Final answer:
The discharge over a broad-crested weir can be determined using the Francis formula. For a broad-crested profile, the discharge coefficient is determined based on the ratio of the weir width to the head. Substituting the given values into the Francis formula, the discharge over the broad-crested weir is calculated to be 1127.56 ft³/s.
Step-by-step explanation:
The discharge over a broad-crested weir can be determined using the Francis formula:
Q = C * L * H^(3/2)
Where:
- Q is the discharge
- C is the discharge coefficient
- L is the width of the weir
- H is the head of water over the crest
For a broad-crested profile, the discharge coefficient (C) is determined based on the ratio of the weir width (b) to the head (H):
C = 3.33 + 0.21 * (b / H)
Given that the weir is 6 ft wide and the head is 2 ft:
C = 3.33 + 0.21 * (6 / 2) = 3.33 + 0.21 * 3 = 3.33 + 0.63 = 3.96
Substituting the values into the Francis formula:
Q = 3.96 * 100 * (2^(3/2)) = 3.96 * 100 * 2.828 = 1127.56 ft³/s
Therefore, the discharge over the broad-crested weir is 1127.56 ft³/s.