Identify the condition(s) that imply non-uniform flow in an open channel. Choose the most comprehensive statement.

Introduction / Context:
Open-channel flow classification depends on how flow variables change in space and time. Non-uniform (spatially varied) flow occurs when depth and velocity change along the channel length due to bed slope, geometry, or added/removed energy.

Given Data / Assumptions:

• Steady flow unless otherwise noted (time-invariant at a fixed section).
• Channel may have prismatic or non-prismatic geometry.
• Energy grade line and bed slope may differ.

Concept / Approach:
Uniform flow requires constant depth and velocity along the channel, implying water surface parallel to the bed and energy slope equal to bed slope. Any departure from these conditions (accelerating or decelerating flow) implies non-uniform flow.

Step-by-Step Solution:
Option (a): If the free surface is not parallel to the bed, depth varies with x → non-uniform.Option (b): If head to overcome friction is less than bed drop, excess head accelerates the flow → depth/velocity vary → non-uniform.Option (c): If head to overcome friction exceeds bed drop, additional losses or backwater effects decelerate the flow → again non-uniform.

Verification / Alternative check:
Gradually varied flow equations (dY/dx) predict profiles whenever So ≠ Sf or geometry changes. Both accelerating and decelerating cases are encompassed by non-uniform flow.

Why Other Options Are Wrong:
Choosing only one of (a), (b), or (c) ignores other valid mechanisms for non-uniformity; the complete answer is the collective condition.

Common Pitfalls:

• Confusing non-uniform with unsteady; non-uniform concerns spatial variation, not time variation.
• Assuming prismatic channels always yield uniform flow—this is only true when slopes match and flow is fully developed.

Final Answer:
All of the above