Cause of a backwater curve in gradually varied flow A backwater curve (M-curve or S-curve rising upstream) in an open channel is typically produced when:

Introduction / Context:
Backwater curves are part of gradually varied flow profiles, important for flood routing, afflux estimation, and design near controls. Recognizing the physical cause helps select the correct profile family (M1, M2, S1, etc.).

Given Data / Assumptions:

• Prismatic, mild or steep channel as applicable.
• Steady flow with gradually varied depth changes.
• Presence or absence of a downstream control (e.g., weir, gate, dam).

Concept / Approach:

A backwater curve is a rising water surface upstream of a control that increases tailwater depth relative to normal depth. The obstruction forces subcritical approach flow to adjust gradually upstream, producing an elevated profile.

Step-by-Step Solution:

Verification / Alternative check:

GVF equation dy/dx = (S0 − Sf) / (1 − Fr^2) predicts positive dy/dx near controls where depth exceeds normal, consistent with backwater formation.

Why Other Options Are Wrong:

Friction vs bed slope balance alone does not create a control; narrowing typically lowers depth for subcritical flow; steepening bed increases energy slope and can lower water surface upstream.

Common Pitfalls:

Confusing drawdown (falling profile) with backwater; ignoring flow regime effects on information propagation.

Final Answer:

A downstream control such as a weir or barrage backs up the water surface