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The Machine
Lv 6
The Machine asked in Science & MathematicsMathematics · 8 years ago

Integrate the equation...?

d(v^2/2) + dp/(rho) = 0 for an isentropic process where p / (rho)^gamma = constant.

Explain the result.

Please help

1 Answer

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  • GusBsAs
    Lv 6
    8 years ago
    Favorite Answer

    p = C rho^gamma

    dp = C gamma rho^(gamma-1) drho

    dp / rho = C gamma rho^(gamma-2) drho =

    = d(C gamma/(gamma-1) rho^(gamma-1)) =

    = d (gamma/(gamma-1) p/rho)

    =>

    d (v^2/2 + gamma/(gamma-1) p/rho) = 0

    =>

    v^2/2 + gamma/(gamma-1) p/rho = constant

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