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: Determine the correct discharge formula. The Francis formula is used for calculating discharge \(Q\) over a rectangular weir or spillway crest:\[Q = C \cdot L \cdot H^{3/2}\]In this formula, \(C\) represents the weir coefficient, \(L\) is the crest length, and \(H\) is the water head above the crest.
Step 2: Input the provided values and select a standard coefficient.
- Crest Length, \(L = 1\) m
- Head, \(H = 1\) m
- A typical coefficient \(C\) for a straight inlet drop spillway (rectangular weir) in SI units is approximately 1.77.
Step 3: Compute the discharge.
Insert the values into the formula:\[Q = 1.77 \times 1 \times (1)^{3/2}\]\[Q = 1.77 \times 1 \times 1 = 1.77 \text{ m}^3/\text{sec}\]