---
title: "Sketch profiles with upstream control and gate"
subject: "Hydraulics"
chapter: 8
key: "semester_4/hydraulics:sketch-profiles-slope-arrangement-uc-ac"
source: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profiles-slope-arrangement-uc-ac
site: BCT Engineering
---

# Sketch profiles with upstream control and gate

Hydraulics · Chapter 8: Non-uniform gradually varied flow (GVF)

- Asked in: 2081 Chaitra, 5 marks
- Video: [Gradually Varied Flow: Sluice Gate and M2 Profile](https://www.youtube.com/watch?v=BonFiKDMcZI) — Glenn Moglen
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profiles-slope-arrangement-uc-ac
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-8

## Question

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]

## 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.

## Answer

**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**

1. **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.
2. **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**.
3. **Steep reach, downstream of the gate.** The vena-contracta depth is smaller than $y_n$, so an **S3** curve rises towards the NDL.
4. **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.

```text
 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 |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What profile forms on the first mild reach before the break to steep slope?
   A. M1
   B. M3
   C. S2
   D. M2 drawdown towards yc at the break
   Answer: D. Uniform subcritical flow must pass through yc at the break, giving an M2 drawdown curve. (Key point: Profile on first mild reach)

2. On the steep reach, flow leaving the break at yc follows which curve?
   A. S2, falling toward the steep yn
   B. S1 rising
   C. S3 rising
   D. M2
   Answer: A. Depth between yc and yn on a steep slope is an S2 curve, falling downstream. (Key point: Flow downstream of the break)

3. How is the water held back by the gate handled?
   A. A hydraulic jump on the steep reach, then S1 rising to the gate
   B. No jump; S2 continues to the gate
   C. M1 curve behind the gate
   D. The flow becomes critical at the gate
   Answer: A. The gate is an artificial control; supercritical flow meets deeper water, so a jump forms followed by S1. (Key point: Gate on the steep reach)

4. Downstream of the gate on the steep reach, the profile is:
   A. S1
   B. S3 rising towards the NDL (vena contracta depth is less than yn)
   C. S2 falling
   D. M3
   Answer: B. The contracted jet is shallower than yn, so depth rises toward yn as S3. (Key point: Below the gate)

5. At the steep-to-mild break, what occurs?
   A. M2 then uniform flow
   B. Direct uniform flow
   C. M3 rising, then a hydraulic jump to the mild normal depth
   D. S1 curve
   Answer: C. Supercritical flow at steep yn is shallower than mild yn, so M3 and then a jump are needed. (Key point: Final mild reach)

## Related in Hydraulics

- [Sketch profile: mild, steep with gate, mild](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asketch-profile-mild-steep-mild-sluice-gate) — Hydraulics, chapter 8, asked 2×
- [Surface profiles on steep slope](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asteep-slope-profiles-analytical) — Hydraulics, chapter 8, asked 2×
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- [Surface profiles on mild slope](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Amild-slope-profiles-analytical) — Hydraulics, chapter 8, asked 2×
- [Locate control points and sketch profiles](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asketch-profiles-three-slope-figures-control-points) — Hydraulics, chapter 8, asked 2×
- [Three successive slopes: profiles and length](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Athree-reaches-profiles-and-length-slope-1) — Hydraulics, chapter 8