Thermodynamics HW Solutions 648

Thermodynamics HW Solutions 648 - Chapter 8 Internal Forced...

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Unformatted text preview: Chapter 8 Internal Forced Convection 8-36 In fully developed laminar flow in a circular pipe, the velocity at r = R /2 is measured. The velocity at the center of the pipe ( r = 0) is to be determined. Assumptions The flow is steady, laminar, and fully developed. Analysis The velocity profile in fully developed laminar flow in a circular pipe is given by ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = 2 2 max 1 ) ( R r r V V where V max is the maximum velocity which occurs at pipe center, r = 0. At r =R /2, R r 0 V max V ( r )= V max (1- r 2 / R 2 ) 4 3 4 1 1 ) 2 / ( 1 ) 2 / ( max max 2 2 max V V V V = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = R R R Solving for V max and substituting, m/s 8 V V = = = 3 m/s) 6 ( 4 3 ) 2 / ( 4 max R which is the velocity at the pipe center. 8-37 The velocity profile in fully developed laminar flow in a circular pipe is given. The mean and maximum velocities are to be determined....
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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