Fluid Mechanics seventh edition by Frank M. White · Problem 3.16

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · conservation-of-mass

Problem

An incompressible fluid flows past an impermeable flat plate, as in Fig. P3.16, with a uniform inlet profile

u = U_0

and a cubic polynomial exit profile

u \approx U_0\left(\frac{3\eta - \eta^3}{2}\right) \quad \text{where } \eta = \frac{y}{\delta}

Compute the volume flow

Q

across the top surface of the control volume.