Explanation:

To understand why the correct answer is option 'B', let's first define the terms mentioned in the question:

1. Discharge: Discharge refers to the volume of water passing through a given cross-section of a channel per unit time. It is typically measured in cubic meters per second (m³/s).

2. Water depth: Water depth, also known as the hydraulic depth, is the vertical distance between the water surface and the channel bottom. It is commonly measured in meters (m).

3. Rate of change: Rate of change refers to how one variable (in this case, discharge or water depth) is changing with respect to another variable (time).

4. Irrigation outlet: An irrigation outlet is a structure that allows water to be released from a channel or pipe to irrigate fields or crops.

Now, let's analyze the statement in the question: "The rate of change of discharge through an irrigation outlet becomes equal to the rate of change of water depth in the channel when its sensitivity is 1."

Rate of change of discharge:
The rate of change of discharge can be calculated by taking the derivative of the discharge with respect to time. This represents how the discharge is changing over time.

Rate of change of water depth:
Similarly, the rate of change of water depth can be calculated by taking the derivative of the water depth with respect to time. This represents how the water depth is changing over time.

Sensitivity:
The sensitivity of the irrigation outlet refers to how it responds to changes in the water level in the channel. A sensitivity of 1 means that the outlet is highly responsive to changes in water depth.

Relationship between discharge and water depth:
The discharge through an irrigation outlet is directly related to the water depth in the channel. As the water depth increases, the discharge also increases, and vice versa. This relationship is governed by various factors such as channel geometry, outlet design, and hydraulic conditions.

Explanation of the correct answer:
The correct answer is option 'B' because when the sensitivity of the irrigation outlet is 1, it means that the outlet is perfectly responsive to changes in water depth. In other words, even a small change in water depth will cause a corresponding change in the discharge through the outlet.

When the sensitivity is 1, the rate of change of discharge will be equal to the rate of change of water depth. This is because any change in water depth will be immediately reflected in the discharge, resulting in equal rates of change for both variables.

On the other hand, if the sensitivity is zero, it means that the outlet is not responsive to changes in water depth. In this case, the rate of change of discharge will not be equal to the rate of change of water depth.

Hence, the correct answer is option 'B' - the rate of change of discharge through an irrigation outlet becomes equal to the rate of change of water depth in the channel when its sensitivity is 1.