Classifying a flow that varies in space and time If the velocities of fluid particles change in magnitude and direction from point to point and also from instant to instant, how should the flow be classified?

Introduction / Context:
Engineers distinguish flows by how properties vary with time (steady vs unsteady) and space (uniform vs non-uniform). This classification underpins when Bernoulli can be applied directly and how to set up control-volume balances or CFD boundary conditions.

Given Data / Assumptions:

• Velocity changes with location → spatial variation (non-uniform).
• Velocity changes with time at fixed points → temporal variation (unsteady).
• No assumptions on viscosity or Reynolds number are explicitly given.

Concept / Approach:

Uniform means no change along the direction considered; steady means no time change at a fixed point. The statement explicitly says the velocity varies with position and with time, so the flow is both non-uniform and unsteady. Many such flows are turbulent, but turbulence is not strictly required by the wording; still, the description often matches turbulent behavior in practice.

Step-by-Step Solution:

Verification / Alternative check:

Examples: gusty wind in a street (changes with both location and time); pump start-up transients in a pipe with varying diameter. Both require time-dependent and spatially varying analyses.

Why Other Options Are Wrong:

(a) Steady & uniform contradicts the description. (b) Uniformity fails (flow varies in space). (c) Steadiness fails (flow varies in time). (e) Laminar refers to orderly layer motion at low Reynolds numbers; the question concerns variability, not laminarity.

Common Pitfalls:

Equating “unsteady” with “turbulent.” Turbulence implies irregular fluctuations, but a laminar flow can still be unsteady (e.g., oscillatory Poiseuille flow).

Final Answer:

unsteady and non-uniform flow (often turbulent)