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Canal discharge for dry and wet crops

Short answer

Dry-season discharge is 8.27 m³/s, wet-season discharge is 11.78 m³/s. Seasons do not overlap, so canal discharge is 11.78 m³/s.

Compute the flow discharge needed of a canal to irrigate dry season crops in 20000 ha and wet season crops in 30000 ha. Kor period and kor depth for dry and wet season crops are 5 weeks, 12.5 cm and 4 weeks, 9.5 cm respectively.

Formula: Q=A dT×86400Q = \dfrac{A\,d}{T\times 86400} with AA in m2^2, dd in m and TT in days.

Dry-season crops: A=20000A = 20000 ha =2×108= 2\times10^8 m2^2, T=5×7=35T = 5\times7 = 35 days, d=0.125d = 0.125 m

Qdry=2×108×0.12535×86400=8.267 m3/sQ_{dry} = \frac{2\times10^8\times 0.125}{35\times 86400} = 8.267\ \text{m}^3/\text{s}

Wet-season crops: A=30000A = 30000 ha =3×108= 3\times10^8 m2^2, T=4×7=28T = 4\times7 = 28 days, d=0.095d = 0.095 m

Qwet=3×108×0.09528×86400=11.781 m3/sQ_{wet} = \frac{3\times10^8\times 0.095}{28\times 86400} = 11.781\ \text{m}^3/\text{s}

The two seasons do not overlap, so the canal is designed for the larger discharge.

Answer: canal discharge = 11.78 cumec (wet season governs; dry season needs 8.27 cumec).

✓ Answer checked by Claude Opus 5.5 (high effort)

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