The discharge over a rectangular notch is 

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  1. inversely proportional to H3/2
  2. directly proportional to H3/2
  3. inversely proportional to H5/2
  4. directly proportional to H5/2

Answer (Detailed Solution Below)

Option 2 : directly proportional to H3/2
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Detailed Solution

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Explanation:

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

Rectangular Notch:

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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

Trapezoidal weir (or) Notch:

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

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.

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