Hydraulic theory

The simplified momentum equation is:

$${\frac{d u}{d x}} {\frac{d h}{d x}} {\frac{d e}{d x}} {\frac{1}{\rho_1}} {\frac{d P}{d x}} {\frac{1}{\rho_1}} {\frac{d\tau}{dz}}$$ (1)

The equation of continuity in the gap wind is:

$$\overline{b}$$ (2)

Define S_P = - (g'$\rho_{1}^{}$)^-1dP/dx. Parameterize friction as:

$${\frac{1}{\rho_1}} {\frac{d\tau}{dz}} \simeq {\frac{-1}{\rho_1}} {\frac{\tau_{s}}{h}} {\frac{-C u^{2}}{h}}$$ (3)