Unsteady Uniform Flow

To understand the correct answer, let's break down the terms in the given options:

a) Unsteady Uniform Flow: This refers to a flow in which the rate of flow decreases but remains the same throughout the pipe. It means that the flow is changing with time but is uniform across the cross-section of the pipe.

b) Steady Non-Uniform Flow: In this case, the flow rate is constant with time, but the velocity or discharge varies across the pipe's cross-section. This means that the flow is not uniform throughout the pipe.

c) Steady Uniform Flow: This refers to a flow in which the rate of flow remains constant with time and is uniform across the cross-section of the pipe. There is no change in flow rate or velocity along the length of the pipe.

d) Unsteady Non-Uniform Flow: This type of flow involves both variations in flow rate with time and non-uniform velocity or discharge across the pipe's cross-section.

Now, let's analyze the given scenario where the flow through a long pipe is decreasing. As the flow is decreasing, it is evident that the flow rate is changing with time. This rules out options c) and d), as both of them assume a constant flow rate.

Since the flow is decreasing, it implies that the discharge or velocity is also decreasing along the length of the pipe. Therefore, the flow is not uniform throughout the pipe, so option b) can be eliminated.

Hence, the correct answer is option a) Unsteady Uniform Flow because it represents a flow in which the rate of flow decreases but remains uniform across the cross-section of the pipe. This means that the flow is changing with time but is the same throughout the pipe.