Understanding Canal Time Factor in Rabi Season

The time factor is a crucial concept in irrigation engineering, particularly when dealing with canal systems. It represents the ratio of the actual time a canal or distributary operates at its full capacity during a specific period (like a crop season) to the total duration of that period.

A time factor less than 1 indicates that the canal or distributary does not run continuously for the entire season, which can be due to various reasons such as maintenance, rotational supply, or insufficient demand at certain times.

Applying Time Factor to Calculate Full Supply Days

In this problem, we are given the time factor for the rabi season and the total length of the crop season. We need to find out for how many days the distributary actually runs with its full supply of water.

Given data:

• Time Factor for rabi season: 0.75
• Total duration of the crop season: 120 days

The formula relating the time factor, the actual running days, and the total season duration is:

$$ \text{Time Factor} = \frac{\text{Actual Running Days}}{\text{Total Season Days}} $$

To find the number of days the distributary will receive its full supply (Actual Running Days), we can rearrange the formula:

$$ \text{Actual Running Days} = \text{Time Factor} \times \text{Total Season Days} $$

Now, let's substitute the given values into this formula:

$$ \text{Actual Running Days} = 0.75 \times 120 \text{ days} $$

Performing the Calculation for Rabi Season Full Supply Days

To calculate the product, we can convert the decimal time factor into a fraction:

$$ 0.75 = \frac{75}{100} = \frac{3}{4} $$

So, the calculation becomes:

$$ \text{Actual Running Days} = \frac{3}{4} \times 120 $$

$$ \text{Actual Running Days} = 3 \times \frac{120}{4} $$

$$ \text{Actual Running Days} = 3 \times 30 $$

$$ \text{Actual Running Days} = 90 \text{ days} $$

Thus, the distributary will receive its full supply of water for 90 days during the 120-day rabi season.