exam_final_18_solnfor19.pdf - ECH 141u2014Fluid Mechanics...

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ECH 141—Fluid Mechanics Winter 2018 Final Exam (Two hours, closed book, no notes) 1. a) (10 pts.) A fermentation broth with density ρis to be fed to a filtration unit at an average velocity v through a pipe with diameter D. A pump is located in the line in advance of the filtration unit to raise the liquid pressure from P0to the value P1that is needed for the filtration to proceed. The pipe leaving the pump has the same diameter as the pipe feeding the pump. Elevation changes between the pump entrance and exit are negligible, as are viscous losses in the line between the pump and filter. What power must the pump deliver to this flow line? b) (5 pts.) What quantity (velocity, stress or pressure) is dotted with the Cauchy stress equations to generate the mechanical energy balance? c) (5 pts.) Which physical property is most relevant to understanding why small particles floating on a liquid aggregate to form “rafts”: i) viscosity ii) density or iii) surface tension? d) (10 pts.) When a glass capillary tube with radius R is lowered vertically into a glass of water, the water rises in the tube to a height H. If the surface tension of the water is γand the air-water interface inside the tube is assumed to be a hemisphere, what is the height the water rises in the tube, in terms of the tube radius R, water density ρ, 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 region outside the boundary layer. Inside the boundary layer, viscous effects are (comparable to/larger than/smaller than) inertial effects. The boundary layer thickness gets (larger/smaller) as the Reynolds number increases. Solutiona) Grading: 0 pts, 5 pts. or 10 pts. From PRR, the engineering Bernoulli equation is 12gv22v12+z2z1+p2p1ρg= WmρgQhfhm. The pipe diameters into and out of the pump are equal, there is no elevation change, and viscous losses in the line between pump and filter are negligible. Therefore Wm=Q P1P0(), where Q=vπD24. b) Grading: 0 pts. or 5 pts. The velocity. c) Grading: 0 pts. or 5 pts. surface tension d) Grading:

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