-Open Channel Flow:

My solution:
(T * Q^2) / (g * A^3) = 1
for rectangulare channel T=B, q=Q/B=Q/T
therefore solving the above equation for yc
yc = (q^2 / g)^(1/3)
yc = ((50/5)^2 / 9.81)^(1/3) = 2.17 m
For reach 1,
Q = (1/n) * A * R^(2/3) * S^(0.5)
50 = (1/0.015) * 5 * yn1 * ((5*yn1) / (5+(2*yn1)))^(2/3) * (0.001^0.5)
solve for yn1, where it founded to be 3.65 m
For reach 2,
50 = (1/0.015) * 5 * yn2 * ((5*yn2) / (5+(2*yn2)))^(2/3) * (0.01^0.5)
solve for yn1, where it founded to be 1.55 m
I need to sketch the water surface profile and define the type of profiles.