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The direct runoff hydrograph of a storm obtained from a catchment is triangular in shape and has a base period of 80 hours. The peak flow rate is 30m3/sec and catchment area is 86.4 km2. The rainfall excess that has resulted the above hydrograph is
  • a)
    5 cm
  • b)
    8 cm
  • c)
    10 cm
  • d)
    16 cm
Correct answer is option 'A'. Can you explain this answer?
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The direct runoff hydrograph represents the flow of water in a river or stream resulting from rainfall events. In this case, the hydrograph is described as triangular in shape, which means that the flow rate increases linearly and then decreases linearly over time. The base period of the hydrograph is given as 80 hours, which is the time it takes for the flow rate to return to zero.

Given:
- Base period (Tb) = 80 hours
- Peak flow rate (Qp) = 30 m3/sec
- Catchment area (A) = 86.4 km2

To calculate the rainfall excess that has resulted in the hydrograph, we can use the following equation:

Rainfall excess (E) = (Qp * Tb) / (A * 3600)

Let's calculate the rainfall excess using the given values:

E = (30 * 80) / (86.4 * 3600)
E = 2400 / 311040
E ≈ 0.0077 m or 7.7 cm

Therefore, the rainfall excess that has resulted in the given hydrograph is approximately 7.7 cm.

Explanation:
- The direct runoff hydrograph is triangular in shape, indicating a linear increase and decrease in flow rate over time.
- The base period of the hydrograph is 80 hours, representing the time it takes for the flow rate to return to zero.
- The peak flow rate is given as 30 m3/sec, indicating the maximum flow rate during the storm event.
- The catchment area is provided as 86.4 km2, representing the area of land draining into the river or stream.
- To calculate the rainfall excess, we use the equation E = (Qp * Tb) / (A * 3600), where E is the rainfall excess, Qp is the peak flow rate, Tb is the base period, A is the catchment area, and 3600 is the conversion factor from seconds to hours.
- Plugging in the given values, we calculate the rainfall excess to be approximately 7.7 cm.
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