The following figure shows a 2-hour unit hydrograph (1 cm rainfall excess) for a catchment area of 540 hectare. Find the peak discharge (in m /s, rounded to one decimal place).
Official Solution
Correct Option: (1)
A unit hydrograph of 1 cm rainfall excess must satisfy: Convert the catchment area: Rainfall excess depth: Thus total runoff volume:
Hydrograph shape: It is a triangle: - Rising limb: 1 hour
- Falling limb: 2 hours
- Total base = 3 hours Let peak discharge = . Area of triangular hydrograph:
Convert base time to seconds:
Thus:
Rounded to one decimal:
A trapezoidal canal lined with cement concrete ( ) is designed to carry a discharge of 20 m /s at a bed slope 1 in 400. The bed width is twice the depth of flow and side slope of the canal section is 2 (1 vertical : 2 horizontal). The corresponding depth of flow will be ............. (in m, rounded off to two decimal places).
Official Solution
Correct Option: (1)
Step 1: Recall Manning’s equation. where, = discharge (m /s), = Manning’s roughness coefficient, = flow area (m ), = hydraulic radius (m), = wetted perimeter (m), = bed slope. Step 2: Define section geometry. Let depth of flow = . - Bed width = . - Side slope = 2H:1V → horizontal projection = . Thus, Step 3: Wetted perimeter. Two side lengths = . Step 4: Hydraulic radius.
Step 5: Substitute values into Manning’s equation. Given: . Step 6: Solve for depth. Raise both sides to power : Final Answer:
