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

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.