ME 330 PS5 Solutions Fall 2010

ME 330 PS5 Solutions Fall 2010 - Problem Set#5 Problem#1...

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Problem Set #5, Problem #1 Given: Flat plate boundary layer with free stream velocity u 0 , x-velocity profile at L , boundary layer thickness δ at L , and constant suction rate at y = 0 Find: The x-velocity at position (x,y) = L,0 and L, Mass flow rate per unit width across surface a-b , c-d , a-d , and b-c Drag force per unit width along length L of the plate assuming a zero pressure gradient flow Assumptions: Steady state, incompressible, Newtonian fluid Analysis: This is a mass conservation, momentum balance problem Based on the profiles given, u(L,0) = 0 , u(L, ) = u 0 The mass flow rate across any surface is the integral of the velocity profile across an area normal to the flow: () = ij A ij ij dA n V m r r ρ
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Assuming an arbitrary width into the page, we the mass flow per unit width across each surface is: = = δ δρ ρ 0 0 o b a u dy u m = = δδ 0 2 0 3 2 2 o d c u dy y y u m = = L d a L v dx v
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This note was uploaded on 09/05/2011 for the course ME 205 taught by Professor Koen during the Spring '07 term at University of Texas.

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ME 330 PS5 Solutions Fall 2010 - Problem Set#5 Problem#1...

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