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Unformatted text preview: ME 309 Fall 2008 Section 2 Homework # 31 Due Monday 17 November 2008 Problem 31-1 Air at 298 K and one atmosphere pressure flows at a velocity of 5 m/s parallel to a thin flat plate with a well-rounded leading edge. The plate is 400 mm long and has a thickness, h = 7.5 mm . Because of the boundary layer, the flow outside the plate sees a plate that has a larger thickness. a) Calculate the apparent thickness of the plate at a downstream distance of 250 mm. Include the boundary layer on both sides of the plate. (Answer: 10.5 mm. ) b) Find the variation of the shear stress on the wall as a function of x and use this variation to find is the drag on the plate (both sides) from the leading edge to 250 mm ? (For this calculation use the exact value from Table 9.2.) c) Find the drag on the plate (both sides) from the integral momentum equation and the exact value of the momentum thickness. Solution: Assumptions : Incompressible flow, steady, laminar, zero pressure gradient. Analysis: The apparent thickness of the plate will be the plates actual thickness plus the displacement thickness of the boundary layer on either side. From Table A.3, the kinematic viscosity of air at 298 K is 5 10 6 . 1- = . The displacement thickness of a laminar, flat plate boundary layer can be obtained from Table 9.2: 344 ....
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This note was uploaded on 03/09/2010 for the course ME 309 taught by Professor Merkle during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08