Question

Flow of fluid through a long pipe of constant diameter at a constant rate is

• A. Steady uniform flow
• B. Steady non-uniform flow
• C. Unsteady uniform flow
• D. Unsteady non-uniform flow

Hint:

Break down flow classification into two simple questions:
1. Is it changing with time? (Constant rate?) $\rightarrow$ No = Steady.
2. Is it changing with location? (Constant diameter?) $\rightarrow$ No = Uniform.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks to classify a specific type of pipe flow based on its characteristics with respect to time and space.

Step 2: Detailed Explanation:
Flow classification is based on two criteria:
1.

Time-dependence: -

Steady Flow: The fluid properties (like velocity, pressure, density) at any single point in the flow do not change with time. A "constant flow rate" implies steady flow. -

Unsteady Flow: The properties at a point change with time.
2.

Space-dependence: -

Uniform Flow: The velocity vector (both magnitude and direction) is the same at all points in the flow field at a given instant. For pipe flow, this means the average velocity is constant along the length of the pipe. This occurs when the pipe has a "constant diameter". -

Non-uniform Flow: The velocity changes from one point to another along the flow path (e.g., in a tapering pipe or around a bend).
Analyzing the given conditions:
- "at a constant rate": This means the flow rate is not changing with time, so the flow is

Steady.
- "a long pipe of constant diameter": Since the diameter is constant and the flow rate is constant, the average velocity ($v = Q/A$) must also be constant along the length of the pipe. This means the flow is

Uniform.

Step 3: Final Answer:
Combining the two characteristics, the flow is Steady uniform flow.