# Tag Info

### Different Bernoulli equation from $F=dp/dt$

It is better to work with small elements and later take the limit. $$\Delta p=\rho A_1\Delta x(v_2−v_1) \implies \frac{\Delta p}{\Delta t} = \rho A_1\frac{\Delta x}{\Delta t}(v_2−v_1)$$ The average ...
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1 vote

### Different Bernoulli equation from $F=dp/dt$

Thank you to whoever telepathically answered my question. The answer can be found by asking yourself what happens if there is a piston pushing in the opposite direction on the volume of smaller cross ...
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### Indeterminism of Bernoulli Equation

The pressure head $h_p$ must be zero otherwise the fluid indeed accelerates without limit (assuming no frictional losses). Mathematically speaking, one is not allowed to solve explicitly for $v_2$ ...
• 78

### Effect of pipe size on water flow rate in municipal water system

You won't have Poiseuille flow (laminar), but if you did have Poiseuille flow, Q would be proportional to $(\Delta P)D^4$. So, without any restriction at the valve end, the volumetric flow rate would ...
• 32.2k

### Time derivative term in Navier Stokes equation for fluid in porous media

Here my guess: the authors are solving fluid equations on a grid moving with the solid matrix, implicitly using an ALE (arbitrary Lagrangian Eulerian) approach. To add some details, in continuum ...
• 6,743
Accepted

### Compressible fluid equation

Let's write density $\rho$ as a function of pressure $P$ and entropy $s$, $$\rho(P, s) \ ,$$ being every thermodynamic quantity a field, function of space and time. Thus, ...
• 6,743
1 vote
Accepted

### What is the Buoyant force experienced by a cube at a certain level inside water?

You are just making some mistakes in what we are trying to say. Let the cube have side length $\ell$ and the top surface be submerged to depth $h$ from the top surface of the water of density $\rho$, ...

### What is the Buoyant force experienced by a cube at a certain level inside water?

There are two problems with your logic: You count the weight of the cube pushing down on the bottom surface, but not the weight of the cube pulling down on the top surface. Though I suggest just not ...
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### What is the area of a hole in an irregular surface?

An engineering problem such as this calls for some "standardization". A similar problem arises in calculating the drag on bodies of arbitrary shape. What we do is calculate the "...
• 6,389

### Does buoyancy force depend on the acceleration of the buoyant object?

You are right. For example, a system in free fall is equivalent to it being inside a gravitation-free space (Equivalence principle) in which case there will be no buoyancy force on any submerged ...
• 6,389

### What exactly is the polytropic index and what definition do I use to describe gas flow when it's choked?

In the formula, the first $k$ should be $\gamma$ and the exponent needs a slash between $\gamma +1$ and $\gamma -1$. With $\gamma = 1.4$ the exponent is 3. $\gamma$ is the ratio of specific heats; ...
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### Does a wind turbine produce thrust?

I'm not a native English speaker and not an expert on aviation, but here's my ideas on this. In case of a plane propeller, I think "thrust" refers to net force of the air on the rotating ...
• 35.3k

### How to get exact solution to Sod shock tube test?

@Andrej This is great question, @Kyle thank you for your response. I combine the notes which @Andrej mentioned in the comments with @Kyle's rarefaction wave region to produce a python code which ...
• 545

### Can you explain the perfume bottle with the Bernoulli effect?

It is not viscosity lowering the pressure in the center of that center section. I know this is old, but a search turned this up. Cummon' people! This is the oldest misconception since Adam & Eve.....
1 vote

### Water traveling on a letter in a water feature

As one can observe by pouring water on a flat surface, the speed it picks up by falling allows it to scoot sideways or even uphill to some extent. In addition, after a drop separates, the rebound ...
• 23.2k
1 vote

### Compressed water

For a fixed volume maintained at room temperature and a sufficiently strong pump, the water would tend to solidify (at equilibrium) into ice-VI at a pressure of ~1 GPa: The compression would tend to ...
• 23.2k
Accepted

### How does one calculate the viscous term in the integral form of navier stokes?

What is this +viscous term is it a number, an equation yielding viscosity or something else? Also from my knowledge $\vec{u}_i$ is an eigenvector but I don't know if it has to do with the velocity. I'...
• 27.7k
1 vote

### How is angular momentum stored in the superfluid component of pulsars?

Note: the accepted answer is already very good. I want to stress here that the understanding and modelling of pulsar glitches is based on some speculative ideas. The (few) robust points and the (many) ...
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### What referential should I use? Ping pong and water cup

Since the experiment can replace the water by sand or by a poorly bouncing heavier ball I think the approach with Archimedes law does not work better than the explanations in the other link.
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### How does one calculate the viscous term in the integral form of navier stokes?

Momentum equation - integral form. Let's start from integral balance, for a fixed control volume $V$ \dfrac{d}{dt} \int_V \rho \mathbf{u} + \oint_{\partial V} \rho \mathbf{u} \mathbf{...
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Accepted

### Second-order tensor contractions and matrix multiplication

Your two contractions are kind of correct, except that the indices were missing in the final term: $$A^T_{ji}B_{ik} = (\mathbf{A}^T\mathbf{B})_{jk}$$ and B^T_{ki}A_{ij} = (\mathbf{B}^T\mathbf{A})_{...
Accepted

### Why does the 'vortex stretching term' not appear in Kelvin Circulation theorem?

The vorticity transport equation views the vorticity as vector value 0-form. However, Kelvin’s theorem views it as a 2-form. In the former formalism, it is nit conserved due to vortex stretching while ...
• 8,714
1 vote

### Are closed streamlines necessary to have vortices?

The terminology 'vortex-flows' is a bit misleading. The term means flow in circular paths. Obviously, a circular path is a closed path. Vorticity is the curl of the velocity vector field. Physically ...
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