onlinechannel_04:   Critical slope in a prismatic open channel

Formulas


Q = (k/n) AR2/3S1/2
Q2 = (k/n)2 A2 R4/3S
R = A/P
Q2 = [(k/n)2 A10/3 S] / P4/3
S = (Q2 P4/3) / [(k/n)2 A10/3]
F = V/(gD)1/2
F2 = V2/(gD)
V = Q/A
V2 = Q2/A2
D = A/T
F2 = (Q2T) / (gA3)
At critical flow:     F2 = 1
Q2T = gA3
S = (Q2 P4/3) / [(k/n)2 A3 A1/3]
S = (g T Q2 P4/3) / [g T (k/n)2 A3 A1/3]
Sc = (g Pc4/3) / [Tc (k/n)2 Ac1/3]
S = (g Pc4/3) / [Tc (k/n)2 Rc1/3 Pc1/3]
Sc = [g (Pc/Tc)] / [(k/n)2 Rc1/3]
Sc = g n2 (Pc/Tc) / (k2 Rc1/3)
In SI Units:

Sc = 9.81 n2 (Pc/Tc) / Rc1/3


In U.S. Customary Units:

Sc = 32.17 n2 (Pc/Tc) / (1.4862 Rc1/3)