Problem $1(20$ points$).$ A two$-$dimensional steady flow in a viscous liquid is described by the equation:

$u\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}=-g(\frac{\text{d}\text{e}\text{l}\text{h}}{\text{d}\text{e}\text{l}\text{x}})+(\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2})$

Find the nondimensional form of this equation using a length scale, $L,$ and a velocity scale, $V_0.$

Hint: the non$-$dimensional quantities will be $x^{**}=\frac{x}{L},y^{**}=\frac{y}{L},h^{**}=\frac{h}{L}$ and $u^{**}=\frac{u}{V_0}.$