New answers tagged fluid-dynamics
2
votes
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 ...
- 15.3k
1
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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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0
votes
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
0
votes
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
-1
votes
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 ...
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2
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Accepted
Compressible fluid equation
Let's write density $\rho$ as a function of pressure $P$ and entropy $s$,
\begin{equation}
\rho(P, s) \ ,
\end{equation}
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 $\rho$, ...
- 7,018
0
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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 ...
- 7,092
2
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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
0
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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
0
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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
-1
votes
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
0
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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
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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
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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
-1
votes
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
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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) ...
- 4,338
0
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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 $V$
\begin{equation}
\dfrac{d}{dt} \int_V \rho \mathbf{u} + \oint_{\partial V} \rho \mathbf{u} \mathbf{...
- 6,743
0
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No-slip condition tangential and normal component decomposition
Let s be distance measured along the surface and $\phi$ be the contour angle of the surface. Then, $$\cos{\phi}=\frac{dx}{ds}$$and $$\sin{\phi}=\frac{dz}{ds}$$The unit tangent to the surface is $$\...
- 32.2k
0
votes
Euler's turbine equation derivation
FROM: https://engineering.stackexchange.com/questions/56375/eulers-turbine-equation-derivation
It looks like Eq. (52) is a general statement of torque and angular momentum transfer across the control ...
1
vote
Accepted
Perfect Conducting (PC) and Perfect Insulating (PI) boundary conditions for magnetic induction in MHD problems in cylindrical coordinates
If you are familiar with fluid mechanics, there is a natural analogy between the magnetic field $B$ and the velocity field $u$. The PI boundary boundary condition correspond to no slip boundary ...
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Bernoulli's principle at molecular level
Suppose that an ideal gas is flowing through a pipe, and there is a reduction of section at some point. If the velocity of the gas is greater after this point, there is a region of transition where ...
- 15.3k
8
votes
Accepted
Bernoulli's principle at molecular level
if pressure is calculated from the this relation : $PV=nRT$ and we don't observe a decrease in any of those factors that would cause a drop in pressure
This statement is not true. $P$, $V$ do change, ...
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Will a metal block float in water in such a scenario?
This doesn't have to do with pressure, it has to do with density. Ocean water varies in density from about 1.03 g/cc at the surface to 1.08 g/cc at the ocean floor. Iron, meanwhile, is 7.9 g/cc. Hence ...
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Is it possible to make large waves from perfectly timed single drops of water?
Given water with no side boundaries, a drop of water generates ripples that spread out. The ripples carry energy. So the energy flows outward and does not return. The amplitude of the wave diminishes ...
- 34.9k
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Is it possible to make large waves from perfectly timed single drops of water?
For conservation of energy, you can't get more energy into the waves per drop than the loss of the gravitational potential energy of each drop. Constructive and destructive interference only changes ...
- 67.6k
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What is meant by "inertial forces", in contrast to the "resultant force"?
What is meant by "inertial forces", in contrast to the "resultant force"?
For example, in the Wikipedia page on Reynolds number it is said:
The Reynolds number is the ratio of ...
- 15.8k
2
votes
Does buoyancy force depend on the acceleration of the buoyant object?
Archimedes principle is only valid for objects in equilibrium. Likewise, Pascal's law is only valid for stationary fluids. There is no simple correction that can be applied to accelerating objects ...
- 38k
0
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Can someone explain 'virtual mass' in fluids in simple words (for a dummy/high schooler)?
Virtual mass, in the context of fluid mechanics, is a concept that can seem a bit counterintuitive but can be explained in simple terms.
Imagine you have an object moving through a fluid like water. ...
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Can someone explain 'virtual mass' in fluids in simple words (for a dummy/high schooler)?
Virtual mass, or added mass, is a concept of fluidodynamics related to the enhanced inertia acquired by a body in a fluid. A short description of the concept can be found on this Wikipedia page.
It is ...
0
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Are the stress and strain tensor covariant or contravariant?
The stress and strain tensors are neither covariant nor contra-variant. They are independent of the basis vectors used to express their components. Their components are considered covariant or ...
- 32.2k
0
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What nonlinear deformations will a fast rotating planet exhibit?
This is not strictly theoretically deduced, just experimentally shown, but for most configurations that don't rely on some sort of differentiated body or highly non-uniform density within the object, ...
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0
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Frame of reference for work done against air resistance by ground vehicle
An equivalent situation goes some way to convince me that ground speed is the correct thing to use.
I am standing on the shore of a deep, wide lake, hauling in a boat at a constant speed of 2m/s ...
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Frame of reference for work done against air resistance by ground vehicle
The faster the thing you're pushing against is moving away from you, the more energy it costs to push it away with a given force. Think about a boxer who moves his head backwards to reduce the force ...
- 12.6k
0
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Does a rigid body rotates in an irrotational flow?
I wanted to place this as a comment, but I do not have the necessary reputation yet.
For an irrotational flow, the net local angular momentum should be zero. So, if a large size stationary object is ...
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What happens when you hold a spoon in a stream of water?
The correct answer to this question is that this lab is demonstrating "the Coanda effect". it has nothing to do with pressure.
The curvature of the spoon, along with the adhesion and ...
0
votes
What causes this corkscrew-shaped object to rise up in a stream of water falling down?
This really seems to be a fake, although there are not enough details given to be 100% certain. The simple intuition they are playing with is strong...if the stick is moving with the fluid, there is ...
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How can flows of gases at low Mach number have approximately constant density despite varying pressure?
Here is another way of looking at Bernoulli's theorem, pressure and Mach number. Your question seems to be talking about two related concepts: (1) Relation between density and pressure and (2) ...
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How can flows of gases at low Mach number have approximately constant density despite varying pressure?
Density is indeed proportional to pressure in an ideal gas at a fixed temperature. So, when Bernoulli's principle states that pressure varies with the square of velocity assuming a fixed density, the ...
0
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Head losses on parallel pipes
This is an old question but there have been a lot of views so maybe it is still of interest.
How is it possible that...? Well, from Darcy's Eqn,
$$\begin{gather}h_L=f\cdot\frac{L}{d}\cdot \frac{v^2}{...
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5
votes
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})_{...
- 35k
3
votes
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 ...
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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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