What profile forms on the first mild reach before the break to steep slope?

M2 drawdown towards yc at the break

On the steep reach, flow leaving the break at yc follows which curve?

S2, falling toward the steep yn

How is the water held back by the gate handled?

A hydraulic jump on the steep reach, then S1 rising to the gate

No jump; S2 continues to the gate

The flow becomes critical at the gate

Downstream of the gate on the steep reach, the profile is:

S3 rising towards the NDL (vena contracta depth is less than yn)

At the steep-to-mild break, what occurs?

M3 rising, then a hydraulic jump to the mild normal depth

2081 Chaitra · 5 marks

Sketch profiles with upstream control and gate

Short answer

Upstream mild reach: M2 drawdown to critical depth at the break. Steep reach: S2 falls from the break, then a hydraulic jump to S1 behind the gate, followed by S3 rising from the vena contracta. Downstream mild reach: M3 from supercritical flow, then a jump to the mild NDL.

Draw water surface profile qualitatively for the following arrangement of slopes. Assume sufficiently long reach for each slope. [Figure: mild slope, then steep slope, then mild slope; upstream controls (U.C.) marked at the upstream end and on the steep slope, a sluice gate as artificial control (A.C.) on the steep slope; NDL and CDL marked]

Controls: subcritical flow (mild reaches) is controlled from downstream; supercritical flow (steep reach) is controlled from upstream. The U.C. at the head of the steep reach is the critical depth at the break; the gate is the artificial control (A.C.) on the steep reach.

Profiles

First mild reach. Uniform subcritical flow at $y_n$ far upstream. The flow must pass through $y_c$ at the break, so the surface falls as an M2 drawdown curve towards the CDL at the break.
Steep reach, upstream of the gate. Flow leaves the break at $y_c$ and falls as S2, approaching $y_n$ (supercritical). The gate holds deeper water behind it, so a hydraulic jump forms on the steep reach and the depth continues to rise to the gate as S1.
Steep reach, downstream of the gate. The vena-contracta depth is smaller than $y_n$ , so an S3 curve rises towards the NDL.
Second mild reach. Supercritical flow at $y_n$ (steep) meets uniform subcritical flow in the mild reach. It rises as M3 and then a hydraulic jump raises it to $y_n$ of the mild slope.

 MILD    |       STEEP        |  MILD
 ---NDL  |                    |
   \_M2  |  S2     J  S1 |G|  S3   M3  J
 CDL.\.__|___      /'''' | |_..__ __/|---- NDL
 yn(st)  |    '--yn.....  |_|    ----'

Reach	Control	Profile
Upstream mild	downstream (critical depth at break)	M2
Steep, break to jump	upstream (break, $y_c$ )	S2 then uniform flow
Steep, jump to gate	gate	jump, S1
Steep, below gate	upstream (vena contracta)	S3
Downstream mild	tailwater	M3, jump, uniform

✓ Answer checked by Claude Opus 5.5 (high effort)

Sketch profile: mild, steep with gate, mild · Hydraulics, chapter 8 · asked 2×
Surface profiles on steep slope · Hydraulics, chapter 8 · asked 2×
Sluice gate profiles and lengths by direct step · Hydraulics, chapter 8
Surface profiles on mild slope · Hydraulics, chapter 8 · asked 2×
Locate control points and sketch profiles · Hydraulics, chapter 8 · asked 2×
Three successive slopes: profiles and length · Hydraulics, chapter 8

All Hydraulics chapter 8 questions →

Sketch profiles with upstream control and gate

Related questions