Steady flow in open channels: which parameter must remain unchanged with time at a section? In a steady open-channel flow (not necessarily uniform), identify which quantity does not change with time at any given cross-section.

Introduction / Context:Steady vs. uniform flow are often confused. In open-channel hydraulics, “steady” refers to no time variation at a point, while “uniform” refers to no spatial variation along the reach. Understanding this distinction is essential for correct modeling and instrumentation.

Given Data / Assumptions:

• Single-phase, single-channel flow.
• Flow is steady (∂/∂t = 0 at a section) but not necessarily uniform along the channel.
• No lateral inflow between adjacent sections for the discharge comparison.

Concept / Approach:In steady flow, discharge Q at any fixed section remains constant with time. However, depth y and mean velocity V can vary from section to section (non-uniform) even though their local values are time-invariant. Therefore, the quantity guaranteed not to vary with time at a section is the discharge (rate of flow) Q.

Step-by-Step Solution:

Verification / Alternative check:Continuity for a control volume without lateral inflow/outflow ensures Q entering equals Q leaving and remains constant in time under steady conditions.

Why Other Options Are Wrong:Depth and velocity can change along the channel (non-uniform flow). “All of these” would require uniform conditions, which are not stated.

Common Pitfalls:Assuming steady implies uniform; misinterpreting short-term fluctuations as unsteadiness when time-averaged flow is steady.

Final Answer:rate of flow (discharge)