A Newtonian fluid flows in the annular space created by a concentric pipe and rod moving to the right at a constant velocity V (this could be the configuration of a wire coating process). The flow is the result of the shear stress created by the moving rod. The flow is steady and incompressible. Assume u, is only a function of r, both u, and ug (as well as their derivatives) are zero, the pipe is horizontal, and the pressure gradient in the z direction is constant. Derive an expression for the velocity profile uz as a function of r. Note: Rois the inside radius of the outer pipe and R; is the radius of the moving rod. Ro R; V
A Newtonian fluid flows in the annular space created by a concentric pipe and rod moving to the right at a constant velocity V (this could be the configuration of a wire coating process). The flow is the result of the shear stress created by the moving rod. The flow is steady and incompressible. Assume u, is only a function of r, both u, and ug (as well as their derivatives) are zero, the pipe is horizontal, and the pressure gradient in the z direction is constant. Derive an expression for the velocity profile uz as a function of r. Note: Rois the inside radius of the outer pipe and R; is the radius of the moving rod. Ro R; V
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A Newtonian fluid flows in the annular space created by a concentric pipe and rod moving to the
right at a constant velocity V (this could be the configuration of a wire coating process). The
flow is the result of the shear stress created by the moving rod. The flow is steady and
incompressible. Assume u, is only a function of r, both u, and ue (as well as their derivatives)
are zero, the pipe is horizontal, and the pressure gradient in the z direction is constant. Derive
an expression for the velocity profile uz as a function of r. Note: R, is the inside radius of the
outer pipe and R; is the radius of the moving rod.
R.
R;
V
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