For the Cipolletti weir, derive the slope (1/4:1) of the sides of the trapezoid

What is the method to derive the slope of the sides of the trapezoid for the Cipolletti weir?

To derive the slope (1/4:1) of the sides of the trapezoid for the Cipolletti weir, we need to set the reduction in discharge due to contraction equal to the increase in discharge due to the triangular area added.

Calculation:

Given: Reduction in discharge due to contraction = Increase in discharge due to the triangular area added Therefore, slope = 1/4:1 This means that for every 1 unit of reduction in discharge due to contraction, there is a corresponding 4 units increase in discharge due to the triangular area added on the sides of the trapezoid.

To determine the discharge observed at a v-notch weir, we use the following formula: Q = 4.28Ctan(∅/2) (h + k)^5/2 Where: Q = Discharge C = Discharge coefficient ∅ = Notch angle (in degrees) h = Head above the weir k = Head correction factor We substitute the given values into the formula: Q = 4.28 × 1 × tan(90/2) (3)^5/2 Q = 4.28 × 1 × 1 × 15.5884 Q = 66.7 in³/s Therefore, the discharge observed at a v-notch weir with the given conditions is 66.7 in³/s.

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