Calculation of Normal Depth for Uniform Open Channel Flow

Using the Manning Equation

1. Trapezoidal Channel Calculations:

Inputs Calculations

Bottom width, b = 6 m 6.393 mp

Manning roughness, n = 0.011

Channel bottom slope, S = 0.0003 m/m Iterative (trial & error) Solution:

Side Slope, z = 2

(horiz:vert = z:1)

1 6.218

Volumetric Flow Rate, Q = 15 mc 2 28.596

1.5 14.859

1.1 7.591

1.01 6.348

1.02 6.479

Q*n/(1.49*S1/2) =

A*R2/3 = (3yo + 2yo2)*{(3yo + 2yo

2)/[3 + 2yo(1 + 22)]1/2}2/3

yo ,m (3yo + 2yo2)*{(3yo + 2yo

2)/[3 + 2yo(1 + 22)]1/2}2/3

NOTE: In this example the value of yo, correct to 3 significant figures is 1.01 m

NOTE: For a trapezoidal channel: A*R2/3 = (3yo + 2yo2)*{(3yo + 2yo

2)/[3 + 2yo(1 + 22)]1/2}2/3