Open Channel Flow – Why a Surface Disturbance Cannot Propagate Upstream A person drops a stone on the surface of a flowing canal and notes that the generated surface disturbance does not travel upstream. What does this indicate about the flow regime in the canal?

Introduction / Context:
In open channel flow, the Froude number Fr = V / √(g y) (for wide channels) governs wave celerity relative to bulk flow velocity. The ability of surface disturbances (gravity waves) to travel upstream depends on whether the mean flow speed exceeds the wave speed.

Given Data / Assumptions:

• Local surface disturbance generated by an object (stone) hitting the water.
• Observation: disturbance does not move upstream against the flow.
• Gravity wave celerity approximately √(g D) for shallow-water waves, where D is hydraulic depth.

Concept / Approach:

If the bulk flow speed V is greater than the shallow-water wave speed c, then Fr = V/c > 1. In that case, waves cannot propagate upstream; the information is convected downstream only. This is the definition of supercritical flow. Conversely, when Fr < 1 (subcritical), disturbances can move both upstream and downstream.

Step-by-Step Solution:

Verification / Alternative check:

Backwater and drawdown curve behavior and hydraulic jump theory similarly hinge on Fr; supercritical reaches transmit disturbances only downstream.

Why Other Options Are Wrong:

• Sub-critical: would allow upstream wave motion.
• Steady/uniform: describe time and spatial uniformity, not wave propagation capability.

Common Pitfalls:

Confusing laminar/turbulent with subcritical/supercritical; they refer to different nondimensional numbers (Re vs Fr).

Final Answer:

Super-critical