Question
Please answer all parts as they are asked PLEASE As shown below, a Newtonian fluid is inside a horizontal pipe with a diameter of D.
Please answer all parts as they are asked PLEASE
As shown below, a Newtonian fluid is inside a horizontal pipe with a diameter of D. A thin rod with a diameter d is pulled at a constant velocity inside the pipe and fluid is flowing from left to right at a steady state rate and is assumed to be fully developed. If the wire is at the center of the pipe, find the answer to the following questions: a- Sketch the velocity profile inside the pipe, choose the coordinate, and identify the velocity components. b- Start with the Newton's second law of motion and determine each component of the equation. c- If the velocity of the wire is U and the pipe is stationary, determine the shear stress (or the momentum flux) as a function of radial position. d- What is the shear stress at the pipe wall? e- What is the velocity profile inside the pipe? Compare your sketch with the calculated velocity profile (draw the velocity profile with excel and attach the plot). f- Determine the fluid rate of deformation as a function of radial location. g- What is the maximum fluid velocity within the pipe? Newtonian fluid
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