Backwater curve in a long mild-slope prismatic channel ending in a pool A long prismatic channel has a mild bed slope. Its downstream end discharges into a pool created by a dam (high tailwater). Identify the resulting gradually varied flow water surface profile upstream of the pool.

Introduction:
Gradually varied flow (GVF) classification uses normal depth yn and critical depth yc to characterize profiles on a given bed slope. On mild slopes (yn > yc), backwater effects such as a downstream pool elevate the water level, producing a characteristic profile shape upstream from the control section.

Given Data / Assumptions:

• Prismatic channel with mild slope (yn > yc).
• Downstream pool imposes a high tailwater level.
• Flow is subcritical and gradually varied upstream from the pool.

Concept / Approach:

For a mild slope, three profile zones exist: M1 (y > yn), M2 (yc < y < yn), and M3 (y < yc). A downstream backwater raises depth above yn near the pool, creating an M1 backwater curve that lies above the normal depth line and asymptotically approaches yn farther upstream.

Step-by-Step Solution:

Verification / Alternative check:

GVF differential equation dy/dx sign confirms that for subcritical flows on mild slopes, backwater curves extend upstream with decreasing surface slope, matching M1 behavior.

Why Other Options Are Wrong:

M2 lies between yc and yn; M3 corresponds to depths below yc (drawdown), not a backwater due to a pool; mention of hydraulic jump (A) is unrelated to the described mild-slope backwater.

Common Pitfalls:

Confusing mild with steep slope classifications; misidentifying the controlling boundary condition (tailwater versus upstream control).

Final Answer:

M1 profile that lies above normal depth line