Derive a relation to evaluate the discharge, Q over a spillway as a function of the water head, H, the depth at the throat, D, the velocity of flow, V, and the gravity acceleration, g. Show that the...

Derive a relation to evaluate the discharge, Q over a spillway as a function of the water head, H, the depth at the throat, D, the velocity of flow, V, and the gravity acceleration, g.

Show that the flow over a rectangular notch can be expressed as

where Q is the discharge, b is the width of the notch, g is the acceleration due to gravity, p is the density, µ, is the fluid viscosity, and
 is the surface tension.