The pressure drop ?P = P1 - P2 through a long section of

Chapter 7, Problem 96P

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Problem 96P

The pressure drop ∆P = P1 - P2 through a long section of round pipe can be written in terms of the shear stress τw. along the wall. Shown in Fig. P7-99 is the shear stress acting by the wall on the fluid. The shaded blue region is a control volume composed of the fluid in the pipe between axial locations 1 and 2. There are two dimensionless parameters related to the pressure drop: the Euler number Eu and the Darcy friction factor f, (a) Using the control volume sketched in Fig. P7-99, generate a relationship for f in terms of Eu (and any other properties or parameters in the problem as needed). (b) Using the experimental data and conditions of Prob. 7-86 (Table P7-86), plot the Darcy friction factor as a function of Re. Does f show Reynolds number independence at large values of Re?. If so. what is the value of f at very high Re?

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