Question

A rectangular channel 6m wide by 1m deep is lain on slope of 0.001 and has roughness coefficient of n = 0.013.

What is the mean velocity of flow (m/s) when the canal is full?

What is the maximum capacity of the channel in m³/s?

If the most efficient rectangular section is used, what depth of canal is required for the same discharge, slope, and roughness coefficient?

Answer 1

A rectangular channel is given having the following parameters:

Width of the channel, B = 6 m

Depth of the channel, y = 1 m

The slope of the channel, s = 0.001

Manning's Roughness Coefficient, n = 0.013

• (a). The mean velocity of flow when the canal is full:

Using Manning's Formula, the mean velocity of the channel is given as:

where, v is the velocity in 'm/s'.

R is the Hydraulic Radius in 'm' and is given as the ratio of Area and Perimeter.

Area, A of the channel when the canal is full = B.y = 6*1 = 6 m2.

The perimeter, P of the channel when the canal is full = B+2y = 6 + 2*1 = 8 m.

i.e. R = 6/8 = 0.75 m

So, the velocity is given as:

• (b). Maximum Capacity of the channel:

• (c). Most efficient rectangular channel:

A channel is considered to be most efficient if it can pass the same discharge keeping the wetted area (A), the slope (s), and roughness coefficient (n) constant.

As per Manning's:

For maximum discharge, the perimeter should be minimum

for rectangular section Area, A = B.y, from here we get;

perimeter P = B+2y, put B from the above we get,

For minimum Perimeter,

{keeping Area as constant}

Hence, we got for the most efficient channel, the width of the rectangular section should be twice the depth of the rectangular section.

So, Area of the most efficient rectangular section will be

The perimeter of the most efficient rectangular section will be

Hydraulic Radius will be

Using Manning's Equation;

On putting all the values;

So, the depth of the most efficient rectangular section to carry the same discharge of 12.048 m3/s will be;