In a gradually varied flow, the velocity varies along the channel. Let's understand why this is the correct answer in detail.

Gradually Varied Flow:
Gradually varied flow refers to the flow of water in an open channel where the water depth changes gradually over a certain distance. This can occur due to changes in channel slope, channel shape, or channel roughness.

Velocity Variation:
In gradually varied flow, the velocity of the flow varies along the channel. This is because the water depth changes, which directly affects the cross-sectional area of flow. As the depth changes, the velocity of the flow also changes to maintain the continuity equation, which states that the product of flow area and velocity remains constant.

Velocity and Continuity Equation:
The continuity equation for open channel flow is given by:

Q = A * V

Where:
Q = Discharge or flow rate
A = Cross-sectional area of flow
V = Velocity of flow

Since the product of area and velocity needs to remain constant, any change in the flow area will result in a corresponding change in the velocity.

In gradually varied flow, as the water depth increases, the cross-sectional area of flow also increases. To maintain the continuity equation, the velocity of flow decreases. Conversely, as the water depth decreases, the cross-sectional area decreases, and the velocity of flow increases.

This variation in velocity along the channel is essential to ensure that the discharge remains constant throughout the flow. It allows the flow to adjust dynamically to changes in channel geometry, such as a widening or narrowing of the channel or changes in slope.

Other Options:
Now let's discuss why the other options are incorrect:

b) In gradually varied flow, the velocity is not constant along the channel. This is because the flow area changes, as explained above.

c) The velocity is not zero when the slope of the channel bed is zero. Even if the slope is zero, there can still be a flow of water in the channel. The velocity will vary based on other factors such as the channel shape and roughness.

d) The velocity is not at its critical value along the channel in gradually varied flow. The critical velocity occurs in specific situations such as critical flow or hydraulic jump, where the flow transitions from supercritical to subcritical or vice versa. Gradually varied flow does not involve such critical conditions.

Conclusion:
In conclusion, in gradually varied flow, the velocity varies along the channel to maintain the continuity equation. As the water depth changes, the flow area changes, resulting in a corresponding change in velocity. This variation in velocity is necessary to ensure a constant discharge throughout the flow.