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Unformatted text preview: Problem # 1 (50 points): Consider the incompressible steady flow of a power law fluid under laminar condition through a vertical pipe of circular cross section (The flow is upward). The pipe radius and length are R and L, respectively. The pressure difference over the pipe length is ∆ P (i.e. outlet pressure minus inlet pressure). It is assumed that the fluid is incompressible, and that the shear stress in this fluid may be described by the following relation z rz du dr τ η ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ where 1 n z du K dr η − ⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠ where z and r are the axial and radial directions, respectively. (a) Using the equation of continuity, show that u z is constant with respect the z direction (15 points). (b) Using the equation of motion, find the velocity profile of the fluid (35 points). Answer: It is appropriate to choose cylindrical coordinate system as shown in the Fig. 1. For one- dimensional flow, u r = u θ = 0....
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas.
- Fall '08