Average Velocity for Mass Balance in Turbulent Flow. For turbulent flow in a smooth circular tube with a radius of R, the velocity profile varies according to the following expression at a Reynolds number of about 10: 1/7 R v = "max R where r is the radial distance from the center and vma the maximum velocity at the center. Derive the equation relating the average velocity (bulk velocity) v to vmax for an incompressible fluid. (Hint: The integration can be simplified by substituting z for R - r.) 49 Ans. v,, = 60 = 0.817vmax max

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