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Unformatted text preview: v2 2.006F08 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.006 Thermal Fluids II Problem Set 4 Issued: Thursday, February 28, 2008 Due: Thursday, March 6, 2008 Problem 0 Please read the White Chapter 7, review course notes Chapter 9. Problem 1 (SAHG 8.3) Please consider a laminar steady flow past an infinite plate. Now, however, fluid is withdrawn by a steady constant suction through the plate, which is slightly porous. In this case, the boundary layer does not grow with distance along the plate but remains constant, so that ¡ u / ¡ x = . a) Starting with the boundary layer equations, please show that u ( y ) = u 1 ¡ exp ¢ y v £ ¤ ¥ ¦ § ¨ £ ¤ ¥ ¦ § ¨ where ¡ is the constant suction velocity at the plate and is a negative value. b) Please find the displacement and momentum thickness. c) Please find the drag on one side of the plate (the plate length is L). v2 2.006F08 2 Problem 2 Air at 20 C and 1 atmosphere pressure flows through a 0.15 m diameter smooth tube with a center velocity of 8 m/s. a) Assume the logarithmic overlap relation is valid at the center of the pipe. Please use the center velocity of the pipe to iteratively solve for the shear velocity u* in the pipe. b) What is the shear stress at the wall? c) What is the pressure drop per unit length in the pipe? d) Apply the momentum equation to a diskshaped control volume centered on the axis of the pipe using the timeaverage flows in the pipe. Using this model, relate the effective shear stress on the constant radius surface of the disk to the local timeaveraged pressure gradient in the pipe as a function of the radius of the control volume. Please determine the effective shear stress on a constant radius surface as a function of radius for the conditions above. Please graph your result....
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This note was uploaded on 10/06/2011 for the course MECHANICAL 2.006 taught by Professor Blah during the Spring '08 term at MIT.
 Spring '08
 Blah

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