TABLE P7-81 V, m/s ΔΡ. Νim? 0.5 77.0 1 306 1218 4 4865 6. 10,920 8 19,440 10 30,340 15 68,330 20 121,400 25 189,800 30 273,200 35 372,100 40 485,300 45 614,900 50 758,700 CV P.P (2)

The pressure drop ΔP = P1 − P2 through a long section of round pipe can be written in terms of the shear stress ?w along the wall. Shown in Fig is the shear stress acting by the wall on the fluid. The shaded 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. , 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. 7–81 (Table P7–81), 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? Answers: (a) f = 2 D LEu; (b) yes, 0.0487