This question was previously asked in

GPSC AE CE 2018 Official Paper (Part B - Civil)

Option 3 : H^{5/2}

ST 22: Geotechnical Engineering

1581

20 Questions
20 Marks
15 Mins

__Concept:__

Weir or notch is a physical structure of masonry constructed across the channel width to calculate the discharge of the channel section.

Rectangular Notch:

The discharge through a rectangular notch weir is,

\(Q = \frac{2}{3}{C_d}L\;\sqrt {2g} \;{H^{3/2}}\)

Where, Q = discharge of fluid, Cd = Coefficient of discharge and H = height of water above the notch

Triangular Notch:

A V-notch weir is also called the triangular notch or weir. The discharge over a triangular weir or notch is given by the:

\(Q = \frac{8}{{15}}{C_d}tan\frac{\theta }{2}\;\sqrt {2g} \;{H^{5/2}}\)

Where, Q = discharge of fluid,

Cd = Coefficient of discharge,

θ = Notch angle and H = height of water above the notch

**From the equation we can see that Q is proportional to H ^{5/2} **

Trapezoidal weir (or) Notch:

\(Q = \frac{2}{3}{C_{{d_1}}}\sqrt {2g} \;LH^{\frac{3}{2}} + \frac{8}{{15}}{C_{{d_2}}}\sqrt {2g} .\tan \frac{\theta }{2}.{H^{\frac{5}{2}}}\)

Where, \(\left( {\frac{\theta }{2}} \right)\) = weir angle of inclination with the vertical.

\({C_{{d_1}}}\) = Coefficient of discharge for rectangular portion.

\({C_{{d_2}}}\) = Coefficient of discharge for the triangular portion.