All Questions
Tagged with conservation-laws fluid-dynamics
159
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154
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Is there any phenomenon where opposite reaction (Newton's 3rd Law) is not fulfilled?
I'm wondering if there is any case in nature/physics where it has been observed "where there is an action, there is not necessarily an exact equal and opposite reaction".
Or is there some ...
- 193
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1
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83
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Continuity Equation for Steady State Flow vs Incompressible flow
Good day guys,
I have been reading on the continuity equations on the slides of my fluid dynamics course.
I was introduced to the following definitions:
Steady state flow: $\forall f \in \text{Flow ...
- 286
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28
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Solving continuity equation under specific conditions
I have been thinking about how to get a general solution for the continuity equation:
$$\frac{\partial \rho(\vec{r},t)}{\partial t}+\vec{\nabla}\cdot\vec{J}(\vec{r},t)=F(\vec{r},t)$$
and I figured the ...
- 1,616
2
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1
answer
135
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Stokes stream function derivation
I want to know a concrete derivation of 3D Stokes stream function.
The statement is, for example in 3D spherical coordinates (with symmetry in rotation about the $z$-axis), if
$$\nabla \cdot u=0\tag{...
- 311
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1
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60
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Large number of infinitesimal particles in an incompressible flow
Consider an expansion channel, where isothermal incompressible flow enters the domain from the smaller channel.
Assume I inject infinitesimal particles (with same density as the flow) into the domain ...
- 3
3
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1
answer
64
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General relativistic version of Rankine–Hugoniot jump conditions in fluid dynamics
Is there anything like Rankine-Hugoniot jump conditions for general relativity?
- 1,335
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45
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Conservation of velocity flux in fluid mechanics
I am currently working through the book Vorticity and Incompressible Flow by Majda and Bertozzi. They define the velocity flux as $\int_{\mathbb{R}^3}udx$, where $u = u(t,x)$ is some smooth vector ...
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2
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406
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How to obtain the continuity and Euler equations by taking moments of the Vlasov equation in Cosmology?
In a set of notes about cosmology, I have found the following claim:
The 0th moment of the Vlasov equation yields the continuity equation. For that, upon integrating over the momentum, we have to ...
- 293
3
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4
answers
634
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Diffusion without mass conservation?
I'm looking for the physical description of a certain diffusion process, but I don't know how to precisely express it, making the search fruitless. I'd like to have some help formulating, or rather ...
- 131
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122
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Bernoulli's equation in a conical pipe
Question
A stream is rushing from a boiler through a conical pipe, the diameter of ends of which are $D$ and $d$; if $V$ and $v$ are the corresponding velocities of the stream and if the Bernoulli's ...
- 11
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1
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79
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Does the flow rate of a falling water column increase further down the column?
Suppose you have a faucet that expels water at a rate r Liters/second. Will the rate at which water flows through some ring beneath the faucet be greater than r or equal to r?
On one hand, if the rate ...
- 23
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82
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Compressible fluid equation
We know the continuity equation of a continuum (in this case I want to discuss fluids, equation reference):
$$\frac{\partial \rho}{\partial t} + \nabla . (\rho u) = 0$$
where $\rho$ is the mass ...
- 78
1
vote
1
answer
91
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What referential should I use? Ping pong and water cup
I'm trying to modelise the ping pong and water cup experiment.
They were already questions on stackexchange about this:
Why does a ping pong ball bounce higher when it is dropped together with a cup ...
- 47
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votes
1
answer
98
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Understanding definition of flux as a vector field
I'm reading about conservation laws in the book Mathematical Models in Biology by Edelstein-Keshet, and I'm a bit confused by the author's definition of flux. For context this is from section 9.3, ...
- 121
6
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516
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Why are the Navier-Stokes equations inconsistent in this case?
Consider the case of a one-dimensional incompressible, non-viscous fluid flowing down a vertical pipe under the influence of gravity. Since we assume the flow is constant along the cross section of ...
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