Fluid Mechanics seventh edition by Frank M. White · Problem P3.18

Integral Relations for a Control Volume — Frank M. White

Physics — Fluid Mechanics · continuity-equation-control-volume

Problem

An incompressible fluid flows steadily through the rectangular duct in Fig. P3.18. The exit velocity profile is given approximately by

u = u_{\max}\left(1 - \frac{y^2}{b^2}\right)\left(1 - \frac{z^2}{h^2}\right)

(a) Does this profile satisfy the correct boundary conditions for viscous fluid flow? (b) Find an analytical expression for the volume flow

Q

at the exit. (c) If the inlet flow is 300 ft

^3

/min, estimate

u_{\max}

in m/s for

b = h = 10

cm.