Fluid Mechanics seventh edition by Frank M. White · Problem 3.15

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · conservation-of-mass

Problem

Water, assumed incompressible, flows steadily through the round pipe in Fig. P3.15. The entrance velocity is constant,

u = U_0

, and the exit velocity approximates turbulent flow,

u = u_{\max}(1 - r/R)^{1/7}

. Determine the ratio

U_0/u_{\max}

for this flow.