In a steady-flow situation in fluid mechanics, which property at a fixed point in the flow field changes with time (if any)? (Assume a continuum fluid and classical definitions of steady versus unsteady flow.)

Introduction / Context:
Understanding what “steady flow” means is fundamental in hydraulics and aerodynamics. The term appears in Bernoulli applications, open-channel analysis, and turbomachinery design. Students often confuse steady with uniform, so this question clarifies the time aspect at a fixed spatial location.

Given Data / Assumptions:

• A continuum fluid (liquid or gas) moving in a control volume or along a streamline network.
• Classical definition: steady versus unsteady is judged at a fixed point in space.
• No phase change or discontinuities at the observation point.

Concept / Approach:

By definition, steady flow means that all flow properties at a given point do not vary with time. Typical properties include velocity components, pressure, density, and temperature. They may vary from point to point in space, but at any one location they remain constant in time while the flow is steady.

Step-by-Step Solution:

Verification / Alternative check:

Contrast with “uniform flow,” where properties do not change with position along a direction. A flow can be steady but non-uniform (e.g., a nozzle with changing area: velocity varies along the axis but not with time at any one cross-section).

Why Other Options Are Wrong:

Velocity (a), pressure (b), and density (c) may vary spatially in steady flow, but at a fixed location they do not vary with time; hence selecting any of them is incorrect. “Temperature only” (e) is also incorrect; temperature is a property like others and would also remain constant at a point in steady flow.

Common Pitfalls:

Equating “steady” with “constant everywhere,” which is false. Steady talks about time at one point; uniform talks about space at one instant.

Final Answer:

None of these