An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare of cropped area. The estimated canal losses are 50 % of the head discharge. The duty (in hectare/cumec) on capacity of this canal is

Question

What is the CORRECT match between the air pollutants and treatment techniques given in the table

Air Pollutants		Treatment techniques
P	NO₂	i	Flaring
Q	SO₂	ii	Cyclonic separator
R	CO	iii	Lime scrubbing
S	Particles	iv	NH₃ injection

Answer 1

This problem has two different discharges in play: the discharge that finally reaches the crop (field discharge) and the discharge the canal must carry at its head (capacity), and the difference between them is exactly the stated 50% conveyance loss. Duty can be reported against either discharge, and the question specifically wants duty against capacity.

Start with the duty measured at the field, since 10 cumec is the flow that meets the crop's peak demand of 7500 hectares:

\[ \text{Duty at field} = \frac{7500 \text{ ha}}{10 \text{ cumec}} = 750 \text{ ha/cumec} \]

Now relate the field discharge to the head (capacity) discharge. The canal loses 50% of its head discharge on the way to the field, so only the remaining 50% arrives as field discharge:

\[ Q_{field} = (1 - 0.5) \, Q_{head} = 0.5\, Q_{head} \]

Since $Q_{field} = 10$ cumec, this gives $Q_{head} = 10 / 0.5 = 20$ cumec. The head discharge is double the field discharge here because exactly half of it is lost in transit.

Duty is inversely proportional to the discharge used for a fixed area, so doubling the discharge (from field to head) halves the duty figure:

\[ \text{Duty on capacity} = \text{Duty at field} \times \frac{Q_{field}}{Q_{head}} = 750 \times \frac{10}{20} = 750 \times 0.5 = 375 \text{ ha/cumec} \]

This confirms option (A): the duty on the canal's capacity is 375 hectare/cumec, exactly half the duty at the field, because the head discharge feeding the canal is twice the discharge that finally reaches the crop.

\[ \boxed{375 \text{ ha/cumec}} \]

Answer 2

This problem has two different discharges in play: the discharge that finally reaches the crop (field discharge) and the discharge the canal must carry at its head (capacity), and the difference between them is exactly the stated 50% conveyance loss. Duty can be reported against either discharge, and the question specifically wants duty against capacity.

Start with the duty measured at the field, since 10 cumec is the flow that meets the crop's peak demand of 7500 hectares:

\[ \text{Duty at field} = \frac{7500 \text{ ha}}{10 \text{ cumec}} = 750 \text{ ha/cumec} \]

Now relate the field discharge to the head (capacity) discharge. The canal loses 50% of its head discharge on the way to the field, so only the remaining 50% arrives as field discharge:

\[ Q_{field} = (1 - 0.5) \, Q_{head} = 0.5\, Q_{head} \]

Since $Q_{field} = 10$ cumec, this gives $Q_{head} = 10 / 0.5 = 20$ cumec. The head discharge is double the field discharge here because exactly half of it is lost in transit.

Duty is inversely proportional to the discharge used for a fixed area, so doubling the discharge (from field to head) halves the duty figure:

\[ \text{Duty on capacity} = \text{Duty at field} \times \frac{Q_{field}}{Q_{head}} = 750 \times \frac{10}{20} = 750 \times 0.5 = 375 \text{ ha/cumec} \]

This confirms option (A): the duty on the canal's capacity is 375 hectare/cumec, exactly half the duty at the field, because the head discharge feeding the canal is twice the discharge that finally reaches the crop.

\[ \boxed{375 \text{ ha/cumec}} \]

An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare of cropped area. The estimated canal losses are 50 % of the head discharge. The duty (in hectare/cumec) on capacity of this canal is

Show Hint

The Correct Option is A

Solution and Explanation

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