compensating for a magnet in a device with a magnetometer

texts:
I'm working on a device that relies on data from a magnetometer. Unfortunately, the device also needs to have a fairly powerful magnet on it. Given that the design is fairly flexible, and within manufacturing tolerance I can know precisely where the magnet is and the layout of the magnetic field it should produce, is there a way to compensate for having a magnet in the device?

Is there some mathematical means of cancelling out the contribution of the inbuilt magnet, or perhaps shielding the magnet from the remainder of the device somehow, as the magnet is only needed for mounting the device to metal surfaces and nothing else?


texts: Device that emits a safe beam of light - doesn't have to be visible (Like laser, but safer)

texts:
I am looking for a light emitting device, which can produce a narrow and accurate beam, with a small "dot" size, for a significant distance (around the 100-150 meters) similar to that of a laser, but that it would be safer when comes in contact with eyes / other body parts.

**Edit: My goal is that I want to be able to point 1 device at another, and that the other device will detect it was pointed at (But it should be placed on the body so that's why I want it to be safe), so the beam doesn't actually needs to be visible

Does such device exist?


texts: Time for oil to flow through Redwood Viscometer

texts:
A viscometer of the Redwood type has an oil-containing cylinder 4.75cm in diam and an agate tube 0.17 cm in diameter and 1.2 cm long. The oil surface, when flow starts, is 9 cm above the outlet from the agate tube. To allow for the sudden contractions at entry to the tube, the effective length of the tube may be taken as the actual length plus the tube radius. Making allowance for the decreasing head of oil, the viscous resistance through the tube, and the KE (kinetic energy) of discharge, calculate using arithmetical integration, the time required for 50 cm3 of an oil of viscosity 0.5 poise and specific gravity 0.92 to flow through the viscometer.

How do you find the time?

From this question, I have tried to use quadratic equation to solve for $v$, but it is proving more difficult than I thought.

So far this is what I have: $$h=\frac{32\mu (l+d/2)v}{\rho g d^2}+\frac{v^2}{2g}$$

$$av^2 + bv + c = 0$$

where $a = 1/ 2g$,  $b=\frac{32\mu (l+d/2)v}{\rho g d^2} and  $c = $-h$

Using $v = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

I eventually got $v = - \frac{32\mu (l+d/2)v}{\rho d^2} \pm (\frac{32\mu (l+d/2)v}{\rho d^2} + \sqrt{2gh})$

In this expression $-b + b = 0$, so how do I deal with this?

Let the fall in level be $dh$ in a small interval of time $\text{d}t$, water area of cylinder be $A$ and area of tube be $a$.
Therefore, continuity equation of tank and pipe yields quantity discharge in $\text{d}t$ seconds = $A \text{d}h$ = $a v \text{d}t$.

How do you integrate the expression for this time for the head level to fall from $H1$ to $H2$ for this question?

Does anyone have any ideas that can help me, so that I can solve this question?


texts: Relationship and interpretation of "discrete" and "continuous" covariance matrices in Kalman Filtering

texts:
I am quite confused about the interpretations/implementation of the system and measurement noise covariance matrices for the continuous and discrete time Kalman Filter. What I want is to initialize those matrices with physically meaningful values for the continuous system (think continuously, implement discrete).
I know that the standard deviation has the same unit as the corresponding quantitiy, e.g., for the (arbitrary) system
$$
\begin{align}
\dot{x}&=Ax+Bu+w,\quad &w\in\mathcal{N}(0,Q_c)\\
y&=Cx+v,\quad &v\in\mathcal{N}(0,R_c)
\end{align}
$$
if $x=[s,\,v]^\top$ are the position and velocity of a falling particle, respectively, the covariances $Q_c=\text{diag}(\sigma_{w,\,1}^2,\,\sigma_{w,\,2}^2)$ have the units [m$^2$/s$^2$] and [m$^2$/s$^4$] (since the standard deviations have the same units as $\dot s$ and $\dot v$), and $R_c=\sigma_v^2$ has unit [m$^2$] (the same as $s$).  So far so good.
For the sake of completeness, the discrete-time Kalman Filter equations read
$$
\begin{align}
&\textbf{Time update}\\
&\hat{x}^-_k=A_d\hat{x}^+_{k-1}+B_du_{k-1}\\
&P^-_k=A_dP_{k-1}^+A_d^\top+Q_{k-1}\\
&\textbf{Measurement Update}\\
&K_k=P_k^-C^\top\left(CP_k^-C^\top+R_k\right)^{-1}\\
&\hat{x}^+_k=\hat{x}^-_k+K_k(y_k-Cx^-_k)\\
&P_k^+=(I-K_kC)P^-_k
\end{align}
$$
where $A_d=(I+\Delta tA),\quad B_d=\Delta tB$ using a forward Euler.
Now, according to "Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches" by D. Simon p.231 ff
it is mentioned that
$$Q_c=\frac{Q_{k-1}}{\Delta t},\qquad R_c={R_{k}}\Delta t$$
and one can substitute these expressions in the discrete KF equations (and look at the limit $\Delta t\rightarrow 0$) to derive the continuous-time Kalman-Bucy Filter
$$
\begin{align}
\dot{\hat{x}}&=A\hat{x}+Bu+K(y-C\hat{x})\\
\dot{P}&=-PC^\top R_c^{-1}CP+AP+PA^\top+Q_c
\end{align}
$$
where $K=PC^\top R_c^{-1}$.
QUESTION
It is not clear to me why the covariances scale with the discretization time? For example if I were to look at the sensor measuring the position and it would tell me in its data sheet it has standard deviation, say, $\sigma_v=0.2\,m$, and I were to implement the discrete KF with a sampling time of $\Delta t=0.01\,s$, i.e. $100\,Hz$, then
$$R_k=\frac{\sigma_v^2}{\Delta t}=\frac{0.04\,m^2}{0.01\,s}=4\frac{m^2}{s}$$
so the "uncertainty" in my measurements would blow up, even though I receive more measurements (which should be a good thing?)! On the other hand, let's say we're not confident with the model so we expect the velocity and acceleration varies with standard deviation $\sigma_{w,\,1}=0.1\,\frac{m}{s}$ and $\sigma_{w,\,2}=1\,\frac{m}{s^2}$. For the discrete KF,
$$
\begin{align}
Q_{k-1}&=\Delta t\ \text{diag}(\sigma_{w,\,1}^2,\,\sigma_{w,\,2}^2)\\
&=0.01\,s
\begin{bmatrix}
 0.1\,\frac{m^2}{s^2}& 0\\
0& 1\,\frac{m^2}{s^4}
\end{bmatrix}=
\begin{bmatrix}
 0.001\,\frac{m^2}{s}& 0\\
0& 0.01\,\frac{m^2}{s^3}
\end{bmatrix}\end{align}$$
meaning that our model gets "better" with smaller step size. This makes somewhat sense, since the discretization gets more accurate, right? Is my reasoning correct? Or did I miss something. Is there a way to interpret the discrete covariances? I never actually see coded Kalman Filters take this into account. Why is that?
EDIT1: Additional question, if I want to add noise to my measurements in Matlab, do I use $R_c$ or $R_{k}$, i.e.,
yk = C*xk+sqrt(Rc)*randn(1,1)
or
yk = C*xk+sqrt(Rk)*randn(1,1)
EDIT2: Changes example system to make more sense


texts:
We make plastic tensile bars per astm 638. The problem that I'm having is the bars are breaking outside the gauge marks in the reduced section of the samples. I'd like to know as to what I can do to prevent this ?
Thanks


texts: Is it possible to cook with low power PV systems (under 300 W)

texts:
This topic is slightly related to this one, with some extra details.

I would like to go off-grid and therefore buy a PV kit. I can see that the prices for PV systems with a power of +3kW are very high, so I was thinking how much I can get from a 300-500W system, which is way cheaper. The fridge, the PC, and other households can easily work with such a power if stored in batteries, but the problem is the stove.

My current stove has a power between 1 and 2 kW, which means that I would need to have this instant power from the PV or have it stored in some batteries. This instant power is of course not available, but I can get more batteries to store let's say at least 1-2kWh of energy, which also costs a lot.

The only thing that I have in mind is to find a stove/oven that has a low power (under 300W). Is the crock pot the only option for this? I would like to use the stove/oven for cooking different dishes, including frying and baking. Any idea if a "standard" 1-2kW oven can be modified to work with lower power? Or does any of you have any other idea how to cook with such a little power?


texts:
Cooling towers for nuclear power plants often have the shape of a hyperboloid. At first glance, I thought that an obvious reason for this would be the smaller sectional area, meaning the tower would be less exposed to wind.

However, I did a quick calculation, based on a cooling tower nearby. I modeled the cooling tower as a hyperboloid and calculated its volume and its sectional area. I then calculated the radius needed for a cylindrical tower with the same volume. Its sectional area was just 1.5% larger. By reducing its height from 150 to 145 meters (and increasing the radius, of course), the sectional areas would have been the same.

I know that hyperboloids can be built using only straight pieces of reinforcement. However, those towers are quite big and the circular shape could be very well approximated by some sort of polygon with e.g. 1000 vertices making circularly shaped reinforcement unnecessary.

I can imagine other reasons:

The waisted shape could probably lead to a certain compression of the hot vapor and thus help/accelerate the condensation. Is this true? How big could that effect be?
Some documents I have read say one needs less material to build a hyperboloid cooling tower. Is there really a big difference in terms of concrete? After a rough calculation, assuming a thickness of 1 meter of concrete all around, I'd estimate that a cylindrical shape would only need approximately 1.5% more concrete.

So, why do almost all cooling towers have this particular shape?


texts: Why is capacitor 2 not grounded on this board?

texts: I'm building a APRS tracker for a high altitude balloon and am tracing the voltage as it's not powering up. I'm confused why it seems that this capacitor's ground appears to not be connected to anything. topside of board


texts:
Would an engine that electrically generates ozone from the oxygen in air then uses it as fuel be efficient or possible? (This is not a Newtonian question – we’re talking chemical reaction not conservation of energy.)
Or what if ozone was used as an additive to the air intake for possible better fuel mileage on gas vehicles? (Those electric arc lighters produce ozone and are marketed as being wind proof so I wonder if an arc were safely maintained within the air intake if that would provide any boost?)
Ozone will combust in certain concentrations and even when in a solution of water if temperature is raised to the combustion temperature (which is quite low.)
As for the use of ozone as an energy source I believe the safest way to do so would be to make it on the fly and not store any amount that is not immediately used because it is a strong oxidizer and unstable.
Years ago I remember using a small van der graaf generator and recall that particular smell of ozone that is emitted while it runs. It doesn’t take long — maybe just a few seconds before I could smell the ozone in the air after turning on the machine. Also, with those electric arc lighters you can smell ozone being generated when you use.
So ultimately I’m asking: would it be possible to use a mix of ozone and air as the source of combustion inside an internal combustion engine? Or what about an ozone and water solution plus air for use as combustion source for combustion engines? What would be the byproduct of this?
Ozone as energy source for electric automobiles, jets, air planes etc?
Disclaimer: If you’re reading this please do not try at home. Ozone is dangerous at certain concentrations.


texts: Is there a loss in light transmission when using acrylic lens, instead of glass, for collimating a led light beam?

texts:
I've got a led headlight for illuminating a small spot region at 30cms distance from my head.
I've let it fall and the glass lens chipped. So I unscrewed the lens and got a piece of acrylic rod which is sold as having 92% light transmittance.
I turned on my lathe a copy in acrylic as close as possible of the shape of the original glass lens, and polished it to a completely transparent look.
When I screwed the new lens to the headlamp case, it worked perfectly, the spot size of the light is the same as the original lens, at least visually, but for me is like the light is not so bright as it is with the glass lens...
Why is that so? Transparent acrylic is worse than glass for transmitting light in a collimated beam?
Thanks!


texts: Effective length for lateral torsional buckling in a laced strut

texts:
When loaded vertically, a beam experiences compression in its top flange and tension in its bottom flange. The top (compression) flange would tend to buckle vertically much like a column, however, the web prevents such buckling from taking place. But if there is enough compression with no lateral support, the flange and web would start to buckle horizontally together. The bottom (tension) flange restrains such movement, causing the beam to twist. This is phenomenon known as lateral torsional buckling (LTB).

A laced strut is a built-up strut made of two (or sometimes three equally spaced) beams joined together by a system of diagonal lacings.

Globally, a laced strut is not susceptible to LTB as its section modulus in the lateral direction is greater than that in the vertical direction. However, the same could not be said of the individual beam component that made up the strut.

If a 20m strut has lacings spaced at 1m intervals, what would be the effective length used to calculate LTB for the individual beam component and why?


texts: What does the abbreviation "B.C." mean on a weld joint diagram?

texts: A translator posted this diagram of a weld joint on a translator's forum (the figure below). What does the abbreviation "B.C." mean on the diagram?


texts: Magnetic treatment of hard water to prevent scale and corrosion? How does this work?

texts:
I ran across this company at their booth at a Tradeshow (2018). They claim to have a chemical free (and as far as I can tell - a power free) treatment method for hard water to minimize scale and corrosion effects downstream. My intuition tells me that this can't be for real, partly because it's "power free", but I also don't understand their explanation for how it works:

"When water is subjected to temperature change (delta T), pressure change (delta P), friction, turbulence and/or evaporation, dissolved minerals, primarily calcium carbonate (CaCO3) and magnesium carbonate (MgCO3), will precipitate out of solution and deposit on the heat transfer surfaces of plumbing systems and equipment in the form of a rock-like build-up, commonly called lime/scale. At the molecular level, the negatively and positively charged ions of these minerals are attracted to, and bond tightly together with, one another, thus forming the lime/scale deposit known as calcite. These mineral deposits are a great insulator and require much more energy to heat or cool water in many different types of residential, commercial, institutional and industrial applications."

They've been around for since 1964, so they are either:

very good salesmen, with a critical threshold of gullible people, or
they've discovered some niche effect (unlikely)...

Thoughts?


texts:
So a product of me being a bored mechanical engineering student and my love of camping has prompted me to attempt to make my own Seebeck generator. It will be powered by a simple wood fire in a can and slightly fan forced so i am expecting 400+ degrees (celsius).

My question is what would be best to conduct the heat from the fire (ideally from stock i already have), a solid copper round bar (8mm), a thicker aluminium or copper heatsink or copper tubing (6.5mm OD 3.7mm ID). the copper tubing will either be left with void in the center or i had the idea of filling it with lead/tin solder as the fire temperature will most likely be above their melting point and hopefully transfer the heat well.

This is more a thought experiment into whether the solder option will work or it i have missed something crucial like it expanding and exploding on me. i have also heard that fin style heat sinks, like that found on PC's, are terrible conductors of heat as the cross section of their fins are too small to carry large amounts of energy.

Any input is great and i'll probably end up testing them all anyway because there is no better way to learn than by doing.

I drew up some quick plans of what I am imagining


texts: Modeling Transient Heat Transfer between two 1-D materials

texts:
I have been working on creating a 1-D model of a material with a layer of heat resistant material stuck to it. For this I have been trying to use the implicit finite-differential method. The equations are as follows:

$$
\dot{E}_{in} - \dot{E}_{out} = \dot{E}_{st}
$$
or
$$
\frac{1}{\alpha} \frac{dT}{dt}= \frac{d^2T}{dx^2}
$$
Where $\alpha = \frac{k}{\rho C_p} $

So, if there is only one material, an internal node equation would look like (I am assuming all flow in into the node for sign convention, n is the node location, p is the time step, and x is the thickness of a node):
$$
\frac{k A}{\Delta x}(T^{p+1}_{n+1}-T^{p+1}_{n}) + \frac{k A}{\Delta x}(T^{p+1}_{n-1}-T^{p+1}_{n}) = \frac{C_p \rho  A \Delta x }{\Delta t}(T^{p+1}_{n}-T^{p}_{n})
$$
or
$$
(1+2*Fo)T^{p+1}_n - Fo(T^{p+1}_{n-1}+T^{p+1}_{n+1}) = T^p_n
$$
Where, $Fo = \frac{\alpha \Delta t}{(\Delta x)^2}$

The surface node equation looks like:
$$
{h A}(T_\infty-T^{p+1}_{n}) + \frac{k*A}{\Delta x}(T^{p+1}_{n-1}-T^{p+1}_{n}) = \frac{C_p \rho A \Delta x }{2 \Delta t}(T^{p+1}_{n}-T^{p}_{n})
$$
or
$$
(1+2Fo + 2FoBi)T^{p+1}_n-2Fo(T^{p+1}_{n-1}+BiT_\infty) = T^p_n
$$
Where, $Bi = \frac{h\Delta x}{k}$

This seems to work pretty good for me when I use just one material. I give it some initial conditions and run it to steady state then check it against a simple steady state resistance model and there is a match.

I begin to bump into issues when I put in an internal material boundary. This is the equation I was using to simulate it (This calculation is for a node in material A adjacent to a node in material B)

$$
\frac{(k_b +k_a )A}{\Delta x_b+\Delta x_a}(T^{p+1}_{n+1}-T^{p+1}_{n}) + \frac{k_a A}{\Delta x_a}(T^{p+1}_{n-1}-T^{p+1}_{n}) = \frac{C_{pa} \rho_a A \Delta x_a }{\Delta t}(T^{p+1}_{n}-T^{p}_{n})
$$
or
$$
(1+ Fo + Fo_{ab})T^{p+1}_n-FoT^{p+1}_{n-1}-Fo_{ab}T^{p+1}_{n+1} = T^p_n
$$
Where, $Fo_{ab} = \frac{\alpha_{ab} \Delta t}{\Delta x_a(\Delta x_b+\Delta x_a)}$ and $\alpha_{ab} = \frac{k_b+k_a}{\rho_a C_{pa}} $ Note: if the materials are the same $Fo_{ab} = Fo$ this equation becomes a same as the boundary equation above.

With this boundary added I again created a steady-state resistive model to check against and found about a 10% difference, which was not expected. (note:updated to add in an averaging of k values to remove this difference, not sure if its right, but it fixed the error)
Below is a diagram showing the two model setups:

For the test case, I used the arbitrary constants:
$$\Delta t = 0.15$$
$$Nodes_a = Nodes_b = 5$$
Note, number of nodes is different than in the picture above (4).
$$\Delta x_a = \Delta x_b = Length/(Nodes-0.5) = 10/4.5 = 2.2222$$
$$h_a = h_b = 1$$
$$\rho_a = \rho_b = 1$$
$$C_{pa} = C_{pb} = 1$$
$$k_a = 5$$
$$k_b = 10$$

Should I be getting this 10% difference between the two models? (updated to fix difference, still not sure if the new equation is correct though)
Is this equation I am using for the material boundary correct?

Btw, many of the equations for surface nodes and boundary nodes came from the book: "Fundamentals of Heat and Mass Transfer" by Incropera and DeWitt.5th edition, section 5.9.2.


texts:
I have system I want to move with a DC motor that requires about 1 kW of power when taking into account rolling resistance, drag resistance and when moving on an inclined plane with a specific velocity. I had trouble finding small enough motors to provide that power so I asked a friend for help and he told me to use a gear system with low power motors.
So I ended having a question in my mind: Does the motor power, say a 1 kW motor, need to match the 1 kW requirement of the system or is it the torque provided by this motor that needs to match the torque of the system I want to move, in this case ((9.55 * 1000 kW)/ 600 rpm) = 15.91 Nm? If it's the torque then that means I can use a 200 W with known torque and a gear system to multiply the torque and match that 15.91 Nm requirement? If it's the power then is my only option using enough motors to match that 1 kW value, say 5 200 W motors? I'm sorry if the question is not totally clear, I'll do my best answer any questions.


texts:
I have following assembly:

and I have following Dowel holes misaligned:

Now, both sets of holes (for both parts) were created using Linear Sketch Pattern tool and now I want to mate these parts "through" these dowel holes sets. The first option is to recheck Linear Sketch Pattern parameters for both sets, however is it possible to automatic creation of holes at exact position from first part?


texts: What is really meant by HW/SW integration?

texts:
In many engineering descriptions I come across this term:
"Hardware/Software integration" or "Hardware/Software integration testing"
I came across couple of articles but they even made me more confused.
Can you give one or two examples which depicts a scenario for "Hardware/Software integration"?
If someone would ask me I would say "writing a piece of software or GUI which controls electronics". But I am not sure whether that would a correct example. Is there any typical example?


texts:
I recently flew on a A380 and I saw this interesting socket.

Could someone explain to me what is the purpose of these 4 golden connections?


texts:
I've read (1) that the efficiency (COP) of a heat pump does not change much with size. If that is true, why don't power companies employ them to produce yet more power from fossil fuels or renewables? I'm aware that air source heat pump efficiency drops in cold wet climates, but aren't there other more stable sources that could be tapped by an industrial scale plant? Ocean currents, for example.
(1) Are smaller heat-pumps more efficient?


texts: How do I build a water Ram Pump that will pump 400 feet and 30 feet vertically

texts:
I'm interested in building a ram pump to pump water from a creek that runs at the bottom of my property to the top where i'm going to make my little homestead. I've seen allot of stuff online on building DIY ram pumps and I had a few questions.

Do I have to use a metal feed pipe as people suggest or can I use plastic?

As I understand it, the distance the water can be pumped is a function of the force that the water in the feed pipe can exert. The rule of thumb is to make the feed pipe twice the output pipe, but if I had two feed pipes, would that not  double the force, and there fore double the distance?

What is the purpose of the stand pipe, will a stand pipe increase the distance the pup will pump?

Here are some of the resources I've found

https://www.bae.ncsu.edu/extension/ext-publications/water/use/ebae-161-92-ram-pump-jennings.pdf

https://www.youtube.com/watch?v=4y_WWxWdn5A

as well as numerous other youtube videos, describing the construction but not the theory.


texts:
I was looking for some element's half-life, on the following website:
http://nucleardata.nuclear.lu.se/toi/listnuc.asp?sql=&A1=214&A2=214&Z=88
For 214,88-Ra, the half-life is shown to be:    2.46 s 3
I am unsure what the "3" stands for, is it  "$\cdot 10^{-3}$"?
Thank you for your help and time guys.


texts: Safely evaporate electrolyte from fragile porous substrate

texts:
We have porous ceramic platelets of ~50x5x1 mm³ thickness infiltrated with ammonium nitrate solution (NH4NO3). We want to decompose and evaporate it w/o damaging the fragile substrate (decomposition should take place at ~210 °C)

Since this is part of a repeated experimental procedure, it shouldn't take longer than ~15 minutes for heating, decomposition and cooling back to max ~50 °C for a batch of 10 to 20 samples at once.

I was thinking about a microwave furnace since it would heat only the samples, or maybe even only the ammonium nitrate within the samples (not sure how well ceramics (ZrO2) couples in the µwave), but since it will heat the material uniformly, I'm concerned about explosive evaporation and damage of the fragile samples. Might still be suitable if the power is tuned well.

What also came to my mind was inductive heating of a small metal sample carrier or sample holding capsule. Could also be quick. However I have no idea if lab devices like this are available, at least I've found nothing.

Any other ideas?


texts: I have an unidentified press-fit nut that I need to reproduce, can anyone tell me how to find this?

texts:
I received these fittings as part of a package, but now we need more of them. Can anyone identify this assembly, or even better help me learn how to recreate it? My coworkers and I are stumped.

Pictures: https://imgur.com/a/1sq4lOK

Thanks!


texts: What effect does the weight of a wall have on the steel in the reinforced concrete below?

texts:
Considering the two options

build internal wall on top of 10 cm deep concrete slab reinforced with 7.7 mm smooth steel wire mesh
build internal wall on top of 30 cm deep concrete floor joist reinforced with a 24x24 cm steel cage made of 12 mm deformed steel rebar

What effect do

the deeper concrete
the greater amount of steel

in the floor joist have in supporting the weight of the wall (which I assume is treated as a compressive load)?

In both cases assume that the concrete used is the same grade. The wall is not load-bearing, as the overall structure is a reinforced concrete frame.


texts: Ways to attach stuff to a cylindrical tube that is in vacuum?

texts:
I am currently trying to attach a small flat piece of plastic (no bigger than 2", could be smaller) to a 1.9" hollow aluminum tube bent into a 2 foot radius torus, spinning at 2Hz.
My first and normal approach would be to drill a tapped hole in the hollow tube; however this is not an option in this situation, as the inside of the cylindrical tube is kept in a vacuum, and has to be in order for the project we are working on to work.
My second approach would be to mill the plastic to match the diameter of the tube, but the problem remains; how would I attach the resulting plastic to the tube?

I have access to a machine shop, so I can do some basic mill and lathe stuff in order to accomplish this.
How should I do this?


texts: Why lead was chosen as the metal for lead-acid batteries?

texts:
I was always curious why lead was chosen as the default for metal acid batteries.  This article describes lead-acid battery operation and there are plenty of resources like this on how lead acid batteries work, but I could not find any resources that explain "why lead?"

What about lead makes it the standard for metal-acid batteries?

Lead Acid Battery on HyperPhysics


texts: How to Understand the Relation of Compression Ratio and the Octane Number?

texts:
In my country are sold gas with different octane number (RON: Research Octane Number): 88, 90, 92, 95, 97, 98, and the latest is 100. RON-88 is still sold since still many old cars, motor bike, and agriculture machines which are using low spec gas. RON-90 is intended for transition, as alternative in case customer want to move forward using better gas but not so expensive. In our country, the higher RON, the more expensive.

As we know, every engine is designed with a specific compression ratio, and that RON is very related to the compression ratio. But many times I read explanation from automotive services claiming that higher RON will be better for car. Not specifically explained which car and what kind of car. Indeed we know that most cars are now having compression ratio 10:1, which according to the petrol producer that kind of is car suitable using petrol with RON 92-95. In my understanding, the compression ratio is related to the Top Dead Center (TDC), which it will produce specific compression that will compress the petrol inside ignition chamber, so it will increase temperature just before ignited by the spark. That compression made engine got hotter. If an engine with specific compression ratio is fed with petrol with RON-88, the petrol will be burned before TDC. Vice versa, if that kind engine is fed with RON-100 petrol, than the petrol will NOT be completely burnt. Hence, the automotive service claim is wrong.

So my question are:
1). am I right with my understanding?
2). for that 10:1 engine, if it fed with lower or higher RON, what will be the impact to the engine?


texts: Can someone help identifying the electrical connectors in this picture? These connectors are from an aftermarket igniter. Also where can one purchase replacement connectors. I have looked connectors from digikey. Any help towards looking for replacement connectors is appreciated.


texts: Finding Horizontal and Vertical Force on Bending Pipe

texts:
I did a Civil Engineering course some years ago and from my textbook I had a question on a bending pipe.
The purpose of this question is to see if the way that I have calculated this is correct, as my answer is slightly out from the textbook answer.

Feedback will be much appreciated on my calculations?

I have the question below


texts:
I’m a chemical engineer learning about fired heaters. I’m learning about draft and I picked this out of a textbook-

For example - Drafts:

Just above the burners = $-0.3\text{in H}_2\text{O}$
At the bridgewall = $-0.05\text{in H}_2\text{O}$
At the breeching = $-0.6\text{in H}_2\text{O}$
Above the stack damper = close to zero.

Why is the draft at the breeching more negative than the draft just above the burned and at the bridgewall  ? Isn’t the draft when moving up the furnace be less negative ?


texts: Is biological tissue a Dynamical System and a Nonlinear System?

texts:
I have biomedical data for analysis and I am using Genetic Algorithm for parameter estimation for the model of the data. As I read about the system identification, I saw terms like dynamical system. I read further and I am still confused whether the electrical impedance readings of a muscle tissue is considered a dynamical system or not.

Is it a nonlinear system? how can I tell? is there a direct rule on whether a biological tissue is a nonlinear system or not?

Thanks in advance


texts: How could I identify the object in the question body?

texts: We're building this thing in AutoDesk Inventor and SolidWorks, yet I don't know what it is. Can someone please tell me? Thanks.


texts: Looking for thin flexible and strong material

texts:
I have a project in which I have to use a up to 2.5mm diameter needle with a 90 degree (L shape) angle similar than the one in the following picture:

I say similar because there is only the tip of the needle is only 1mm since the 90 degree angle

I need to find some kind of material I can get a wire of that goes inside the needle that will bend so it moves back and forward throughout the L shape of the needle and strong enough so it can push a springed metal present at the 2 or 3 mm from the tip of the needle.

I have the dilemma that if the material is too stiff it won't easily go back and forward because of the L shape but if it is not enough it won't have enough strength to make the spring to compress on the tip end.

I thought about a wooden snake alike solution but since the wire must be so thin I can't find anything to make it of.

Maybe you have a better idea.

Thank you so much in advance


texts: The rubber casing for my iPhone cable has frayed and split near the phone port, and I would like to seal it somehow to stop the split from spreading further. Would Krazy Glue be an effective sealant? I've heard that superglue can eat away at some materials.


texts: Beam element stiffness matrix for variable area cross section with mass and shear center not coinciding

texts: I would like to find the full (12 by 12) Timoshenko beam element stiffness matrix for a variable cross section with mass center axis and elastic center does not coincide. I have the full stiffness matrix for a constant cross section with mass center axis and shear center axis does not coincide as shown here. Now I need to find the stiffness matrix for a tapered beam such as the one below.


texts: Are pontoon bridges being considered to extend bridge span?

texts:
Pontoon bridges differ from traditional bridges in that they are supported not by structures anchored to the floor of the body being spanned but by floating pontoons that are connected by a more rigid structure that supports a roadway. They're often used by militaries to provide a temporary crossing point, but they're also used for permanent civilian crossings.

I would assume that they make it easier to cross larger bodies of water because there is less structure to be secured below the surface. In areas of deep water, support structures can become unfeasibly large. These larger spans could, though, make the pontoon bridges susceptible to damage from strong winds and currents. Are there plans to use pontoon bridges to cross long distances?


texts:
Steels 316L, 420, 17-4PH and 316LVM are often chosen for medical products and labelled as "surgical grade".

I am curious as to how these types of steel are used for the production of common medical tools, for example ball-tipped tools such as "dental ball burnishers". Are these cast? If so, I suppose the parting line would be visible along the tool. Or alternatively, could the steel ball, rod and handle be manufactured separately and then welded? I guess this doesn't make much economic sense. As a third approach, I have noticed piercing parts being manufacture by screwing threaded steel balls on threaded rods. Again more labour intensive than casting, but less setup costs (no molds needed).


texts: foam earplugs: what’s the composition of the (non washable) substance that slow down their expansion?

texts:
What’s the composition of the (slighlty sticky) substance we find on foam earplugs that allow them to be easily moldable?

This substance slows down the expansion of the foam, so it makes the foam a little bit more rigid and help the foam to stick into the ear canal. (It might also have some insulation property in combination with the foam.) This substance get out when you wash the earplugs with soap, it's probably sprayed on the foam, or impregnated on the foam.

Any idea ?


texts: Siding for Industrial Shed: Rain protection vs Ventilation

texts:
When building a 12 m tall industrial shed with a peaked roof it is desirable that the sides of the shed should stay open as much as possible for ventilation / safety / access concerns.

On the other hand, an entirely open side from top to bottom might cause a lot of rain exposure when the rain comes in angled?

Is there a trade-off possible? Perhaps to enclose sides till a certain distance below the roof edge? Any heuristics about how much? (I've shown 4000 mm in the sketch below)

The contents inside the shed are relatively robust / waterproof & hence absolute rain protection is not needed.


texts: What really is so special about principal stresses or stress invariants?

texts:
At any point inside a structural element under deformation, we can always find three planes such that when we define a coordinate system with basis vectors lying on those planes, the shear stresses at that point are zero and the stress tensor is diagonal.

The principal stresses are the eigenvalues of the stress tensor, and are invariant of the rotation of the coordinate system.

This last feature on bold is recited everywhere.But my question is, so what? Why is it so useful to find these stresses whose components don't change with rotation of the coordinate system? And why would I even want to rotate my coordinate system?


texts: How can I kill the sound as much as possible in a rounded box? Acoustic panels/other option?

texts:
(I posted this in the Sound-Design section but got advised to post here instead).

I just purchased a 3d printer and I am working on a product with a box that has a hole in the bottom and the top. Inside this box I have a few electronics that has a pretty loud sound. What I now look to do is to kill that sound as much as possible so it is not possible to hear it as loud.

At home I have a few acoustic panels looking like this and as they are very lightweight it seems like a very good solution for this design: EQ Acoustics Classic Wedge 30 Tile grey

If I cover the interior of the box on all the walls would this make the sound not leave the box as much which would result in a lower sound? I am very novice when it comes to this area so any help/tips is very appreciated!

Width and length is around 30cm.


texts: How do you ensure physical network interfaces always get the same interface name across reboots on an embedded Linux system?

texts:
For an embedded Linux system, if I have two or more network interfaces, how do I ensure that they always get the same interface names every boot

In other words, I want, for example, eth0 to always map to one physical Ethernet port, eth1 to the next, etc.

My Linux "distribution" is home-grown, and I use devtmpfs for populating /dev. I use busybox for init (and most everything else), along with custom init scripts for system startup and shutdown.

I do not need hotplug facilities of mdev or udev -- I'm referring to "fixed" Ethernet ports.


texts: Do kids under a certain age not hear the warning beeps that smoke detectors make when they are running out of battery power?

texts:
I've always been very annoyed by those regular single beeps that smoke detectors start doing increasingly often as the batteries start to run out, to warn the user to replace the batteries.

Lately, I've been observing how a bunch of kids seem to sit in a room and just ignore those beeps completely, even after I point it out and ask them to really listen. They can't hear them. I seriously believe that they just don't physically hear them. Kind of like those dog whistles.

Is this backed up by science? Do kids under a certain age literally not hear those "low battery" warning beeps? Is this maybe per design, even? If so, why? Isn't it important that as many humans as possible hear this so that they replace the old batteries with new ASAP?

It's really frustrating to me when they don't even hear it, but I hear it very well.

I already asked this question a few days ago in "Biology", but it was "off-topic".


texts:
I am learning about gears, hobs and things of this sort. The main book is the machinist handbook which does a pretty good job of explaining things but things are in imperial scale.

This causes me a lot of confusion, especially when dealing with gear cutting blades where imperial uses DP and metrics uses Modules.

Are there any recommended books as thorough as the machinist handbook about gears but one that uses metric system instead?


texts:
With the hype around COVID-19 DIY technology, everyone seems to circle around the same concepts.

I'm trying to think outside the box and I was wondering:

Is it possible to controllably create an aerogel that is extremely permeable and also captures virus particles?

This is in essence a Yes/No question, but I'd love to get some mid-lengthy answers.

I think it's a very interesting concept.


texts: Deriving the turbulent kinetic energy equation

texts:
I'm trying to understand the derivation of the turbulent kinetic energy equation, as described in this link: Evaluation of RANS turbulence models for flow problems with significant impact of boundary layers.

I'm able to follow up to equation 2.26 on slide 11 (i.e. page 9), which states

$$\rho \overline{\frac{\partial u_i'}{\partial t}u_i'} + \rho\left( \overline{u_j\frac{\partial u_i}{\partial x_j}u_i} -\bar{u}_j\frac{\partial u_i'}{\partial x_j}\bar{u}_i\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i,$$

where the overbars denote the ensemble averages of the quantities under the bars.  Note that here, the average of a product is not necessarily equal to the product of the average of each term.

According to the link, using only averaging rules, the term

$$\left( \overline{u_j\frac{\partial u_i}{\partial x_j}u_i} -\bar{u}_j\frac{\partial u_i'}{\partial x_j}\bar{u}_i\right)$$

can be simplified to become

$$\overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \overline{\frac{\partial u_i'}{\partial x_j}u_j'}\bar{u}_i + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}.$$

If I substitute this directly into the previous equation, I get

$$\rho  \left( \overline{\frac{\partial u_i'}{\partial t}u_i'} + \overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \underbrace{\overline{\frac{\partial u_i'}{\partial x_j}u_j'}\bar{u}_i}_{\text{my 4th term}} + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i.$$

However, their derivation yields

$$\rho  \left( \overline{\frac{\partial u_i'}{\partial t}u_i'} + \overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \underbrace{\overline{\frac{\partial u_i'u_j'}{\partial x_j}}\bar{u}_i}_{\text{their 4th term}} + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i.$$

The only difference between my derivation and theirs is the 4th term on the left hand side of the equation.  I'm sure that their 4th term is correct, since it is supposed to cancel out with a term on the right hand side of the equation.  However, I can't seem to figure out how they obtained their 4th term on the LHS of the equation.  The link suggests that the chain rule and the incompressiblity assumption are involved, but I'm not sure how.

In particular, the overbar term $\overline{u_i'u_j'}$ is treated as a single term.  Thus, how can I apply the chain rule to  $\frac{\partial (\overline{u_i'u_j'})}{\partial x_j}$?

Any hints to complete the missing steps would be greatly appreciated.


texts: Vibration table for tests (7-200Hz) from extruded aluminium profiles bolted together - good idea (?)

texts:
I need to design a vibration table (approx. 1000mx1000mm) to test products between 7-200Hz.

I was wondering if it is recommended to make the table structure from standardised, extruded aluminum profiles bolted together to reduce the cost (material + time) or does one have to go with a welded structure?

Yes, I am aware of the results of the Junker vibration test with regards to bolted connections and it seems like a bad idea because all the fasteners would loosen. However, maybe there is a workaround to use these aluminum profiles?

I sincerely appreciate any advice and/or previous experiences with these.


texts: Air colliding with surface, local effects?

texts:
When a fluid, like air, is moving at some velocity and "hits" or collides with a surface:

If the surface is at an angle, the fluid will tend to be propelled in a similar direction (anything else?).
If the surface is perpendicular, the fluid will tend to kind of splash out in all directions (anything else?).

For generally turbulent, laminar, or mixed flow conditions?
The surface has mass and is relatively stationary for the purposes of this question.

In each of those scenarios, what are the (qualitative) local effects of physical properties like pressure, density, etc. for both turbulent or laminar flow conditions?  Does the air-like fluid compress into a denser form and the local pressure increase where the fluid is coming in contact with the surface?


texts: How to design a coaxial 1:2 gear without reversing direction?

texts:
I am trying to design a gear that has a 1:2 speed ratio (input:output).  This design is very limited in space and for simplicity and space savings requires the input and output shafts to be coaxial.

This leads me to think of using a planetary gearset, but in order to achieve a 1:2 gear ratio, we must use a fixed planet carrier gear, which reverses the direction of the output, which is not desired.  Using a fixed ring or sun is not possible when targeting a 1:2 ratio because the ring and sun would have to be the same size.  Am I missing something, or is there no simple way to make a 1:2 gear ratio with coaxial shafts, or do I require a reverse gear attached to the output of a planetary gear with fixed planet carrier?


texts: Setting up a centrifugal pump with a piston pump in parallel

texts: I have a centrifugal pump (Q: 64 m3/hr, H: 30 m) connected to a balance tank but it can't provide enough flow for my purpose. One quick option is to add a firefighting truck's piston pump to the circuit. I'm not sure about the features of the pump but I'm sure it delivers more flow and pressure than the centrifugal pump. My question is, do I have to worry about back flow when I'm not using none-return valves?


texts: Is it possible for a microphone/sensor to detect soundwaves before it physically reaches the sensor?

texts:
I'm sorry if this is the wrong place to ask. I understand that for typical microphones, the sound waves need to physically reach the microphone and cause vibrations in the diaphragm before an electrical signal can be created.
My question is, is there existing technology that makes it possible to detect soundwaves from a distance before the soundwaves physically reach the actual sensor? (i.e if the distance is x metres, we have a buffer time of x/(speed of sound) before the waves hit the sensor) Googling has not gave me much leads and I'll really appreciate someone pointing out some keywords and concepts I can further research on. Thank you!


texts: simplified acceleration and max speed calculations for a game?

texts:
Are there any simplified formulas that could be used to generate plausible airplane, spaceplane/SSTO, and spacecraft performance specs for a game given some basic vehicle and contextual attributes? By plausible, I mean within 25% of the value a full analysis might achieve. For example, could I roughly determine maximum acceleration and top speed from the following attributes:

VEHICLE
thrust (in real units)
mass (in real units)
aerodynamics (any intuitive scale: e.g. 0.0 = horrible, 1.0 = ideal, Boeing
747 set arbitrarily at 0.50)

CONTEXT
atmosphere (density? pressure? friction? How best to measure simply?)
gravity (real units)
angle of travel (0 = parallel to planet, 90 = perpendicular to planet)


texts:
Generally, in a pressure drop control valve that uses a piston and a spring (for example, in jet engines to control fuel flow), there is always potential for error in terms of the height of the spring. As we know, a shim is usually used to fix this. However, I was wondering if there are alternatives to such a procedure. Are there other ways to correct the height on a valve spring, or perhaps produce the spring in a way that reduces the need for a correction method like shimming?

I was thinking maybe laser correction could be a viable method for correcting a spring that is off by a few thousands of an inch? It is extremely accurate, but then the main disadvantage is cost. Are there other methods or technologies that exist or are perhaps being worked on at the moment?


texts: Is making a toilet flush backwards problematic?

texts:
The Coriolis effect impacts the way water tends to circle before going down the drain.  Many (most, all?) toilets are designed to work with the Coriolis effect.  I am considering a line of toilets that would flush opposite of this, this is strictly a marketing device.  But I am concerned that if the toilet design, forces the water to circle opposite of the Coriolis effect before going down the drain it could cause issues.

Is it problematic if we build toilets that flushes backwards?


texts: Learn thermodynamics before beginning with control engineering ?

texts: I'm about to start learning about control engineering. But am I advised to learn first Thermodynamics? (Since control engineering has applications in Thermodynamics)


texts: What are the correct reactions of a rotating arm connected to a vertical pipe restricted by bearings at its ends?

texts:
Since the title is a mouthful, here goes an explanation and a sketch I've drawn a so that I can describe it correctly:

I'm trying to design a rotating arm. The rotational part will be a small pipe, installed vertically. It will be spatially restricted by two bearing, each in an end and they will be fixed to a larger structure. The arm itself is an I beam that's relatively long. I'm trying to calculate the minimum cross section of the pipe as well as the correct bearing forces. The rotating arm will be subjected to a vertical force in its end.

What I already have: I believe that once the arm is deflected, each bearing will suffer horizontal and vertical forces. I also believe that the horizontal reactions are such that they neutralize the vertical force where the bodies meet, such as that: $2*R_F*H = F*arm_{length}$.

I suppose the vertical reaction will be just $F$ in the lower bearing.

I've tried using a software to determine the support reactions and fooling around with it I've figured that sometimes the support can have a moment reaction in it and I have no clue what would this situation would be and where is this moment coming from.

Am I correct in my assumptions?


texts: Chamfering with a conical bit makes a table drill vibrate

texts:
I have a slow-speed drill press which seems quite solid, the play is minimal. Normally, it does not cause problems. This conical bit:

when applied to this 8 mm hole:

is an exception: the bit jumps and squeaks loudly, the machine resonates. As seen in the image, it is impossible to make an even chamfer. I was thinking about filling the hole with a 3d-printed plastic cylinder with a small pilot hole, but I am not sure it it would help, given that the material is a hard stainless steel. It is fastened in a 4.5 kg vice which can move freely, so that the bit position can be adjusted. The vice seems to be stable, despite the vibration.
How to make an even chamfer? Its angle of 45 deg is important.


texts: Concrete rebar cover requirements - Hook lift anchors

texts:
ACI 318 7.7 covers requirements for cover when designing rebar placement within concrete. However, they are for general components and makes no exceptions for small irregularities such as lifting hook anchors that one may wish to place. I am not an expert with concrete so I wondered if anyone can point out to me whether there are exceptions to these requirements and whether these minor irregularities are actually required to have the same cover requirements, or are they small enough that it's usually not a significant concern.
Example of hook lift anchors:
https://meadowburke.com/product/hook-lift-anchor/
https://meadowburke.com/product/hook-lift-recess-former/

**EDIT:**
So, actually, I am more curious about the recess that I am putting in as you can see within that catalogue (I added a link above). It's obvious that the recess can reduce cover for some of the rebars involved, and I wondered if that will be an issue or whether or not that will create issues later. Any advice?


texts: Generating a Blank Seismic Tripartite Graph

texts:
I am performing a calculation in which I need to plot a generated response spectrum to a seismic tripartite graph.  However, I am having a heck of a time finding a blank tripartite graph online.  A low-resolution example is shown below.

How might I go about generating a blank seismic tripartite graph?  As far as I know, Excel does not have this functionality, since you need to be able to plot four separate axes in 2D with two of the axes at an angle.  All axes are in logarithmic scale.
The unit system should be as such:

Spectral displacement: inches
Spectral velocity: in/sec
Spectral acceleration: % of $g$
Frequency: Hz

Otherwise, a link to a high-resolution graph would be acceptable.

Edit January 29, 2021
I have figured out how to make one of these graphs using LaTeX.  Please see this post on my website for details.


texts:
Is there some kind of graph or relation between laser power and efficiency. What I'm trying to find out is whether the efficiency of a laser decreases with increase in power or is it that there is no definite relation.

For example, which would be better; using 10 nos 100 mW laser diodes concentrated to one point or a single 1 W laser diode.

Found these two laser diodes:

Here are the links to the datasheets of the same, ML520G73 ML562G84

So which will be more efficient using one 2.5 W laser diode or five 0.5 W laser diode (the five are set up to point to the same location). And what would be the advantages or disadvantages of both setups?

Thinking of making a laser engraver, but had this idea of using multiple low powered laser diodes instead of a single high powered one. But in a dilemma of what's a better choice. I don't feel complicated in using a multiple lasers instead of a single one.


texts:
This is from Stephen Hawking's latest book; Brief Answers to the Big Questions.

  The speed at which we can send a rocket is governed by two things, the speed of the exhaust and the fraction of its mass that the rocket loses as it accelerates.


texts: Selecting the correct strain gauge and metal thickness for custom load cell

texts:
I'm working on project and after a good amount of research I've ended up with a final design that looks roughly like this:

The design is inspired by load cells used in bathroom scales, but I found them to be too clunky for my application so I have to make a custom set of load cells. Each T-shaped arm will have a strain gauge on top of the section that gets narrower where hopefully most of the strain will be. I've kept the 8 load cells on one piece of metal to gain rigidity.
On top of this plate I will mount four 80x20mm bars of wood So I can measure four different forces at the same time and also the where the force is being applied on the bar.
My main obstacle is to calculate the optimal thickness of the metal, width of the t-shaped arm and find the right strain gauge so I can measure weights up to 100kg per load cell without breaking. Lets say I use steel or stainless steel for this. Should I use a strain gauge with 1000ohm?
Updated:
This whole part will be bolted down flat on a thick wooden surface and will be used to measure weight distribution on my fingers when I do climbing related excercises like pullups. The part is mounted completely horizontal.


texts: Differential equations of a (simplified) loading bridge

texts:
I am having trouble to calculate the differential equations of a simplified loading bridge.

The system is build as shown in the picture below (just a sketch):

If I use the Newton approach, I am getting the following equations by neglecting friction, air resistance and changes in the length of rope:

$$
m_k \ddot{x}_{k} = F_{A} + F_{S} \sin(\varphi) \\
m_G \ddot{x}_{G} = -F_{S} \sin(\varphi) \\
m_G \ddot{z}_{G} = m_{G} g - F_{S} \cos(\varphi)
$$

When I look at the kinematic relationships from the gripper (the circle with the weight $m_G$) I get the following equations.

$$
x_{G} = x_{k} + l \sin(\varphi) \\
z_{G} = l \cos(\varphi)\\
\varphi = \omega t = \dot{\varphi} t
$$

I know the weights $m_k$ and $m_G$ and the length $l$ but the values are not important right now.

The goal is to have two differential equations at the end.
One equation shall show the relationship between the driving force $F_A$ and the path of the trolley $x_k$ (with derivations)
The other equation shall show the relationship between driving force $F_A$ and angle of the rope $\varphi_G$.

After that I want to make the transfer functions (Laplace transformation etc.) but that is not the problem.

The problem is that I can not seem to find those equations. My best approach so far looks like this:

$$
m_{k} \ddot{x}_{k} = F_{A} + F_{S} \sin(\varphi)
$$

So that means if

$$
m_G \ddot{x}_{G} = -F_{S} \sin(\varphi) \\
F_{S} \sin(\varphi) = -m_{G} \ddot{x}_{G} \\
$$

I can say:

$$
m_{k} \ddot{x}_{k} = F_{A} - m_{G} \ddot{x}_{G} \\
$$

and if I derive $x_{G}$ like this:

$$
x_{G} = x_{k} + l \sin(\varphi) \\
\dot{x}_{G} = \dot{x}_{k} + l \dot{\varphi} \cos(\varphi) \\
\ddot{x}_{G} = \ddot{x}_{k} + l \left[ \ddot{\varphi} \cos(\varphi) - \dot{\varphi}^{2} \sin(\varphi) \right]
$$

I am actually getting stuck here because I can not find a way to eliminate $\varphi$ from the equations. The addition theorems are not helping me at all (or I'm using them correctly).

Does anyone have an idea of how I should continue at this point?
I hope I don't need a complete solution. I am actually more interested at doing this myself and hope to get a push towards the right direction.


texts: How to show that the total angular velocity vector of a rigid body is the sum of all angular velocity vectors acting on it

texts:
I am trying to prove the additivity propety for the angular velocity vectors acting on a body in three dimensions. Particularly also in the case when the axes of rotation do not cross each other (the body may not be rotating about a fixed point).
In plane motion it is easier to see. Grab two coins, fix one flat on a table and make the other one rotate around the edge of the fixed one without slipping. One can see that the total angle of rotation of the one rotating is 2 times the angle that it has traveled around the fixed one. One can build a proof from this for plane motion (the case when angular velocity vectors are parallel to each other) but i don't know how could one show the same thing for 3d.


texts: What are the essentials of a good PRD (product requirements document) for a new mechanical device

texts:
I need to write a non-technical product requirements document (PRD) for a new machine that I want designed.
I need to ensure that I have included all the salient information concisely and to the point.
I have searched online for template PRDs but all of the documents I have come across, assume that the product is software so do not fit the needs of a PRD for a mechanical device.
Can someone outline here, the structure and sections required for a PRD for a mechanical device (e.g. an engine), failing that, a link to such a document would suffice.


texts: I've read the yield strength of a material can be improved either by age hardening or mill hardening treatment. Age hardening is primarily a function of time and temperature with some environmental and chemical factors. But what is mill hardening? Hardening a material by ... milling something like a hole through it?


texts:
problem 1-5, James M. Gere's mechanics of materials text book

in the given example :

for a, b and c he used the full 12k value of P to get the bearing and shear values. my logic was to analyse the forces when getting the shear on the pin G.

my instructure said we were using the max values of P, but that wasn't a satisfactory answer for me.

also :
in a, the value for the bearing area is chosen to be 2dt where d is the diamter as shown. why isnt the bearing area as shown here? (hopefully that's a clear enough aiding diagram )


texts: Component selection type for fluid-mechanical system

texts:
I am creating an enclosure and need to get a water supply through a plastic wall inside to the core device. I imagine this water line will be a flexible tube and will screw on or snap to an adapter on the outside of the enclosure. On the inside of the enclosure there will be another tube feeding the core device.
I am an electrical engineer and don't know where to get started to speak eloquently on this topic. Could someone point me in the right direction to defining the type of fluid-mechanical components that would be involved for this function or at least help me refine my question because I am shooting in the dark.
I imagine the tube feeding the device would look similar to a line of what that feeds a refrigerator.


texts: Sensitivity analysis: How do I perform the adjoint method?

texts:
Suppose I have a rectangular plate (width $a$, height $b$, thickness $t$). By using a Finite-Element discretization I obtain the system

$M \ddot{x} + Kx= f$

with mass matrix $M$, stiffness matrix $K$ and force vector $f$. Now I want to know whether the solution vector $x$ does change if I vary $a,b$ or $t$; this is called sensitivity analysis. I know the direct method, but the adjoint method is also known. How I obtain the sensitivities by the adjoint method?

I did not understand this method well after I looked in literature.


texts: How to calculate traction force w.r.t. rotational speed of a shaft mounted at a certain angle on a surface?

texts:
I am designing a new mobile robot platform and i need a generic solution for the robot in order to establish a proper mathematical modeling. My question is about calculation of the traction force of the robot with respect to rotational speed of the direct contact motor shafts which is mounted as the figure below.

There is a vehicle with 3 contact points with the ground. Two contact points are edges of steel cylindrical shafts with diameter d_c. Other contact is provided by spherical wheel with diameter d_s in order to provide static balance.

Cylindrical shafts are rotating with a high speed, n. The angle between the shafts and the ground is a. Coefficient of static friction is f. Shaft is slipping on the ground because of high speed and low friction. The weight of the vehicle is w. The distances between the contact points and the center line is b.

How to calculate traction force T with respect to rotational speed n for a shaft mounted at a certain angle a on a surface?

Given Parameters:

These parameters are just for example, i need a generic mathematical solution.

d_c = 1 mm

d_s = 10 mm

b = 25 mm

n = 10000 rpm

a = 60 degrees

f = 0.25

w = 0.1 kg

Required:

T(n, a) = ?


texts: What is the actual natural gas and electricity consumption of a Haber Bosch plant?

texts:
Plants running the Haber Bosch process provide the vast majority of nitrogen used in fertilizers. Collectivly, they consume about 3–5% of the world's natural gas production [...] (around 1–2% of the world's annual energy supply). Other sources stress that natural gas use accounts for roughly half the energy budget of these plants, the other half beeing electricity to run the turbocompressors. With casual googling, I only found numbers at the global level.

I want to have more exact numbers for the natural gas and energy consumption of a typical Haber Bosch plant, relative to the fertilizer output.


texts: Could house fires be prevented by increasing dryer vent speed?

texts:
In the US, clothes dryers are one of the leading causes of house fires:

  In 1998, CPSC estimates that there were approximately 15,600 clothes dryer fires resulting in 20 deaths, 370 injuries and $75.4 million in property damage.

Or more recent numbers:

  In 2010, an estimated 16,800 reported U.S. non-confined or confined home structure fires involving clothes dryers or washing machines resulted in 51 civilian deaths, 380 civilian injuries and $236 million in direct property damage.
  Clothes dryers accounted for 92% of the fires; washing machines 4%, and washer and dryer combinations accounted for 4%.

A fairly comprehensive study about lint ignition was completed by the Consumer Protection Safety Commission (CPSC) in 2003. This study showed that the dryer's internal temperature greatly increased once the vent pipe's area was reduced by 50%. In homes, this reduction is due to lint gathering in the pipe.

This manual for a random dryer mentions that minimum air flow through the 4" (10 cm) diameter vent pipe is 1,200 feet per minute (20 ft/s or 6.1 m/s).

There is a concept of minimum velocity in drainage pipes and culverts to ensure that they are self cleaning, i.e. debris does not build up.

Obviously air and lint are different than water and sediment. I haven't been able to find any particle properties for lint.

Is the solution to lint clogging dryer vents just to increase the velocity of the air in the vent?


texts: USB solenoid valve driver (<1A) with hit and hold

texts:
Hi I'm looking for a USB controllable (or less ideally a serial interface of some other kind) solenoid controller that can switch up to 8 small (<1A) solenoid valves with hit and hold*.
The best I could find is the phidgets 16x solidstate relay  which acts as a low side switch but lacks the flyback diodes since the driving voltage needs to be external.  I've used this in the past but without diodes it can't freewheel when outputting PWM and so the performance is poor.
Obviously I could add the diodes myself but I have more money than time so ideally an industry focused solution would be best.
*: "hit and hold" is a solenoid driving technique that drives a solenoid at DC for long enough to actuate the plunger (usually a few hundred ms) then PWM's the driving current to reduce power consumption (and HEAT!) while still holding the plunger in place.


texts: How to measure and verify ultrasound frequency and intensity from a cheap ultrasonic body contouring device?

texts:
Research shows that applying 1 MHz non-focused ultrasound at 3 W/cm2 may reduce subcutaneous fat thickness. In fact, high-end and expensive (costs $5000 >) HIFU ultrasonic transducers are now being used in cosmetic clinics that allow the user to regulate ultrasound frequency, pulsing, power and time in order to target body fat.

To my surprise, I noticed that one can also buy inexpensive (costs only $50), portable 1Mhz Ultrasound cavitation device from Ebay or Aliexpress that also claims to reduce body fat. Scam or not, one way to justify its claim will be to measure and verify the emitting frequency and intensity.

I bought such a device from Aliexpress (costed $130) to play around with it. My skin can feel a definite vibration when I turn on the device, however, it is very hard to tell if ultrasound is actually exciting my tissue lesions.

I want to know how to set up an inexpensive testing setup and:

1) Find out if the device is really emitting ultrasound. If yes, how would I measure its frequency? Device manual says 1MHz, but I suspecting it might be a bs.

2) How to measure the intensity and penetration depth. Finding one value should lead me to calculate another.

3) Find out if the device's ultrasound is focused or non-focused. My gut feeling is the ultrasound is non-focused or weakly focused.

One way to find more clues would be to rip through the device and look at the transducer circuit. The transducer hardware might have a model number that can be used to find it's spec sheet online. However, I haven't unscrewed the device yet and I doubt I would find anything helpful on the circuit board as it probably came directly from a questionable Chinese factory.

Further reading:
There has been plenty of research conducted so far regarding effects of non-focused ultrasound on animal contouring:

1) The effects of nonfocused external ultrasound on tissue temperature and adipocyte morphology.
2) Ultrasound dose calculation


texts: Which is more important XY plane thermal conductivity or z direction thermal conductivity?

texts:
Im seeking an alternative to thermal grease/ pastes. I was researching graphite pads when I stumbled across the soft PGS line from Panasonic.

I need to choose a suitable thermal interface material to connect the CPU die to a heat sink. I do not wish to use thermal paste ( it is greasy). I was wondering which material would be most suitable.

PGS :Excellent thermal conductivity : 700 to 1950 W/(m·K) ( no data for z direction; I found some sources stating that the z direction was about 15W/m-K but I can not verify this).

“GraphiteTIM(Compressible Type) PGS with thermal conductivity : X-Y direction 400W/m∙K, Z direction (28W/m∙K).

The heat sink will be made of aluminium ( roughly 200-250W/m-k) or copper  (roughly 350-386W/m-k).

Which is more important? XY thermal conductivity or Z direction thermal conductivity?

Since the heat-sink has a defined thermal conductivity, is there any advantage in choosing a conductivity greater than the heat sink's value? (Example, two materials A and B with a thermal conductivity of 700 and 1000W/m-k  respectively for xy plane; assume both have similar z direction conductivity. Does choosing the 1000W/m-k over the 700W/m-k material provide any benefit to the overall system, considering that the heat sink is limited to 386W/m-k? Thanks.


texts: Does an external force at a joint between two members act on one member or on both?

texts:
I am trying to find the internal forces in the member at point G in the following illustration:

My answer is different from the solution in the textbook and I think it has to do with how I'm looking at the 1500 lb external force acting on point A.

I've included the 1500 lb force in my free body diagrams for both AB and AE. I'm getting the feeling that it should only be acting on one of these members; however, I am unsure.

Does the load at the joint act on only one member, or on all members in the joint?


texts:
I have a mechanical engineering question that I can seem to figure out.

Basically I have an object this is being pulled down by two forces. Each force is 10N in the downward direction. There is a nut welded to the bottom of a plate and a threaded rod runs through the plate and into the nut.

I can't figure out how much torque will be needed on the threaded rod to lift the the object. Let's ignore friction for the time being. A diagram is included to show what I've got.

It would be really helpful if I could get some insight into how to setup the problem. I did well in my college physics courses but I'm was an applied math major.. 8-) And they really didn't talk about how to convert rotational work into translational work.


texts:
I am struggling to understand how to take the KCL equation from time domain to Phasor domain.
The time domain KCL equation is easy to understand and represented here:

The phasor domain equation looks like this:

And the book i am using describes the phasor domain equation like this:

They tell me that "the time factor $e^{jwt}$ has disappeared because it was contained in all three terms". I am having a hard time convincing myself that this is true and was hoping someone could provide me with some clarity on this.
Thank you!


texts:
I want to understand working of AC at a basic level. Hence following is my question.

Let there be a closed room of volume V at indoor temperature $T_1$. It has to be cooled down to temperature $T_2$. If Q amount of heat is removed from the room every second, then how much time will it take to reach the desired temperature?

Assume $D < Q$ is the amount of heat input to the room every second. If required assume outdoor temperature to be $T_3$.

Temperatures are in °C, heat in joules and volume in $m^3$.

My understanding:

Cooling rate is directly proportional to $Q-D$.
Mass of air, $M = pV$ , where $p$ is density of air.
Desired heat loss, $H = cM(T_1 - T_2)$ , where $c$ is specific heat of air.
Time taken to get the desired cooling, $T = \frac{H}{Q-D}$.

Are my calculations correct?


texts: penetration of rolled homogeneous steel, issues with finding the joules required to punch through

texts: So I am making a tech demo demonstrating fairly realistic penetration physics. I Have run into some confusion due to my lack of knowledge. If I have the resistance of the armor in MPa, that means I have the amount of joules acting in a square meter, so i divide by the area of the cross section of the shell, in meters (assuming it's a cylinder) then multiply by the thickness of the armor, also in meters, to get the required joules to punch through the armor of the given thickness with a round of the given cross sectional area?


texts:
I have a project in mind where I want to measure the pulling force of each finger while doing a climbing exercise. My original plan was to build a wooden climbing hold that used 4 load cells under a hold that looks more like 4 piano levers with the cells mounted under each lever. After a bit of research I found these strain gauges and was wondering if it's possible to mount these on the wooden levers (approx 20x80mm surface area) to make the the piece of wood itself into a load cell and get good enough data. My criteria for each load cell is a max load of 75-100kg and accuracy to be within +/-1kg. Is this possible with wood using strain gauges or should I go for a more complex build using movable parts pressing down on a load cell?
Short description: Is it possible to turn a wooden stick 20mm wide and 80mm long into a load cell capable to measure force up to 100kg using a strain gauge?
Update:
Here is a image of what I had in mind:

As alephzero said, its better to use plastic, but how can I find a type of plastic and calculate the correct thickness/height that can hold 100kg without breaking or deform over time?


texts: How to calculate the clock cycle in relation to bytes per clock bus?

texts:
In wikipedia there is the following

With the speed of instruction fetch reduced by 50% in the 8088 as
compared to the 8086, a sequence of fast instructions can quickly
drain the four-byte prefetch queue. When the queue is empty,
instructions take as long to complete as they take to fetch. Both the
8086 and 8088 take four clock cycles to complete a bus cycle; whereas
for the 8086 this means four clocks to transfer two bytes, on the 8088
it is four clocks per byte.

And the following example:

Therefore, for example, a two-byte shift or rotate instruction, which
takes the EU only two clock cycles to execute, actually takes eight
clock cycles to complete if it is not in the prefetch queue.

I don't understand how the example works


texts: Maximum Carbon content on the surface of Mild Steel that is Pack Carburized

texts:
Starting from a piece of Mild Steel that is then Pack Carburized, what's the maximum Carbon content that the surface can soak in? Given that we keep it around less than 1000°C and enough time, is it limited to 6.67%, the Carbon content of Cementite?

It would be helpful also if you can describe the depth of penetration of the Pack Carburization, given enough time. Something like:

Casedepth ~ $K \sqrt{time}$,

where K is the Diffusivity constant

Of course, that's wrong as I think there's a limit to the depth considering the alloy, exact temperature and dimension.


texts: Has there been any deliberate implementation of combinational logic soft error correction in any consumer-level product, like a CPU/microcontroller?

texts: It is well known that many error detection, mitigation, and correction methods, such as parity or ECC, have been available in large memory banks, like for RAM, for decades now, and even in CPU caches and sometimes parts of state machines. These are mostly large implementations of sequential logic where single event upsets from cosmic rays have a significant enough chance of causing a lasting bit flip, due to the smaller feature size, density, number of latches, etc. Throughout most of computer history, the combinational logic of the CPU, or small sequential logic like singular latches or registers, have remained unprotected. This is mostly due to the unintentional electrical, logical, and temporal masking effects that are due to the low transistor count, number of logic gates, size of transistors, etc., which has made combinational logic soft errors due to SEUs mostly negligible. Over the past few years, the reduced feature size has become a large concern because it may be making combinational logic errors common enough to be a real problem, so I was wondering if there have been any significant implementations of soft error mitigation or correction in combinational logic circuits or single latches/registers in any consumer-level product, like a CPU or microcontroller? Thank you!


texts:
I want to simulate a turbine in Fluent. For this reason, I studied some papers. In these papers, Turbulence is modeled using the realizable k–e model and Non-equilibrium wall functions are used in the near wall flow modeling. There are the following sentences in these papers:

The Boussinesq approach is applied to relate the Reynolds stresses to the mean velocity gradient.
The Reynolds stress is related to the mean velocity gradient by means of the Boussinesq approach.

What is the exact meaning of above sentences? And is there a direct option in Fluent?

Is there any adjustment that must be made in Fluent before starting the calculation for this approach?


texts: How would I create a stress curve using this given data: Time(s),Extension(mm),Load(N,Tensile strain (Extension)(mm/mm),Tensile extension(mm)


texts: Would a Maisotsenko cycle evaporative cooler work more efficiently with a return air duct?

texts:
The "Coolerado M50" evaporative cooling unit uses a "Maisotsenko cycle" heat exchanger.
It's installation instructions and all diagrams indicate air intake from external air only, with no mention of return air anywhere.
Presumably, on a hot day, return air would be significantly cooler than outside air.
This leads me to think that if the external air intake duct included a return air leg, mixing both together, this would provide marginally cooler supply air with no additional running cost for the following reasons:

slightly cooler intake air will reach a slightly cooler output temperature because of its lower starting point.

that extra slight cooling effect would increase over time, as more air is recirculated.

a return leg would improve airflow, relieving some of the positive pressure in the cooled space, experienced as a backpressure by the unit's fan.

the humidity of the return air would decrease with each recirculation, which would further increase an evaporative unit's cooling capacity.

So, have I misunderstood something, or would mixing return air into the intake be a good idea?


texts: Pressure loss of a shape change of an ar duct, keeping the area the same

texts:
I have an air duct 400x400 mm that will attach to an engine with a ventilation opening 981 x 167 mm. I assume a smooth funnel of about 500m length between the two shapes (that's about as much space as there is).
The air duct will run horizontally along the ceiling (the direction is along the length of the opening), the ventilation opening is pointing upward.
I'm at loss how to calculate or estimate the pressure loss of this part - it's not a reduction as the area stays approximately the same. Until a better approach comes along I will just assume a right angle joint in the 400x400 duct and a 981x167 duct for the last part.
This has not much bearing on the question, but to provide some context: The machine is a combined heat and power plant, drawing cooling and combustion air through the long opening (~2500m³/h). It will be placed alongside a gas powered boiler, so the machine may never draw air from the room, hence the ventilation duct. As of now it seems likely that the internal blower is sufficient, no extra blower is needed - but I want to confirm that.


texts: Best spout shape to ensure minimal water sticks after pouring?

texts:
I have a tipping bucket rain gauge whose accuracy I feel could be improved by redesigning the shape of the bucket lip. In particular, after tipping, there tends to be a bead of water (approx 0.1 - 0.2ml) attached to the lip of the bucket. The bucket tips with only 4.2mls of water and that is collected close to the pivot point so that a 0.1ml drop at the lip of the bucket (as far from the  pivot as you can get) is not insignificant and adds quite a bit of random noise to the measurements.

As seen in the image the current bucket lip is a smooth scallop shape and (although difficult to see in the image) the lip profile is a flat downward sloping bevel. Essentially the bucket has a similar shape and lip profile as a curved woodworking chisel.

My thoughts are that there must be some modification that I could make to the lip to encourage that drop to fall off and follow its brethren down the drain? I've had many different ideas to try: cutting a valley in the centre of the lip, having a thin protrusion sticking out from the lip, or maybe a fine sawtooth edge would work to draw the drop off? I have also thought that having a semi-circular rather than bevelled lip profile would work better to draw the drop over the edge?

The problem I have is that I have no easy way of testing any of these hypotheses. I only have one tipping bucket and can't afford to buy more just to experiment on so I don't want to go modifying it unless I am reasonably sure that it will be an improvement.

Google searches have brought up plenty of results on hydrophobic surfaces and the like (which would be fantastic but are a little beyond my reach) but nothing on surface shape or edge geometry.

Obviously I'm looking for ideas for modifications that I can easily make at home but any links to theoretical info on the subject would be welcome also.

(https://i.stack.imgur.com/vvHs1.jpg)


texts:
I'm trying to cut some bendable flaps on aluminium sheets for hooking/clipping onto some fabric. The flaps I have in mind look like this:

Are these common features? Does anyone know the geometry of the cutout? I wish SolidWorks had them as standard features.


texts: What are the electronic readout versions of Dial Indicators called?

texts:
These items: https://www.parktool.com/product/dial-indicator-gauge-set-for-ts-2-2-and-ts-2-truing-stands-ts-2di are mechanical gauges with roller tips that are intended to measure deviations from true in bicycle rims.

What is this kind of instrument called in general?

In particular, what are good keywords to look for devices like this the output of which can be read electronically?


texts: Cutting silicon samples with plastic thin films

texts:
I'm measuring thicknesses of ~15 $\mu$m nickel thin films electroplated on a silicon substrate. I only have access to a SEM for this task. I need to cut the samples to get a side view of the film. However, the nickel film is plastic and the silicon undergoes a brittle fracture. As a result the nickel film often detaches from the substrate near the fracture point before I have the chance to cut it, making imaging impossible.

How could I cut through both the plastic thin film and the brittle silicon simultaneously? I'm getting access to liquid nitrogen in a week or so with the intention of freezing the sample. Is there a ~room temperature process which would allow me to prepare samples meanwhile?


texts: Control theory - Differential equations and state variable description

texts:
I'm a 3rd-year bachelor student and I may be mistaken but from what I have understood:
In control theory we assume that the studied systems have a State Variable Description. Then from there we can derive that for such systems the transfer function must be proper.
But, to have a State Variable Description means that the system can be described by a simple differential equation or equivalently by a system of differential equations.
I am not really convinced that all physical systems can be described by such equations. Although I don't know what kind of other description there could be, I would like to find some strong argument. I guess it must have to do with the equations of fluid or Newtonian dynamics but if someone could be more specific I would appreciate it.


texts: Why can we assume the stress distribution under a pad footing to be linear?

texts: In structural engineering, a pad footing under a normal load N and a moment M is assumed to have a linear distribution of stress under it. Is there any intuition why we can make this assumption?


texts: Computation of the moment of restoring forces for a floating vessel

texts:
Some slides associated to the book Handbook of Marine Craft Hydrodynamics and Motion Control (2021 edition) are provided by the author of the book here.
At page 12 of the slides for Chapter 4, the moment due to the restoration forces (gravity, buoyancy) of a floating vessel is computed, expressed in the body frame of the vessel. According to page 14, such moment is computed in the Center of Flotation; however, the lever arm computed at page 12 is the following:
$$r_{\text{GM}}^b = \begin{bmatrix}
-\text{GM}_L \sin\theta \\
\text{GM}_T \sin\phi \\
0
\end{bmatrix}$$
where $GM_L$ is the longitudinal metacentric height, $GM_T$ is the transverse metacentric height, $\theta$ is the pitch angle of the vessel, $\phi$ is its roll angle, and the superscript $b$ indicates that the arm is represented in the vessel body frame.
The geometrical meaning of the second component of the arm is shown in a figure on page 10, as follows:

where $CB$ stands for Center of Buoyancy, and $CG$ is the Center of Gravity.
Then the moment is computed as follows:
$$\mathbf{m}_r^b=\mathbf{r}_{GM}^b\times \mathbf{f}_b^b$$
where $\it{f_b^b}$ is the buoyancy force expressed in body frame.
By looking at this, it seems to me that the moment was computed about the Center of Gravity, not about the Center of Flotation, as claimed later.
Is this right, or is there any implicit assumption here that makes the assertion on the slides correct (for example the vessel is boxed-shaped)?


texts: How to remove/replace a screw with a lock washer in a tight place

texts:
I'm trying to remove the screw in the images below from a metal cover.

The screw is locked in place by what I believe is called a locked washer. The screw can rotate, but I can't move it in and out. The height to the "lip" is about 12mm (see first image), which doesn't give me much room to get tools in there.
Any thoughts on the best way to remove this screw without damaging the cover? Ideally, I'd also prefer not to damage the screw too much. At least, I'd like to be able to perform some measurements on it after to find a replacement.
I've tried prying the washer out with needle nose pliers, but the washer is pretty solid. I've also tried cutting it off with a dremel cutting tool, but I've mostly just managed to cut some groove marks into the inside of the cover and I haven't done much damage to the washer. I've also considered using one of the thin, cylindrical cutters on the dremel to saw off the head of the screw, but I don't think I can do this without damaging the outside coating of the cover.


texts: Is there a spherical joint equivalent to a 4 bar linkage?

texts:
In a 4-bar linkage, all the joints are regarded as hinge joints. However, when I searched "spherical 4-bar linkage system", I didn't get a 4-bar system with spherical joints but instead a 4 bar system curved over the surface of a sphere.

Could someone show me an example of a 4-bar linkage system with straight rods that uses spherical joints? I want to understand the mathematics of the kinematic equations for one and I need a standard example. Is there a name for this?


texts: Why do lvdt sensors give us different results?

texts:
We take a cylindrical concrete sample and apply compression load on it, perpendicular to its head. To measure its strain we use 2 Lvdt(strain measurement devices)on both sides of the concrete sample . Surprisingly they give us different numbers (close but not the same). Why is that?
Firstly I think that it is because concrete sample might not be fully homogeneous (in preparation the mixture process might not have been perfectly mixed. The second reason is that it might have some bulk defects inside.
Let me know what you think


texts: Why not only GSM (3G/4G/..)? Why do we need Bluetooth, Wifi,etc...?

texts:
It is quite frustrating to have multiple adapter for connecting to desktop. For example, if I want to connect my phone to desktop I need Bluetooth/wifi; why can't I just just use the Mobile's main telecommunication.

This was the case with mobile charger wherein we had to find the correct charger to charge the mobile, now no more it is the case; we can do it with MicroSD charger which is now generally available.

Can't we connect the mobile to desktop (or other way round) each other without the need to have Bluetooth or Wifi (We do have Wireless Modem from telecom companies which work on Mobile's main telecommunication.


texts: Modulus of Rigidity (Shear Modulus) of string

texts: Does anybody know of what magnitude should the Modulus Of Rigidity of a wool string should be? I know that neither wool or string are "materials" but if anybody can give me a rough estimate of a value I would be very thankful.


texts: What is the smallest size of pipe to which I can Weld a 1 inch pipe Perpendicular to the Axis?

texts: I would to know what is (or how to calculate) the size (dia) if the smallest pipe to which I can weld a 1 inch pipe from the side of the bigger pipe perpendicular to its axis (like a tee).


texts: Derivation of the weak form for the euler-bernoulli beam equations

texts:
I am master student and doing an assignment of Finite element method. In the instruction I could not understand the derivation of the weak form, which should not be difficult. I'm sorry for posting this easy and most likely not helpful question for other people.

So the derivation is about the weak form of the integral formulation of 4th ODE. It is a simple beam deformation in the interval 0 and L.
$$ \int_0^L\frac{d^2 w}{d x^2}EI\frac{d^2 \hat{u}}{d x^2}dx = ...$$
$$ \left( \left. w EI \frac{d^3 \hat{u}}{d x^3} \right|_{x=0} \right.
-\left( \left. \frac{d w}{dx} EI \frac{d^2 \hat{u}}{d x^2} \right|_{x=0} \right.
-\left( \left.  w EI \frac{d^3 \hat{u}}{d x^3} \right|_{x=L} \right.
+\left( \left. \frac{d w}{dx} EI \frac{d^2 \hat{u}}{d x^2} \right|_{x=L} \right. $$

I thought about partial integration
$$\int u(x) v'(x) \, dx = u(x) v(x) - \int v(x) \, u'(x)  dx $$
then I ended up
$$\frac{d^2u}{dx^2}\frac{dw}{dx} - \int \frac{dw}{dx}\frac{d^3x}{dx^3}d x$$
if I continue the partial integration to the 2nd term then derivative will be 4th order...

How can I get the following?
$$ \left( \left. w EI \frac{d^3 \hat{u}}{d x^3} \right|_{x=0} \right.
-\left( \left. \frac{d w}{dx} EI \frac{d^2 \hat{u}}{d x^2} \right|_{x=0} \right.
-\left( \left.  w EI \frac{d^3 \hat{u}}{d x^3} \right|_{x=L} \right.
+\left( \left. \frac{d w}{dx} EI \frac{d^2 \hat{u}}{d x^2} \right|_{x=L} \right. $$


texts: How Do You Determine Truss Stability in a Modeling Program?

texts:
This question originates from this and that question. I have realized the concerns boil down to the following figure.

Simply put, is the truss above, with the displayed boundary/internal fixity conditions and distributed loading, structurally stable?


texts: Why in the construction of power transmission towers , the rods are hinged oblique?

texts: I know if a rod is hinged at its two ends and if there is no load act upon it along its length then the forces exist only along its length but i don't see how  this characteristic comes into play ?


texts: What is the name of a half wall with posts on top that divides a space into two?

texts:
I am looking for specific terminology around a half wall that acts as a divider to split a space into two separate uses. The top half of this features a series of wooden posts. It essentially resembles a balustrade except is not for stairs.
Is there a specific name for this?
Here are a few examples:


texts: Validation of Lightweight Chassis (measuring deflection of structures/strain gauging)

texts:
How can we validate the structural integrity of a small lightweight chassis manufactured from 6063-T6 aluminium that has been welded and then heat treated (back to t6 condition)? A simple FEA model has been created but does not consider any thermal analysis and just gives a basic approximation. We are setting up strain gauges and will perform the test today at around 5pm UK time. I am wondering, is it possible that while performing the strain gauging, could we also measure deflection somehow? Even using a string as a baseline then crudely get a deflection measurement etc. Any suggestions?

This is our first time strain gauging so using it as a sole method to validate our FEA will maybe not be wise.

Thanks for all replies!


texts: How to code this iterative scheme for solving 2-group diffusion equation?

texts:
I am trying to write a python code to solve the neutron diffusion equation to model neutron flux distribution in a one-dimensional two-group setting. The governing equations of the system are:

$$-D_1\nabla^2\phi_1+(\mathcal{E}_{a_1}+\mathcal{E}_{s12})\phi_1=\frac{1}{k}[\nu_1\mathcal{E}_{f_1}\phi_1+\nu_2\mathcal{E}_{f_2}\phi_2]+\mathcal{E}_{s21}\phi_2$$

$$--D_2\nabla^2\phi_2+(\mathcal{E}_{a_2}+\mathcal{E}_{s21})\phi_2=\mathcal{E}_{s12}\phi_1$$

where $D$=Diffusion Co-efficient, $\phi$=neutron flux, $\mathcal{E}_{a}$=absorption cross-section, $\mathcal{E}_{s}$=scattering cross-section, $\nu$=neutrons per fission,  $\mathcal{E}_{f}$=fission cross-section and $k$=multiplication factor.

I divided the geometry into 420 mesh elements and discretized the equations using Forward Difference Method (FDM). Putting the whole system into matrix form yields:

$$\Bigl[C_1\Bigr]\Bigl[\phi_1\Bigr]=\frac{1}{k}\Bigl[h\Bigr]\Bigl[\nu_1\mathcal{E}_{f_1}\Bigr]\Bigl[\phi_1\Bigr]+\frac{1}{k}\Bigl[h\Bigr]\Bigl[\nu_2\mathcal{E}_{f_2}\Bigr]\Bigl[\phi_2\Bigr]+\Bigl[h\Bigr]\Bigl[\mathcal{E}_{s21}\Bigr]\Bigl[\phi_2\Bigr]$$

$$\Bigl[C_2\Bigr]\Bigl[\phi_2\Bigr]=\Bigl[h\Bigr]\Bigl[\mathcal{E}_{s12}\Bigr]\Bigl[\phi_1\Bigr]$$

Where $\Bigl[C\Bigr]$=Co-efficient Matrix and $h$=mesh element length.

Now, for the $n$th iteration, I am supposed to use $\phi_{1}^{n-1}$, $\phi_{2}^{n-1}$ and $k^{n-1}$ to solve the two above equations and calculate  $\phi_{1}^{n}$, $\phi_{2}^{n}$ and $k^{n}$ using the iterative scheme:

$$\Bigl[C_1\Bigr]\Bigl[\phi_1\Bigr]^n=\frac{1}{k}\Bigl[\nu_1\mathcal{E}_{f_1}\Bigr]\Bigl[\phi_1\Bigr]^{n-1}+\frac{1}{k}\Bigl[\nu_2\mathcal{E}_{f_2}\Bigr]\Bigl[\phi_2\Bigr]^{n-1}+\Bigl[\mathcal{E}_{s21}\Bigr]\Bigl[\phi_2\Bigr]^{n-1}$$

$$\Bigl[C_2\Bigr]\Bigl[\phi_2\Bigr]^n=\Bigl[\mathcal{E}_{s12}\Bigr]\Bigl[\phi_1\Bigr]^n$$

$$k^n=k^{n-1}\frac{\int dr(\nu_1\mathcal{E}_{f_1}\phi_1^n+\nu_2\mathcal{E}_{f_2}\phi_2^n)}{\int dr(\nu_1\mathcal{E}_{f_1}\phi_1^{n-1}+\nu_2\mathcal{E}_{f_2}\phi_2^{n-1})}$$

I am confused about how to code the last equation. Do I take the differential length $dr$ as mesh element length $h$ and turn the integration into a summation over the geometry? Or do I actually try some kind of integration? I cannot imagine how an integration can be introduced here given that $\phi_1$ and $\phi_2$ are not known as functions but as matrices.

Please help! And thanks for reading through such a long question!


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texts: classes and grades of steel and stainless steel

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I'm trying to learn the standard nomenclature for the steel and stainless steel mainly used in the bolts, screws, nuts, and other fasteners in general. So far I have created this table:

|      Metric / Class     |   Imperial / Grade  |        Material        |
|:-----------------------:|:-------------------:|:----------------------:|
|      ISO 898-1 / 8.8    |     SAE J429 / 5    |          steel         |
|     ISO 898-1 / 10.9    |     SAE J429 / 8    |          Steel         |
|           12.9          |       ASTM A574     |          Steel         |
|            304          |          A2         |     Stainless steel    |
|            316          |          A4         |     Stainless steel    |

For example, metric system categories steels into classes according to the ISO 898-1 standard. While the Imperial system uses the SAE J429 standard to distinguish steels by grades. It seems like my table makes sense for steel, but for the stainless steels, I do not understand the grades/classes. For example, I'm not sure if 316 designates a metric class equivalent to the A4 imperial grade?
From time to time I also see notations such as A4-80 EPK. I understand that the 80 part determines the minimum tensile strength. But I have no clue what the EPK could stand for.


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In the making of firework explosives, the explosive mixtures are handled with great care to avoid static electricity induced detonation of the explosives. Is it a good idea that they store the explosives in a plastic container - isn't there a risk of static buildup that could detonate the explosives?

How It's Made Fireworks