Final Exam Course 58 160 Fall 2007 Name Time 120 min I D 1 The viscous sublayer is normally less than 1 percent of the pipe diameter and therefore very difficult to probe with a finite sized instrument In an effort to generate a thick sublayer for probing Pennsylvania State University in 1964 built a pipe with a flow of glycerin Assume a smooth 12 in diameter pipe with V 60 ft s and glycerin at 20 C Compute a the sublayer thickness in inches b the pumping horsepower required at 75 percent efficiency if L 40 ft For glycerin at 20 C take 2 44 slug ft3 and 0 0311 slug ft s 2 Heat exchangers often consist of many triangular passages Typical is figure below with L 60 cm and an isosceles triangle cross section of side length a 2 cm and included angle 80 If the average velocity is V 2 m s and the fluid is SAE 10 oil at 20 C estimate the pressure drop For SAE 10 oil take 870 kg m3 and 0 104 kg m s 3 In the flow of air at 20 C and 1 atm past a flat plate in figure below the wall shear is to be determined at position x by a floating element a small area connected to a strain gage force measurement At x 2 m the element indicates a shear stress of 2 1 Pa Assuming turbulent flow from the leading edge estimate a the stream velocity U b the boundary layer thickness at the element and c the boundarylayer velocity u in m s at 5 cm above the element For air at 20 C take 1 2 kg m3 and 1 8E 5 kg m s 4 A 2 in diameter sphere weighting 0 14 lb is suspended by the jet of air shown in figure below The drag coefficient for the sphere is 0 5 Determine the reading on the pressure gage if friction and gravity effects can be neglected for the flow between the pressure gage and the nozzle exit For air take 0 00238 slug ft3 Next Page Final Exam Course 58 160 Fall 2007 Name Time 120 min I D 5 Consider water at 20 C flowing past a 1 m diameter cylinder a What doublet strength in m2 s is required to simulate this flow b If the stream pressure is 200 kPa use inviscid theory to estimate the surface pressure at 135 If circulation K is added to the cylinder flow c for what value of K will the flow begin to cavitate at the surface d Where on the surface will cavitation begin e For this condition where will the stagnation points lie For water at 20 C take vapor pressure 2337 Pa Choose only one of the following problems 6 Consider steady flow at velocity U at y past an infinite plane y 0 as shown in the figure Let the plate be porous and has constant suction v v0 Assume that pressure is constant and v v0 everywhere in the flow and u u y only a By using continuity equation solve the Navier Stokes equation for u y and apply boundary conditions on it b Sketch u y roughly Hint for solving differential equation au yy bu y c 0 with constant coefficients a b and c assume that the solution is e y and find 7 The sluice gate in figure below controls flow in open channels At sections 1 and 2 the flow is uniform and the pressure is hydrostatic The channel width is b into the paper a Neglecting bottom friction and atmospheric pressure drive a formula for the horizontal force F required to hold the gate Express your final formula in terms of the inlet velocity V1 and eliminating V2 b Assume that V1 and h1 are constant For what h2 is the force largest
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