Question

The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the CCA is 140 days. Watering depth for the crop is 40 cm. The outlet discharge (in \(m^3/s\)) lies between

• A. 3 and 4
• B. 13 and 14
• C. 23 and 24
• D. 33 and 34

Hint:

Find duty from D = 8.64B/delta, then divide the CCA by the duty to get the discharge.

Answer 1

The Correct Option is A

This is a direct application of the duty-delta-base period relation used to size a canal outlet. Duty $D$ tells us how large an area, in hectares, a flow of one cumec run continuously for the whole base period can water to the specified depth. Once we know $D$, dividing the total command area by it gives the discharge needed.

1. Get delta in consistent units: the watering depth is given as 40 cm, which is 0.4 m. The base period is $B=140$ days.
2. Use $\Delta=8.64B/D$: rearranged, $D=8.64B/\Delta=8.64(140)/0.4$. Working the numerator first, $8.64\times140=1209.6$, then $1209.6/0.4=3024$ ha per cumec.
3. Convert CCA into a required discharge: $Q=\text{CCA}/D=10000/3024$, which comes to about $3.307\ m^3/s$.
4. Check the options: '3 and 4' fits 3.307 exactly. The bands '13 and 14', '23 and 24', '33 and 34' would only be reached if the duty were far smaller, around 300 to 700 ha/cumec, not consistent with a fairly long base period of 140 days and a moderate depth of 0.4 m.

So the discharge works out to roughly $3.31\ m^3/s$, falling between 3 and 4.

Let's summarize:

• Duty from delta and base period: $D=8.64B/\Delta=3024$ ha/cumec.
• Discharge from CCA and duty: $Q=\text{CCA}/D\approx3.31\ m^3/s$.

The correct option is (A): 3 and 4.