HEC-RAS has the option for using Hager's weir equation for lateral weirs. The equation is the same as the standard weir equation, except the weir discharge coefficient is computed automatically based on physical and hydraulic properties. Hager's equation for the lateral discharge coefficient is (Hager, W. H., 1987):

1) \displaystyle C= \frac{3}{5} C_0 \sqrt{g} \left[ \frac{1-W}{3-2y-W} \right] ^{0.5} \left\{ 1-( \beta + S_0 ) \left[ \frac{3(1-y)}{y-W} \right] ^{0.5} \right\}
SymbolDescriptionUnits

W

\displaystyle \frac{h_w}{H_t +h_w}


y

\displaystyle \frac{H+ h_w}{H_t + h_w}


C_0

Function (weir shape)

H

Height of the water surface above the weir

h_w

Height of the weir above the ground

H_t

Height of the energy grade line above the weir

S_0

Average main channel bed slope

\beta

Main channel contraction angle in radians (zero if the weir is parallel to the main channel)



C_0 =Base Discharge coefficient. C_0 = 1.0 for a sharp crested weir. C_0 = 8/7 for a zero height weir.

For a broad crested weir (b = weir width):

\displaystyle C_0 =1- \frac{2}{9 \left[ 1 + \left( \frac{H_t}{b} \right) ^4 \right]}

For round or ogee crested weirs (r = weir radius):

\displaystyle C_0 = \frac{\sqrt{3}}{2} \left[ 1 + \frac{\frac{22}{81} \left( \frac{H_t}{r} \right)^2}{1 + \frac{1}{2} \left( \frac{H_t}{r} \right) ^2} \right]