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Q:

At each shock wave, Why there is a sudden increase of pressure and density but a reduction in velocity?

A:

A shock wave forms in supersonic flow when the pressure somewhere else in the flow needs to be high. When the pressure increases, the density will increase as well, because there has to be equal mass flow across the shock wave. The mass flow per unit area is equal to density times velocity. Because the density is higher behind the shock wave, the velocity must be lower.

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