Problem $7$

A $\frac{1}{16}$ th $-$scale model of a weir has a measured flow rate of $Q=2\mathrm{.}1f\frac{t^3}{s}$ when the upstream water height is $h=6\mathrm{.}3in.$ The flow rate is known to be a function of the acceleration due to gravity, g$,$ the weir width $($into the page$),$ b$,$ and the upstream water height, h$.$ Furthermore, the flow rate is found to be directly proportional to the weir width, $b.$

a$)$ Rewrite the functional relationship in dimensionless form.

Governing Equation$($s$)$

b$)$ What is the flow rate over the prototype weir when the upstream water height is $h=3\mathrm{.}2ft.$