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The drainage discharge of a town of 16 hectares area, consisting of 40% hard paved (k = 0.8), 30% unpaved (k = 0.20), and remaining as wooded (k =0.1), with a max. rain intensity of 5 cm/hr, would be computed by Rational formula, as equal to
- a)0.91 cumecs
- b)0.091 cumecs
- c)9.1 cumecs
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Calculation of Drainage Discharge Using Rational Formula
Given:
Area of town = 16 hectares
Percentage of hard paved area = 40%
Percentage of unpaved area = 30%
Percentage of wooded area = 30%
Maximum rain intensity = 5 cm/hr
Step 1: Calculation of Runoff Coefficient (C)
The runoff coefficient (C) can be calculated using the following formula:
C = (C1 × A1 + C2 × A2 + C3 × A3) / A
Where C1, C2, and C3 are the runoff coefficients for hard paved, unpaved, and wooded areas respectively. A1, A2, and A3 are the areas of hard paved, unpaved, and wooded areas respectively. A is the total area of the town.
Substituting the given values, we get:
C = (0.8 × 40% + 0.2 × 30% + 0.1 × 30%) / 100%
C = 0.42
Step 2: Calculation of Time of Concentration (Tc)
The time of concentration (Tc) is the time taken for the rainwater to travel from the most remote point of the town to the outlet. It can be calculated using the following formula:
Tc = L / V
Where L is the length of the longest flow path and V is the average velocity of flow.
Since the town is assumed to be flat, the length of the longest flow path can be taken as the diagonal of the town. Assuming the town to be square, the diagonal can be calculated as:
Diagonal = √(16 hectares × 10000 m^2/hectare × 4) = 800 m
The velocity of flow can be assumed as:
V = 0.6 × √S
Where S is the slope of the land. Assuming the slope to be 1%, we get:
V = 0.6 × √1% = 0.06 m/s
Substituting the values, we get:
Tc = 800 m / 0.06 m/s = 13333 s
Step 3: Calculation of Design Rainfall Intensity (I)
The design rainfall intensity (I) can be obtained from the rainfall intensity-duration-frequency (IDF) curves for the location. Assuming a maximum rainfall intensity of 5 cm/hr, we can take the design rainfall intensity as:
I = 0.8 × 5 cm/hr = 4 cm/hr = 0.04 m/hr
Step 4: Calculation of Drainage Discharge (Q)
The drainage discharge (Q) can be calculated using the Rational formula:
Q = C × A × I / 3600
Substituting the values, we get:
Q = 0.42 × 16 hectares × 10000 m^2/hectare × 0.04 m/hr / 3600 s/hr
Q = 0.91 cumecs
Therefore, the drainage discharge of the town is 0.91 cumecs.
Given:
Area of town = 16 hectares
Percentage of hard paved area = 40%
Percentage of unpaved area = 30%
Percentage of wooded area = 30%
Maximum rain intensity = 5 cm/hr
Step 1: Calculation of Runoff Coefficient (C)
The runoff coefficient (C) can be calculated using the following formula:
C = (C1 × A1 + C2 × A2 + C3 × A3) / A
Where C1, C2, and C3 are the runoff coefficients for hard paved, unpaved, and wooded areas respectively. A1, A2, and A3 are the areas of hard paved, unpaved, and wooded areas respectively. A is the total area of the town.
Substituting the given values, we get:
C = (0.8 × 40% + 0.2 × 30% + 0.1 × 30%) / 100%
C = 0.42
Step 2: Calculation of Time of Concentration (Tc)
The time of concentration (Tc) is the time taken for the rainwater to travel from the most remote point of the town to the outlet. It can be calculated using the following formula:
Tc = L / V
Where L is the length of the longest flow path and V is the average velocity of flow.
Since the town is assumed to be flat, the length of the longest flow path can be taken as the diagonal of the town. Assuming the town to be square, the diagonal can be calculated as:
Diagonal = √(16 hectares × 10000 m^2/hectare × 4) = 800 m
The velocity of flow can be assumed as:
V = 0.6 × √S
Where S is the slope of the land. Assuming the slope to be 1%, we get:
V = 0.6 × √1% = 0.06 m/s
Substituting the values, we get:
Tc = 800 m / 0.06 m/s = 13333 s
Step 3: Calculation of Design Rainfall Intensity (I)
The design rainfall intensity (I) can be obtained from the rainfall intensity-duration-frequency (IDF) curves for the location. Assuming a maximum rainfall intensity of 5 cm/hr, we can take the design rainfall intensity as:
I = 0.8 × 5 cm/hr = 4 cm/hr = 0.04 m/hr
Step 4: Calculation of Drainage Discharge (Q)
The drainage discharge (Q) can be calculated using the Rational formula:
Q = C × A × I / 3600
Substituting the values, we get:
Q = 0.42 × 16 hectares × 10000 m^2/hectare × 0.04 m/hr / 3600 s/hr
Q = 0.91 cumecs
Therefore, the drainage discharge of the town is 0.91 cumecs.
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The drainage discharge of a town of 16 hectares area, consisting of 40% hard paved (k = 0.8), 30% unpaved (k = 0.20), and remaining as wooded (k =0.1), with a max. rain intensity of 5 cm/hr, would be computed by Rational formula, as equal toa)0.91 cumecsb)0.091 cumecsc)9.1 cumecsd)None of theseCorrect answer is option 'A'. Can you explain this answer?
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