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GeologistInDisguise
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- How is the pictured equation a conservation of momentum equation and what does pressure have to do with it?
I am trying to follow a derivation of the Rankine-Hugoniot equations in a paper by Peter Krehl titled:
The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality
This paper talks about the RH equations which relate kinematic properties to thermodynamic ones when a shock is transiting a material. See photo above for an illustration. In section 2.2.2 when discussing this relation in terms of Lagrangian coordinates, equation 4a is introduced and described as conservation of linear momentum:
Where P is pressure, rho is density, u is particle velocity, 0 indicates downstream or preshock and 1 indicates upstream or post shock.
While the units do make sense, how is this conservation of momentum? if momentum is m*v, I suppose you could divide by volume to replace mass with density, but then why is velocity squared? And why is pressure being added?
I understand pressure is force/area and also that force is the change in momentum with time. I am guessing this has something to do with it but I am not getting anything that would give me a squared velocity. Obviously if I integrate my mass normalized momentum equation with respect to time, that would give me a velocity squared. But why would I do that?
The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality
This paper talks about the RH equations which relate kinematic properties to thermodynamic ones when a shock is transiting a material. See photo above for an illustration. In section 2.2.2 when discussing this relation in terms of Lagrangian coordinates, equation 4a is introduced and described as conservation of linear momentum:
Where P is pressure, rho is density, u is particle velocity, 0 indicates downstream or preshock and 1 indicates upstream or post shock.
While the units do make sense, how is this conservation of momentum? if momentum is m*v, I suppose you could divide by volume to replace mass with density, but then why is velocity squared? And why is pressure being added?
I understand pressure is force/area and also that force is the change in momentum with time. I am guessing this has something to do with it but I am not getting anything that would give me a squared velocity. Obviously if I integrate my mass normalized momentum equation with respect to time, that would give me a velocity squared. But why would I do that?