Cantaloup, Let me know where I am messing it up
I got a critical depth of 5.4' from app 19.D CERM
and angle of 285 deg
solving for V gives me 11.5 ft/sec
This problem is taken from Schaum's 2500 Hydraulics Solved Problems
Crit D = 5.4 ft is correct.
Now we gotta find V, we already have Q so we want to find A since V=Q/A
d/D = 5.4/8=0.68
Appendix 16A CERM, with d/D= 0.68 give
A/D^2 = 0.569 so A=0.569*8^2 = 36.4 ft^2
V=450/36.4=12.4 fps
So A is correct
Now use App 16A to find hydraulic radius R with d/D=0.68:
R/D = 0.294 So R= 2.35 ft
Now use Appendix 19B nomograph to find S with n=0.013 (concrete pipe) and V=12.4 fps and hydr. radius = 2.35 ft
S=0.0037; therefore C is correct
Instead of using the nomograph I use HP33s to solve for S with the equation solver:
V=1.486/N*R^0.667*S^0.5
and get the result S = 0.0038 , very close
Note: when we encounter Critical depth problem, we have to know if it's rectangular x-section or pipe flow
the formula Vcrit = SQRT(g*Ycrit) is for rectangular x-section