Question

For a fluid element in a steady, uniform flow, which of the following statements is true regarding the flow velocity at any point in the flow field?

• A. It changes with time.
• B. It is the same at every point.
• C. It varies from point to point but is constant in time at each point.
• D. It is zero.

Hint:

Steady Uniform Flow. Steady \(\implies\) No change with time at a point. Uniform \(\implies\) No change with position at an instant. Steady Uniform \(\implies\) Velocity is constant everywhere and always.

Answer 1

The Correct Option is B

Definitions: - Steady flow: Velocity (and other properties) at any given point does not change with time (\(\partial \vec{V}/\partial t = 0\)).
- Uniform flow: Velocity vector (\(\vec{V}\)) is the same (magnitude and direction) at all points in the flow field at any given instant.
The question specifies the flow is both steady and uniform.
- Because it's steady, the velocity at any point is constant over time (rules out Option 1).
- Because it's uniform, the velocity is the same at every point in the flow field.
(matches Option 2).
- Option (3) describes steady, non-uniform flow.
- Option (4) is incorrect unless the fluid is stagnant.
Therefore, for steady, uniform flow, the velocity is the same at every point and does not change with time.