Engr Help

Open Channel Flow - Uniform Flow

Example: A rectangular channel, made of finished concrete, is 1.25 meters wide and has a

downward slope of 0.01. Determine the depth for equilibrium flow if the discharge is 0.8 m³/sec,

the critical depth, and the Froude number. Is the slope mild or steep? Is the flow subcritical or

supercritical?

Strategy: Apply Manning's equation. Q = (K/n) A R_H^2/3 S_o ^1/2

Data: From tables: n = 0.012 for finished concrete

Q = 0.8 m³ / sec, K = 1.0 for metric units

A = 1.25 y_N , wetted perimeter = 1.25 + 2 y_N, R_H = 1.25 y_N / ( 1.25 + 2 y_N )

0.8 = (1 / 0.012 ) (1.25 y_N ) [1.25 y_N / ( 1.25 + 2 y_N ) ]^2/3 (0.01)^1/2

Solution for y_N is by iteration since y_N is a complicated algebraic expression.

After several iterations: y_N = 0.23 m is the equilibrium depth.

The critical depth, y_c = (q²/g)^1/3 where q = Q/w = 0.8/1.25 m²/sec and g = 9.8 m/sec²

y_c = 0.35 m (result) Since y_N < y_c the slope is mild (result)

Now A V = Q, (0.23)(1.25)(V) = 0.8 So V = 2.78 m/sec

Froude Nb = V/√( gy_N ) = 2.78 / √ (9.8)(0.23) = 1.85 m/sec (result)

Since the Froude Nb > 1, the flow is supercritical. (result)