57:020 Mechanics of Fluids and Transport Fall 2008 EXAM #3 December 16, 2008 1. Determine the flow rate through the Venturi meter shown below if ideal conditions exist. 2. A prototype water pump has an impeller diameter of 2 ft and is designed to pump 12 ft3/s at 750 r/min. A 1-ft-diameter model pump is tested in 20°C air at 1800 r/min. According to a di-mensional analysis the pump power can be expressed as following when the Reynolds-number effects are negligible: ΩΩ where, is the pump power, is the volume flow rate, is the density, Ω is the impeller rota-tion speed, and is the impeller diameter. For similar conditions, (a) what will be volume flow of the model be in ft3/s, and (b) what horsepower is required for the prototype if the model pump requires 0.082 hp to drive it? (For air at 20°C, = 0.00234 slug/ft3, and for water at 20°C, = 1.94 slug/ft3) 3. Water at 20°C is to be pumped through 2000 ft of pipe from reservoir 1 to 2 at a rate of 3 ft3/s as shown below. If the pipe is cast iron of diameter 6 in. and roughness ε = 0.00085 ft, what horsepower pump is needed? Use the equation given below to calculate the friction factor if necessary, and assume that the pump efficiency is 100%. (ρ = 1.94 slug/ft3, μ = 2.09 × 10-5 slug/ft⋅s, g = 32.2 ft/s2, 1 hp = 550 lb⋅ft/s) 1.325ln3.75.74.57:020 Mechanics of Fluids and Transport Fall 2008 EXAM #3 December 16, 2008 4. Water flows steadily through the 0.75-in. diameter galvanized iron (ε = 0.0005 ft) pipe system shown in Fig. 4 at a rate of 0.020 cfs. What is the ratio between the major and minor losses? Loss coefficients are 1.5, 2.0, and 0.15 for 90° threaded elbows, tee, and reducer, respective-ly. Use the same equation in problem 3 for a friction factor if necessary. (ν = 1.21 × 10-5 ft2/s) 5. Consider water flow past a thin flat plate. On both sides of the plate, the boundary layer is tripped at the leading edge. For flow speed 5 m/s, estimate (a) the local wall sear stress at a po-sition 40 cm downstream from the leading edge and (b) the total friction drag if the plate is 2 m long and 1m wide. Transition to turbulent flow occurs at Re = 5 × 105. ( = 998 Kg/m3, = 0.001 kg/m⋅s) 6. A 10-cm-diameter ball is supported by an air jet as shown below. Estimate the weight of the ball if the jet velocity is 14.5 m/s. Drag coefficients of a smooth sphere is given below as a function of Reynolds number (solid line). ( = 1.225 kg/m3, = 1.78 × 10-5 kg/m⋅s) Part Threaded elblow 1.5Tee 2.0Reducer
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