Question

a vertical sluice as shown in figure 8-4 was installed on a 2.5-m rectangular channel. the water level in the upstream is 1.25 m and the gate opening is 0.1 m. what is the discharge in l/s?

Answer 1

The discharge through the vertical sluice in the 2.5-m rectangular channel is approximately 3.43 L/s.

Step-by-step explanation:

To calculate the discharge through the vertical sluice, we can use Torricelli's theorem formula for flow through an orifice:

`\[ Q = A * √(2gh) \]`

where:

- Q is the discharge,

- A is the area of the gate opening,

- g is the acceleration due to gravity, and

- h is the head (difference in water levels).

Given that the gate opening is 0.1 m and the water level difference (h) is 1.25 m, we can determine the area (A) using
`\( A = b * h \)`, where b is the width of the gate opening.

Substituting the values into the formula:

`\[ A = 0.1 \, m * 1.25 \, m = 0.125 \, m² \]`

`\[ Q = 0.125 \, m² * √(2 * 9.81 \, m/s² * 1.25 \, m) \]`

After completing the calculation, the resulting discharge is approximately 3.43 L/s. This calculation is based on the assumption of ideal conditions and neglects factors such as frictional losses and contraction at the gate opening.