$1($a$).$ The volumetric flow or discharge $Q$ over a triangular notch with angle $2$ for a head $H$ is given

by $Q=C_m\sqrt[\phantom{2}]{2g}tan.H^m.$ See Fig. If the coefficient of discharge $C_m$ over the notch is dimensionless,

what should be the value of $m?$ What is the increase in the discharge if the head over the notch is

doubled? It is said that the dimensionless coefficient remains the same irrespective of the system of

units chosen. Show that this is indeed the case for the discharge over the notch.