$5\mathrm{.}11$ A small sharp crested triangular weir with a half angle $(\frac{}{2})$ of $15$ is calibrated in a laboratory. The actual discharge, $Q_A$ over the weir is measured by collecting a known mass $(M)$ of water in a time, $T.$ The corresponding head over the weir crest, $H,$ is as shown below. $($a$)$ Plot a graph of $Q_A$ against $H^{\frac{5}{2}}$ and use it to calculate the average value of the coefficient of discharge. $($b$)$ Plot a graph of $log{Q}_A$ against $logH$ and use it to evaluate $($i$)$ the exponent of the discharge equation; $($ii$)$ the constant of the discharge equation; and $($iii$)$ the corresponding coefficient of discharge.

$[($a$)0\mathrm{.}64$ ; $($b$)($i$)2\mathrm{.}41$ ; $($ii$)0\mathrm{.}317$ so

$[$:$Q_A=0\mathrm{.}317H^{2\mathrm{.}41}$; $(iii)0\mathrm{.}50$