Fluid Mechanics seventh edition by Frank M. White · Problem P3.37

Integral Relations for a Control Volume — Frank M. White

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

Problem

If the rectangular tank full of water in Fig. P3.37 has its right-hand wall lowered by an amount

\delta

, water will flow out as it would over a weir or dam. The outflow

Q

is given by

Q = Cbg^{1/2}\delta^{3/2}

where

b

is the tank width into the paper,

g

is the acceleration of gravity, and

C

is a dimensionless constant. Assume that the water surface is horizontal. Let the initial excess water level be

\delta_o

. Derive a formula for the time required to reduce the excess water level to (a)

\delta_o/10

and (b) zero.