Assignment Details:

A V$-$notch weir, is a type of weir characterized by a V$-$shaped opening. The angle of the Vnotch is denoted by $,$ and this weir is typically installed in an open channel. As the fluid approaches the weir, it accumulates upstream before spilling over the notch. The flow rate, or discharge $(Q),$ across the weir is primarily influenced by the water head $(H),$ which is the height of the water upstream. Moreover, the discharge is affected by both the gravitational acceleration $($g$)$ and the approach velocity $(V_0)$ of the fluid. Using the Pi$-$Buckingham method, your task is to derive the general form of the discharge equation that correlates these parameters.

$($Hint: Discharge is the amount of fluid passing over the weir per time $(\frac{m^3}{s}).)$