Question #262827

a one dimensional steady flow is given by the following velocity;

u=2γ+1(xta0)u=\frac{2}{\gamma+1}(\frac xt-a_0)

And density field;

ρρ0=(γ1γ+1xt1a0+2γ+1)2γ1\frac{\rho}{\rho_0}=(\frac{\gamma -1}{\gamma+1}\frac xt\frac{1}{a_0}+\frac{2}{\gamma+1})^{\frac{2}{\gamma-1}}

a)Calculate the substantial change of density.

b) check the validity of the continuity equation

DρDt+ρux=0\frac{D\rho}{Dt}+\rho\frac{\partial u}{\partial x}=0

for this flow field.



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Expert's answer
2021-11-08T08:52:40-0500

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