Problem 4.32

Problem 4.32 - Problem 4.32[Difficulty 2 Given Data on flow...

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Problem 4.32 [Difficulty: 2] Given: Data on flow through device Find: Velocity V 3 ; plot V 3 against time; find when V 3 is zero; total mean flow Solution: Governing equation: For incompressible flow (Eq. 4.13) and uniform flow A V dV A = 0 = Applying to the device (assuming V 3 is out) V 1 A 1 V 2 A 2 V 3 A 3 + 0 = V 3 V 1 A 1 V 2 A 2 + A 3 = 10 e t 2 m s 0.1 × m 2 2 cos 2 π t () m s 0.2 × m 2 + 0.15 m 2 = The velocity at A 3 is V 3 6.67 e t 2 2.67 cos 2 π t + = The total mean volumetric flow at A 3 Q 0 t V 3 A 3 d = 0 t 6.67 e t 2 2.67 cos 2 π t + 0.15 d m s m 2 = Q t 2 e t 2 1 5 π sin 2 π t + lim 2 = 2m 3 = Q2 m 3 = The time at which V 3 first is zero, and the plot of

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Problem 4.32 - Problem 4.32[Difficulty 2 Given Data on flow...

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