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

The correct option is 375.

Step-by-step Explanation:

To find the duty on the capacity of the canal, we need to determine the discharge required at the head of the canal (also known as the canal capacity) and relate it to the total cropped area.

1. Identify the given parameters:
- Area of the cropped land ($A$) = 7500 hectare
- Required discharge to be delivered at the field/outlet ($Q_{\text{outlet}}$) = 10 cumec (cubic meters per second)
- Canal losses = 50% of the head discharge ($Q_{\text{head}}$)

2. Calculate the head discharge ($Q_{\text{head}}$):
The discharge delivered at the outlet is equal to the head discharge minus the canal losses:

$Q_{\text{outlet}}=Q_{\text{head}}-\text{Canal Losses}$

Since the canal losses are 50% of the head discharge:

$Q_{\text{outlet}}=Q_{\text{head}}-0.5\times Q_{\text{head}}$

$Q_{\text{outlet}}=0.5\times Q_{\text{head}}$

Substituting the given value of $Q_{\text{outlet}}=10\text{cumec}$:

$10=0.5\times Q_{\text{head}}$

$Q_{\text{head}}=\frac{10}{0.5}=20\text{cumec}$

3. Calculate the duty on capacity:
The duty on capacity of the canal (also known as the head duty) is the area irrigated per unit of discharge at the head of the canal:

$\text{Duty on capacity}=\frac{\text{Cropped Area (A)}}{\text{Head Discharge (}{Q}_{\text{head}}\text{)}}$

Substitute the values of area and head discharge:

$\text{Duty on capacity}=\frac{7500}{20}=375\text{hectare/cumec}$

Thus, the duty on the capacity of this canal is 375 hectare/cumec.