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A 12-hr unit hydrograph of a catchment is triangular in shape with a base width of 144 hours and a peak discharge value of 23 m3/s. This unit hydrograph refers to a catchment of area
- a)756 km2
- b)596 km2
- c)1000 km2
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A 12-hr unit hydrograph of a catchment is triangular in shape with a b...
Unit hydrograph refers to 1 cm of rainfall excess
∴ Let area of catchment = A(km2)
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A 12-hr unit hydrograph of a catchment is triangular in shape with a b...
Given:
- A 12-hr unit hydrograph of a catchment is triangular in shape.
- The base width of the hydrograph is 144 hours.
- The peak discharge value is 23 m3/s.
To find:
- The catchment area.
Solution:
1. Calculate the time of concentration (Tc) using the base width of the hydrograph:
Tc = 0.8 x base width
Tc = 0.8 x 144 hours
Tc = 115.2 hours
2. Determine the time interval (Δt) between ordinates of the hydrograph:
Δt = Tc / 12
Δt = 115.2 / 12
Δt = 9.6 hours
3. Find the area under the hydrograph by multiplying the peak discharge value by the time interval and dividing by 2:
Area = (23 x 9.6) / 2
Area = 110.4 m3
4. Calculate the catchment area (A) using the formula:
A = Area / (0.278 x Tc)
A = 110.4 / (0.278 x 115.2)
A = 595.89 km2
Therefore, the catchment area is approximately 596 km2, which corresponds to option (B).
- A 12-hr unit hydrograph of a catchment is triangular in shape.
- The base width of the hydrograph is 144 hours.
- The peak discharge value is 23 m3/s.
To find:
- The catchment area.
Solution:
1. Calculate the time of concentration (Tc) using the base width of the hydrograph:
Tc = 0.8 x base width
Tc = 0.8 x 144 hours
Tc = 115.2 hours
2. Determine the time interval (Δt) between ordinates of the hydrograph:
Δt = Tc / 12
Δt = 115.2 / 12
Δt = 9.6 hours
3. Find the area under the hydrograph by multiplying the peak discharge value by the time interval and dividing by 2:
Area = (23 x 9.6) / 2
Area = 110.4 m3
4. Calculate the catchment area (A) using the formula:
A = Area / (0.278 x Tc)
A = 110.4 / (0.278 x 115.2)
A = 595.89 km2
Therefore, the catchment area is approximately 596 km2, which corresponds to option (B).
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A 12-hr unit hydrograph of a catchment is triangular in shape with a base width of 144 hours and a peak discharge value of 23 m3/s. This unit hydrograph refers to a catchment of areaa)756 km2b)596 km2c)1000 km2d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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