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A triangular DRH due to a storm has a time base of 80 h and a peak flow of 50 m3/s occurring at 20 h from the start. If the catchment area is 144 km2, then the rainfall excess in the storm is ________ cm.
Correct answer is '5'. Can you explain this answer?
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A triangular DRH due to a storm has a time base of 80 h and a peak flo...
(Area under DRH) = (Rainfall Excess) x (Catchment Area)
Area under DRH = Area of triangle = 0.5 x Peak Flow (in m3/s) x Time Base (in seconds)
= 0.5 x 50 x 80 x 60 x 60 = 72 x 105 m3
Catchment Area = 144 km2 = 144 x 106 m2
(Area under DRH) = (Rainfall Excess) x (Catchment Area)
Therefore, Rainfall excess = (72 x 105)/ (144 x 106) = 0.05 m = 5cm
= 0.5 x 50 x 80 x 60 x 60 = 72 x 105 m3
Catchment Area = 144 km2 = 144 x 106 m2
(Area under DRH) = (Rainfall Excess) x (Catchment Area)
Therefore, Rainfall excess = (72 x 105)/ (144 x 106) = 0.05 m = 5cm
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A triangular DRH due to a storm has a time base of 80 h and a peak flo...
To determine the rainfall excess in the storm, we need to calculate the total rainfall and subtract the initial abstraction. Here is the step-by-step explanation:
1. Calculate the total volume of rainfall:
Total volume of rainfall = peak flow * time base
Total volume of rainfall = 50 m3/s * 80 h = 4000 m3
2. Convert catchment area to square meters:
Catchment area = 144 km2 = 144 * 10^6 m2
3. Calculate the average rainfall over the catchment area:
Average rainfall = Total volume of rainfall / catchment area
Average rainfall = 4000 m3 / 144 * 10^6 m2 = 0.0278 m or 2.78 cm
4. Calculate the initial abstraction:
The initial abstraction is the rainfall that is lost due to interception, depression storage, and other losses before runoff starts. Given that the peak flow occurs at 20 h, the initial abstraction can be calculated as follows:
Initial abstraction = average rainfall * 20 h
Initial abstraction = 0.0278 m * 20 h = 0.556 m or 55.6 cm
5. Calculate the rainfall excess:
Rainfall excess = Average rainfall - Initial abstraction
Rainfall excess = 2.78 cm - 55.6 cm = -52.82 cm
6. Interpretation:
The negative rainfall excess value indicates that the initial abstraction is greater than the average rainfall. This means that the storm event did not generate enough rainfall to cause runoff, and all the rainfall was lost through interception, depression storage, and other losses.
However, it is worth noting that the given correct answer is '5' cm, which implies that there might be an error in the calculations or in the given data.
1. Calculate the total volume of rainfall:
Total volume of rainfall = peak flow * time base
Total volume of rainfall = 50 m3/s * 80 h = 4000 m3
2. Convert catchment area to square meters:
Catchment area = 144 km2 = 144 * 10^6 m2
3. Calculate the average rainfall over the catchment area:
Average rainfall = Total volume of rainfall / catchment area
Average rainfall = 4000 m3 / 144 * 10^6 m2 = 0.0278 m or 2.78 cm
4. Calculate the initial abstraction:
The initial abstraction is the rainfall that is lost due to interception, depression storage, and other losses before runoff starts. Given that the peak flow occurs at 20 h, the initial abstraction can be calculated as follows:
Initial abstraction = average rainfall * 20 h
Initial abstraction = 0.0278 m * 20 h = 0.556 m or 55.6 cm
5. Calculate the rainfall excess:
Rainfall excess = Average rainfall - Initial abstraction
Rainfall excess = 2.78 cm - 55.6 cm = -52.82 cm
6. Interpretation:
The negative rainfall excess value indicates that the initial abstraction is greater than the average rainfall. This means that the storm event did not generate enough rainfall to cause runoff, and all the rainfall was lost through interception, depression storage, and other losses.
However, it is worth noting that the given correct answer is '5' cm, which implies that there might be an error in the calculations or in the given data.
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A triangular DRH due to a storm has a time base of 80 h and a peak flow of 50 m3/s occurring at 20 h from the start. If the catchment area is 144 km2, then the rainfall excess in the storm is ________ cm.Correct answer is '5'. Can you explain this answer?
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