Question: The incompressible-flow form of Bernoullis relation, Eq. (3.77), is accurate only for Mach numbers less than about 0.3. At higher speeds, variable density must be

The incompressible-flow form of Bernoulli’s relation, Eq. (3.77), is accurate only for Mach numbers less than about 0.3. At higher speeds, variable density must be accounted for. The most common assumption for compressible fluids is isentropic flow of an ideal gas, or p = Cρk, where k = cp/cv. Substitute this relation into Eq. (3.75), integrate, and eliminate the constant C. Compare your compressible result with Eq. (3.77) and comment.

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