All Questions
Tagged with adiabatic fluid-dynamics
10
questions
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Origin of ideal gas fluid dynamics equations including the adiabatic index
I was given a system of equations that supposedly describes the fluid dynamics of an ideal gas.
The equations are:
$$
\begin{align}
&\frac{\rho}{m} = \frac{p}{T} &\text{(ideal gas law)} \\\\
&...
- 241
2
votes
1
answer
84
views
Is sound really adiabatic because it is a fast process?
In many books I have consumed so far there is the statement that sound is adiabatic because heat transfer does not have nearly enough time to reach isothermal equilibrium. Doesn't this contradict ...
- 1,299
2
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134
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How to prove that $\gamma \le 2$ for *causal* relativistic polytrope fluids?
The definition of the adiabatic index of a relativistic polytrope fluid is this:
$$\tag{1}
\gamma = \frac{\rho + p}{p} \, \frac{dp}{d\rho},
$$
where $\rho$ is the energy density (not the mass density)....
- 7,592
1
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1
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58
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Relation of first adiabatic exponent to adiabatic index
I'm going through a fluid dynamics text and I'm a little confused by a listed relation. The first adiabatic index is defined as
$$ \Gamma_1 = \left(\frac{\partial \ln P}{\partial \ln \rho}\right)_s, $$...
- 462
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2
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154
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How does the adiabatic coefficient $γ$ vary with temperature (200K-20000K)? [closed]
At high temperatures, such as those encountered in hypersonic flight, γ varies a lot. My problem is that I can‘t find a graph accompanied by an explanation as to how & why it changes under ...
0
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1
answer
80
views
Adiabatic sound speed in static spherically-symmetric perfect-fluid solutions (SSSPF) of Einstein field equations (EFE)
Why $\sqrt{dp/d\rho}$ is interpreted in SSSPF solutions as adiabatic speed of sound although the corresponding equations are static? In static world all times derivatives are zero and without wave ...
- 1,948
1
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1
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124
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Normal Shockwaves and its Thermodynamics
Please read this page before going to my question.
When we derive the relation between Mach no. to the left side of the shock wave (M1) and that to the right side of the shock wave (M2),we do that ...
- 339
-1
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2
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270
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Adiabatic free expansion
Let us assume there is an ideal gas in a thermally insulated vessel and it is free to expand into vacuum through a small hole in the vessel.Would the mass flow rate be a constant? What would be the ...
- 268
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0
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Shockwaves speed through rarer and denser atmosphere
I was going through the different speed of sound through different atmospheric/air conditions and the Newton-Laplace equation gives
$ c=\sqrt{\frac{\gamma P}{\rho}} $
So, where does the ...
- 169
2
votes
1
answer
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Bernoulli Equation for isentropic ideal gas flow
If one derives the Bernoulli Equation for the isentropic ideal gas flow you get:
$$ \frac{1}{2}v^2 + g z + \left(\frac{\kappa}{\kappa -1} \right) \frac{p}{\rho} = const. $$
Two questions:
Is ...
- 208