Question

A 12-h unit hydrograph of a catchment is triangular in shape with a base width of 144h and a peak discharge of 23 cumec. This unit hydrograph refers to a catchment area of

• A. 786 km\(^2\)
• B. 596 km\(^2\)
• C. 900 km\(^2\)
• D. 1200 km\(^2\)

Hint:

Remember that the area under a unit hydrograph must equal 1 cm of runoff depth spread over the whole catchment.

Answer 1

The Correct Option is B

Step 1: A neat way to solve this without converting hours to seconds right away is to work in the unit "cumec-hours," since 1 cumec flowing for 1 hour equals \(3600\ m^3\) of water, and this shortcuts the arithmetic.
Step 2: The triangle's area, in flow times time, is \(\tfrac12 \times 144\ h \times 23\ m^3/s = 1656\) cumec-hours.
Step 3: Convert cumec-hours to cubic metres using \(1\) cumec-hour \(= 3600\ m^3\): \[1656 \times 3600 = 5961600\ m^3\] which is the same runoff volume as before, just reached through a different bookkeeping path.
Step 4: This entire volume is what 1 cm of effective rain would produce over the catchment, so divide by the depth in metres, \(0.01\ m\), to isolate the plan area: \[A = \frac{5961600}{0.01}\ m^2 = 596160000\ m^2\]
Step 5: Since 1 square kilometre holds \(10^6\) square metres, divide once more: \[A = 596.16\ km^2\]
Step 6: Rounding to match the answer choices given, this lands on 596 km\(^2\).\[\boxed{596\ km^2}\]