At the foot of a spillway, water flows at a depth of 23 cm with a velocity of 8.1 m/s, as shown in the figure

Q. At the foot of a spillway, water flows at a depth of 23 cm with a velocity of 8.1 m/s, as shown in the figure.

The flow enters as an M-3 profile in the long wide rectangular channel with bed slope =  1/1800 and Manning’s n = 0.015. A hydraulic jump is formed at a certain distance from the foot of the spillway. Assume the acceleration due to gravity, g = 9.81 m/s². Just before the hydraulic jump, the depth of flow 𝑦₁ (in m, round off to 2 decimal places) is   

Solution:

Given, At a given section, y = 0.23 m and velocity (v) = 8.1 m/s

q (discharge per unit width) = 8.1 × 0.23 = 1.863 m2/s

Now, For a wide rectangular channel (B ≫≫ y)          

A = B × y

P = B + 2y