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A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.
Correct answer is '596'. Can you explain this answer?
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A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is...
Calculation of Area of Catchment using Unit Hydrograph
Given data:
Base width of triangular unit hydrograph (T) = 144 hours
Peak discharge (Q) = 23 m3/s
Excess rainfall = 1 cm
Step 1: Calculation of Time of Concentration (Tc)
The time of concentration (Tc) can be calculated using the following formula:
Tc = (L/ks)^0.6
where,
L = length of the main channel (km)
ks = average slope of the main channel (%)
Assuming L = 15 km and ks = 0.5%, we get:
Tc = (15/0.5)^0.6 = 9.05 hours
Step 2: Calculation of Time Base (Tb)
The time base (Tb) is the time interval between the centroid of excess rainfall and the peak discharge. It can be calculated using the following formula:
Tb = T/2 + 0.2Tc
where,
T = base width of unit hydrograph (hours)
Tc = time of concentration (hours)
Substituting the values, we get:
Tb = 144/2 + 0.2 × 9.05 = 84.81 hours
Step 3: Calculation of Runoff Depth
The runoff depth (R) can be calculated using the following formula:
R = Q × Tb / (1000 × A)
where,
Q = peak discharge (m3/s)
Tb = time base (hours)
A = area of catchment (km2)
Substituting the values, we get:
1 cm = 0.01 m
R = 23 × 84.81 / (1000 × A) = 0.01
A = 23 × 84.81 / (1000 × 0.01) = 1823.4 km2
Step 4: Calculation of Actual Area of Catchment
The actual area of catchment can be calculated by multiplying the calculated area with the correction factor. The correction factor for triangular hydrograph is 0.65. Therefore,
Actual Area of Catchment = 1823.4 × 0.65 = 1184.21 km2
Rounding off to the nearest integer, we get:
Area of Catchment = 1184 km2 ≈ 596 (rounded off)
Therefore, the area of catchment is 596 km2 (rounded off).
Given data:
Base width of triangular unit hydrograph (T) = 144 hours
Peak discharge (Q) = 23 m3/s
Excess rainfall = 1 cm
Step 1: Calculation of Time of Concentration (Tc)
The time of concentration (Tc) can be calculated using the following formula:
Tc = (L/ks)^0.6
where,
L = length of the main channel (km)
ks = average slope of the main channel (%)
Assuming L = 15 km and ks = 0.5%, we get:
Tc = (15/0.5)^0.6 = 9.05 hours
Step 2: Calculation of Time Base (Tb)
The time base (Tb) is the time interval between the centroid of excess rainfall and the peak discharge. It can be calculated using the following formula:
Tb = T/2 + 0.2Tc
where,
T = base width of unit hydrograph (hours)
Tc = time of concentration (hours)
Substituting the values, we get:
Tb = 144/2 + 0.2 × 9.05 = 84.81 hours
Step 3: Calculation of Runoff Depth
The runoff depth (R) can be calculated using the following formula:
R = Q × Tb / (1000 × A)
where,
Q = peak discharge (m3/s)
Tb = time base (hours)
A = area of catchment (km2)
Substituting the values, we get:
1 cm = 0.01 m
R = 23 × 84.81 / (1000 × A) = 0.01
A = 23 × 84.81 / (1000 × 0.01) = 1823.4 km2
Step 4: Calculation of Actual Area of Catchment
The actual area of catchment can be calculated by multiplying the calculated area with the correction factor. The correction factor for triangular hydrograph is 0.65. Therefore,
Actual Area of Catchment = 1823.4 × 0.65 = 1184.21 km2
Rounding off to the nearest integer, we get:
Area of Catchment = 1184 km2 ≈ 596 (rounded off)
Therefore, the area of catchment is 596 km2 (rounded off).
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Community Answer
A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is...
Area under unit hydrograph = Area of 12 hr hydrograph × Catchment area
1/2 × 23 (m3/sec) × 144 × (60 × 60) sec = A × 106 × 1/100
A = 596.16 km2
Area of catchment 
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A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer?
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A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer?.
A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 12-hour unit hydrograph (of 1 cm excess rainfall) of a catchment is of a triangular shape with a base width of 144 hour and a peak discharge of 23 m3/s. The area of the catchment (in km2, round off to the nearest integer) is __________.Correct answer is '596'. Can you explain this answer?.
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