Cress Help -
Flow - Open channel flow - A18.3
Cress Help -
Flow - Open channel flow - A18.3
Trapezoidal profile
The average flow velocity in a prismatic flow profile at equilibrium
depth is given by the equation of Chézy:
Moreover for a trapezium-shaped flow profile with a flat bottom:
in which:
If an equilibrium depth must be substituted for h (if backing up are negligible),
this can be determined with the following formulas. If the equilibrium depth in unknown this can be determined by the
following iterative method from:
When the roughness C is unknown the equilibrium depth can be estimated with the aid of two water depth measurements
hx-Δx and hx+Δx and the equation of Bélanger, if hx/B << 1 :
in which:
The value for C can then again be determined from the previous equation.
Following this:
For the limit depth (critical flow; Froude-number = 1) :
A: area of flow profile [m2]
bb: width of the flat bottom [m]
C: roughness coefficient according to Chézy [m½/s]
h: depth of flow profile [m]
i: hydraulic gradient [-]
m: cot α [-], with α = angle of slope [°]
Q: flow rate [m3/s]
R: hydraulic radius [m]
u: depth averaged flow velocity [m/s]
B: breath of the flow profile (by approximation: water level) [m]
he: equilibrium depth [m]
hg: limit depth [m]
hx: Width at average water depth at location x [m]
hx+Δx: width at average water depth at location x+Δx [m]
hx-Δx: width at average water depth at location x-Δx [m]
ib: slope of the bottom [-]
