Exam2 - veloped, and there is no pressure gradient in the...

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57:020 Mechanics of Fluids and Transport Fall 2009 Exam 2, November 9, 2009 1. The water jet shown in Fig. 1 strikes a vane that is fixed on a frictionless cart. The cart is re- strained by a horizontal force, F x . If ρ = 999 kg/m 3 , V j = 30 m/s, A j = 0.01 m 2 , and θ = 30 ° , com- pute the force F x . The jet velocity magnitude remains constant along the vane surface. 2. When the pump in Fig. 2 draws Q = 220 m 3 /h of water at 20 ° C ( = 999 kg/m 3 ) from the reser- voir, the total friction head loss ݄ is 5 m. The flow discharges through a nozzle ( D e = 5 cm) to the atmosphere. Calculate the pump power in kW delivered to the water. Assume the kinetic energy correction factor α = 1 in the energy equation. Fig. 1 Fig. 2 3. Two horizontal, infinite, parallel plates are spaced a distance b = 5 mm apart, as shown in Fig. 3. A viscous liquid is contained between the plates. The bottom plate is fixed, and the upper plate moves parallel to the bottom plate with a velocity U = 0.2 m/s. The flow is steady and fully de-
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Unformatted text preview: veloped, and there is no pressure gradient in the direction of flow. (a) Start with the Navier-Stokes equations and determine the velocity distribution u ( y ) across the plates. (b) Determine the flowrate q passing between the plates (for a unit width). 4. Flow characteristics for a 30-ft-diameter prototype parachute (Fig. 4) are to be determined by tests of a 1-ft-diameter model parachute in a water tunnel. (a) The drag, D , can be expressed as D = f ( , V , d ), where is the fluid density, V is the parachute velocity, and d is the parachute di-ameter. Use the dimensional analysis and find a suitable pi parameter for this problem. (b) Some data collected with the model parachute indicate a drag of 17 lb when the water velocity is 4 ft/s. Use the model data to predict the drag on the prototype parachute falling through the air at 10 ft/s. ( water = 1.94 slugs/ft 3 and air = 2.38 10-3 slugs/ft 3 ) Fig. 3 Fig. 4...
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