Roughness in the remaining panels will be calculated as a specified proportion
of ks for the Manning, Strickler, and Keulegan equations. The iterative solution
for ks uses the secant method for convergence as follows.
f ( X2)
( X2 - X1)
X 3= X 2 -
Equation 2-37
)- f ( X 1 )
f(
X2
where
X1 = is the first trial value of ks
f(X1) = is the difference between Qtrue and the calculated Q for X1
X2 = is the second trial value of ks
f(X2) = is the difference between Qtrue and calculated Q for X2
X3 = is the next trial value of ks.
Of the several equations for hydraulic roughness, the Strickler equation is the
most likely to converge. The Limerinos, Brownlie, and grass equations are
independent of ks and therefore cannot be used to solve for ks. This algorithm is
primarily intended for use with equations using ks. Expect convergence
problems with other equations.
Water Discharge Calculation
This option allows the water discharge to become the dependent variable in
the uniform flow equation.
Q = f (Q,W, D, z, S)
Equation 2-38
This calculation, like the other solutions of the uniform flow equation which
involve compositing, is trial and error. It also uses the secant method for
convergence. When convergence fails, assume a range of discharges and use the
normal depth calculations to arrive at the correct value.
Riprap Size for a Given Velocity and Depth
When flow velocity and depth are known, the riprap size is calculated using
the following equation, taken from EM 1110-2-1601(1991,1994):
30
Chapter 2
Theoretical Basis for SAM.hyd Calculations
Previous Page
