Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at thesame speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flowvelocity is given by(1-2/2).v (7) = vo20where 20 is a known constant. Here, the direction of the flow is along the axis of the pipe, and risthe usual radial coordinate in cylindrical coordinates.Use the "fluid flow analogy" of Section 22.2 in your textbook to calculate the total volume flow rate,through the pipe. Note that when the velocity is constant the answer is just . A, as given inthe textbook. Now, however, the velocity must be integrated over the surface aready twwwBugunŨ2006ĐÃ,Söwhich is mathematically identical to the definition of electric flux.Express your answer algebraically in terms of the quantities given: vo and R.NOTE: to enter answers algebraically, use the equation editor denoted by √ in the menu. Figure 12.29K&HR↑rCross section of acylindrical pipeU VS. rVelocity profile for a viscous fluid in a cylindrical pipe.FThe velocity profile forviscous fluid flowing inthe pipe has a parabolic shape.

Name: Consider a flow through a pipe - see Figure 12.29 in your textbook. N
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Description: Consider a flow through a pipe - see Figure 12.29 in your textbook. Not all the fluid moves at thesame speed, but the fluid at the center moves faster. In a cylindrical pipe of radius R, the flowvelocity is given by(1-2/2).v (7) = vo20where 20 is a