58:160 Intermediate Mechanics of Fluids FINAL EXAM – 12/ 15/ 04 1. The jet pump in the figure injects water at U1= 40 m/s through a 3-in-pipe and entrains a secondary flow of water U2= 3 m/s in the annular region around the small pipe. The outer pipe diameter is 10 inches. The two flows become fully mixed downstream, where U3 is approximately constant. For steady incompressible flow, compute U3 in m/s. If pressures p1= p2 = 172.4 kPa, and the distance between sections 1 and 3 is 80 inches. and the average wall shear stress between sections 1 and 3 is 335 Pa, estimate the pressure p3. Why is it higher than p1? 2. A helium-filled balloon is tethered at 20oC and atmospheric pressure with a string of negligible weight and drag. The diameter is 50 cm. the balloon material weighs 0.2 N not including the helium. The density of helium in the balloon is 0.197 kg/m3. Estimate the tilt angle θ if the air-stream velocity is a) 5 m/s and b) 20 m/s. 13. A smooth flat pate is oriented parallel to a 3 m/s air flow at 20o C and atmospheric pressure. The plate is 1 m long in the flow direction and 0.5 m wide. On one side of the plate the boundary layer is tripped at the leading edge to stimulate turbulence. On the other side there is no tripping device. Find the total drag force on the whole plate. 4. Consider water at 20oC at 200 kPa flowing at 6 m/s past a 1-m-diameter circular cylinder with circulation. What is the required vortex strength K in m2/s to place stagnation points at θ = 35o and 145o. Compute the resulting pressure and surface velocity at a) the stagnation points and b) the upper and lower shoulders. U∞=6 m/s
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