- #1
Anashim
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Choking mass flow seems to reflect the fact that fluid momentum density has a maximum value (in stationary conditions) equal to ##\rho_* c_*## where ##\rho_*## is the critical mass density and ##c_*## is the critical velocity, which is closely related to the speed of sound (see Landau-Lifchitz,"Fluid Mechanics", section 83).
If this result also held in transient flows, would it not imply that the Navier-Stokes Equations should be modified so that they explicitly exhibited pseudo-Lorentzian symmetry (in momentum density) instead of Galilean symmetry?
The momentum density field would then become explicitly causal.
The velocity field does not seem to make much sense if detached from the mass density field.
What I have in mind was the fact that, in a stationary fluid flow, from thermodynamic considerations, it can be proven that:
$$\frac{d(\rho v)}{dv}=\rho\big[1-\frac{v^2}{c^2}\big]$$
Landau and Lifhchitz, "Fluid Mechanics", section 83.
where ##\rho## is the mass density, ##v## the local velocity and ##c## the local speed of sound.
This indicates that the momentum density does have a maximum, at least in stationary flows (where the local velocity is equal to the local speed of sound).
Since the momentum Navier-Stokes equations are Galilean invariant, a sufficiently large pressure gradient should make possible to attain larger momentum densities and this contradicts the previous equation.
I was wondering if one should not enforce the maximum local momentum density as a pseudo-Lorentzian symmetry. (In incompressible flows, at least, I think that one does need to enforce this symmetry).
If this result also held in transient flows, would it not imply that the Navier-Stokes Equations should be modified so that they explicitly exhibited pseudo-Lorentzian symmetry (in momentum density) instead of Galilean symmetry?
The momentum density field would then become explicitly causal.
The velocity field does not seem to make much sense if detached from the mass density field.
What I have in mind was the fact that, in a stationary fluid flow, from thermodynamic considerations, it can be proven that:
$$\frac{d(\rho v)}{dv}=\rho\big[1-\frac{v^2}{c^2}\big]$$
Landau and Lifhchitz, "Fluid Mechanics", section 83.
where ##\rho## is the mass density, ##v## the local velocity and ##c## the local speed of sound.
This indicates that the momentum density does have a maximum, at least in stationary flows (where the local velocity is equal to the local speed of sound).
Since the momentum Navier-Stokes equations are Galilean invariant, a sufficiently large pressure gradient should make possible to attain larger momentum densities and this contradicts the previous equation.
I was wondering if one should not enforce the maximum local momentum density as a pseudo-Lorentzian symmetry. (In incompressible flows, at least, I think that one does need to enforce this symmetry).
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