Question

1. Numerically solve for the normal depth using either MS-Excel or Matlab. Hint: your spreadsheet for critical depth in HW3 is a good place to start.

14.13 (a) only

Spreadsheet from HW 3:

Manning:

Answer 1

Hi,

Solution as follows:

Given Data:

· Manning’s roughness coefficient for rock cut channel = 0.035

· Bed Width B = 3.5 m

· Longitudinal Slope S = 0.2% = 0.002

· Side Slope = 30ᵒ

· Discharge Q = 22 m3/sec

Discharge from a channel given by Manning’s equation:

Where

Q= Discharge (m3/sec)

A = Cross sectional Area of flow (m2)

R = Hydraulic Radius (m) = A/P

P = Wetted Perimeter (m)

S = Longitudinal Slope (m/m)

n = Manning’s Roughness

Assume the normal depth of flow = y

Top Width W = B+ 2a

Wetted Perimeter P = B+2l

Hydraulic Radius (R) = A/P

For various depths of y, flow calculated in below table:

Accordingly graph is plotted below:

From graph,

Normal depth for a flow of 22 m3/sec = 2.71 m