# exam final 18 solnfor19.pdf - ECH 141—Fluid Mechanics...

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ECH 141—Fluid MechanicsWinter 2018 Final Exam(Two hours, closed book, no notes)1. a)(10 pts.) A fermentation broth with densityρis to be fed to a filtration unit at an average velocityv through a pipe with diameter D.A pump is located in the line in advance of the filtration unit to raisethe liquid pressure from P0to the value P1that is needed for the filtration to proceed.The pipe leavingthe pump has the same diameter as the pipe feeding the pump.Elevation changes between the pumpentrance and exit are negligible, as are viscous losses in the line between the pump and filter.Whatpower must the pump deliver to this flow line?b)(5 pts.) What quantity (velocity, stress or pressure) is dotted with the Cauchy stress equations togenerate the mechanical energy balance?c)(5 pts.) Which physical property is most relevant to understanding why small particles floating on aliquid aggregate to form “rafts”:i) viscosityii)densityoriii) surface tension?d)(10 pts.) When a glass capillary tube with radius R is lowered vertically into a glass of water, thewater rises in the tube to a height H.If the surface tension of the water isγand the air-water interfaceinside the tube is assumed to be a hemisphere, what is the height the water rises in the tube, in terms ofthe tube radius R, water densityρ, and surface tension.e) (10 pts.) Choose the correct word inside parentheses:Hydrodynamic boundary layers form at(high/low) Reynolds numbers, corresponding to (inertial/viscous) effects being dominant in the regionoutside the boundary layer.Inside the boundary layer, viscous effects are (comparable to/largerthan/smaller than) inertial effects.The boundary layer thickness gets (larger/smaller) as the Reynoldsnumber increases.Solutiona)Grading:0 pts, 5 pts. or 10 pts.From PRR, the engineering Bernoulli equation is12gv22v12+z2z1+p2p1ρg=WmρgQhfhm.The pipe diameters into and out of the pump are equal, there is no elevation change, and viscous lossesin the line between pump and filter are negligible.ThereforeWm=Q P1P0(),whereQ=vπ24.b)Grading:0 pts. or 5 pts.The velocity.c)Grading:0 pts. or 5 pts.surface tensionD