Relation: Velocity and Denstiy

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Consider a steady, one dimensional and frictionless flow, we can apply the Euler equation expressed as: v_d_1

Here

  • p= pressure
  • ρ= density
  • V= flow velocity
  • z= height relative to reference level

For ideal gas flow, the potential energy difference term dz is small enough to be negligible. Thus we can now rewrite the Euler equation as:

v_d_2

This expression indicates that the increase (decrease) of flow velocity leads to the decrease (increase) of the pressure in the direction of flow.

Now we try to let the Mach number appear in this equation: v_d_3

We notice that the relative change in velocity is proportional to relative velocity change.

For subsonic (Ma<<1): v_d_4

That means, the relative change in density is very small in subsonic case.

For supersonic (Ma>>1): v_d_5

That means, the relative change in density is very high in supersonic case.

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