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Question: problem 5 6 marks a for a steady inviscid and...

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Problem 5 (6 marks) a) For a steady, inviscid, and adiabtaic flow, the stagnation enthalpy is constant along a streamline, i.e. ho-hconst 2 If the flow is also a perfect gas, use this enthalpy relation to derive the compressible form of Bernoullis equation: + const. 1) Po b) Derive the same compressible Bernoulli equation obtained in eq. (2) using only the conservation of mass and momentum. To do this, first show that for steady flow in a duct of constant area: + udu-0 This is obtained by letting 11 = u, pi = p, ρι = ρ, and u2 = u+ du, p2 = p+ dp, p2-ρ+ dp. Then, by assuming isentropic flow, make use of the relation for p/p = C (Hint: substitute for p) then integrating eq. (3) c) Starting with eq. (3) derive an alternate compressible Bernoulli equation if the flow is isothermal instead of isentropic. i.e. p/ρ RT-C

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