Question:hard

A \(0.80\) km\(^2\) agricultural watershed has a slope of \(0.30\%\) and the maximum length of travel of water is \(1\) km. The \(10\)-year maximum depth of rainfall is tabulated below:
Duration (minutes)51020304060
Maximum depth of rainfall (mm)162439506065

Half of the watershed has row crops (runoff coefficient = \(0.40\)), whilst the other half of the watershed has pasture (runoff coefficient = \(0.35\)). The peak flow rate for the watershed (in m\(^3\)/s) for the \(10\)-year return period is ________. (Rounded off to two decimal places)

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Find the time of concentration first, then read intensity from the depth-duration table before applying the Rational method.
Updated On: Aug 6, 2026
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Correct Answer: 7.69

Solution and Explanation

Step 1: Get the time of concentration.
Kirpich's formula gives $T_c(\text{min}) = 0.01947\,L^{0.77}S^{-0.385}$. With $L=1000$ m and $S=0.003$: $L^{0.77}\approx204.2$, $S^{-0.385}\approx9.36$, so $T_c \approx 0.01947\times204.2\times9.36\approx37.2$ min.

Step 2: Interpolate the storm depth at this duration.
Between the $30$ min ($50$ mm) and $40$ min ($60$ mm) rows, the extra $7.2$ min out of $10$ adds $7.2$ mm, so depth $=50+7.2=57.2$ mm, giving intensity $i=57.2\times60/37.2\approx92.3$ mm/hr.

Step 3: Split the watershed by land use instead of averaging first.
Each half covers $0.40$ km$^2 = 40$ ha: row crop ($C=0.40$) and pasture ($C=0.35$).

Step 4: Find the peak contribution of each half separately, then add.
\[ Q_{row} = \frac{0.40\times92.3\times40}{360} \approx 4.10\ \text{m}^3/\text{s} \] \[ Q_{pasture} = \frac{0.35\times92.3\times40}{360} \approx 3.59\ \text{m}^3/\text{s} \] \[ Q_p = Q_{row}+Q_{pasture} \approx 4.10+3.59 = 7.69\ \text{m}^3/\text{s} \]
Final Answer:
Adding the two land-use contributions gives the same peak, close to $7.69$ m$^3$/s. \[ \boxed{Q_p \approx 7.69\ \text{m}^3/\text{s}} \]
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