The equations of gradually varied flow with constant and variable $($spatially varied$)$ flow

are shown below. $($a$)$ Explain what each term in the equations represents. $($b$)$ Indicate the

difference between the two equations.

$\frac{dy}{dx}=\frac{S_o-S_f}{1-\frac{Q^{2}T}{g{A}^3}}=\frac{S_o-S_f}{1-\frac{Q^2}{g{A}^{2}D}}$

$\frac{dy}{dx}=\frac{S_o-S_f-2Q\frac{q_{**}}{g}{A}^2}{1-\frac{Q^2}{g{A}^{2}D}}$

Gradually varied flow

Spatially varied flow