Question

For a straight inlet drop spillway with 1 m crest length and 1 m head above the crest, the discharge capacity will be:

• A. 1.0 m\(^3\)/sec
• B. 1.5 m\(^3\)/sec
• C. 1.77 m\(^3\)/sec
• D. 2.0 m\(^3\)/sec

Hint:

The formula \( Q = C \cdot L \cdot H^{3/2} \) is fundamental for calculating flow over weirs. The main challenge is choosing the correct coefficient \(C\), which depends on the weir's shape and flow conditions. For a standard rectangular weir, \(C \approx 1.77-1.84 \) is a good estimate.

Answer 1

The Correct Option is C

Step 1: Identify the appropriate formula for discharge. The discharge \(Q\) over a rectangular weir or spillway crest can be calculated using the Francis formula: \[ Q = C \cdot L \cdot H^{3/2} \] where \(C\) is the weir coefficient, \(L\) is the length of the crest, and \(H\) is the head of water above the crest.
Step 2: Assign the given values and a standard coefficient.
- Crest Length, \(L = 1\) m
- Head, \(H = 1\) m
- For a straight inlet drop spillway (rectangular weir), a standard value for the coefficient \(C\) in SI units is approximately 1.77.
Step 3: Calculate the discharge.
Substitute the values into the formula: \[ Q = 1.77 \times 1 \times (1)^{3/2} \] \[ Q = 1.77 \times 1 \times 1 = 1.77 \text{ m}^3/\text{sec} \]