Question

Calculate the approximate specific energy of a trapezoidal channel having a bottom width of 6 metres, ratio of side slopes is 1: 1 and the depth of flow at a discharge speed of 15 cubic metres per second is 1.5 metres.

1. 2.6
2. 1.6
3. 3.6
4. 4.6

Answer 1

Correct Answer - Option 2 : 1.6

Concept:

Specific Energy is given by:

\(E = y + \frac{{{V^2}}}{{2g}} = y + \frac{{{Q^2}}}{{2g{A^2}}}\)

where,

y = Depth of flow

Q = Discharge of flow

A = Area of cross-section

V = Velocity of flow

and, 

Area of cross section of trapezoidal section is given by:

A = By + my²

where, 

B = Bottom width of channel

m = Side slope of channel 

Calculation:

Given Data:

y = 1.5 m

Bottom width, B = 6 m

Q = 15 m³/sec

Side slope, m = 1

Let's find area of the cross section from the above formula 

A = (6 × 1.5) + (1 × 1.5²) = 11.25 m²

Now, Putting all these data in Specific Energy formula, we get,

\(E = 1.5 + \frac{{{{15}^2}}}{{2 \times 9.81 \times {{11.25}^2}}} = 1.591\;m = 1.6\;m\)