j = ρ_{1} u_{1} = ρ_{2} u_{2}, p_{1} + ρ_{1} u_{1}^{2} = p_{2} + ρ_{2} u_{2}^{2}, C_{B} = \frac{u ^{2}}{2} + \frac{c _{s}^{2}}{γ - 1} .

1/ ρ = u / j

give

p_{2} - p_{1} = j (u_{1} - u_{2}) .

Direct elimination of the two pressures and densities from these three jump conditions gives

u_{1} u_{2} = \frac{2 ( γ - 1 )}{γ + 1} C_{B} .

Part c identifies the right side with the square of the critical speed, so the Prandtl shock relation is

u_{1} u_{2} = c_{cr}^{2} .

It maps the unique upstream supersonic state on a given Bernoulli streamline to its downstream subsonic state.

 Ancestors (10)

 Discussion (0)

There are no discussions about this article yet.

There are currently no matching articles.