Flow classification – definition of uniform flow in pipes or open channels A flow in a pipe or channel is said to be uniform when which of the following conditions holds true (at a given instant in time)?

Introduction:
Every flow field can be classified along two axes: spatial variation (uniform vs non-uniform) and temporal variation (steady vs unsteady). This question specifically tests your understanding of the spatial criterion for uniform flow in internal or open-channel systems.

Given Data / Assumptions:

• Single-phase, incompressible fluid.
• Cross-section may be constant or varying; we focus on the definition, not a particular geometry.
• Comparison is made across positions along the flow at the same instant.

Concept / Approach:

Uniform flow means the mean velocity (and thus discharge per unit width, etc.) is the same at all locations along the streamline direction at that instant. In a constant-area pipe with no inflow/outflow along the length, uniformity implies v(x) is constant with x. Steady flow, by contrast, refers to invariance with time at a fixed point, i.e., ∂/∂t = 0; it is different from uniformity even though both often co-occur in simple cases.

Step-by-Step Solution:

Verification / Alternative check:

A diffuser operating at constant Q is steady but non-uniform (velocity decreases along x). This counterexample confirms the distinction between steady and uniform.

Why Other Options Are Wrong:

Different velocities at sections: That is the definition of non-uniform flow.Constant discharge: Steady flow criterion.Definite path: Laminar flow idea; not the uniformity criterion.Reynolds number condition: Turbulence criterion, not uniformity.

Common Pitfalls:

Equating “steady” and “uniform”. They are orthogonal; a flow can be steady non-uniform or unsteady uniform.

Final Answer:

the liquid particles at all sections have the same velocities