--- title: "Sketch profile: mild, steep with gate, mild" subject: "Hydraulics" chapter: 8 key: "semester_4/hydraulics:sketch-profile-mild-steep-mild-sluice-gate" source: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profile-mild-steep-mild-sluice-gate site: BCT Engineering --- # Sketch profile: mild, steep with gate, mild Hydraulics · Chapter 8: Non-uniform gradually varied flow (GVF) - Asked in: 2072 Magh, 4 marks; 2072 Asoj, 3 marks (asked 2 times) - Video: [Study of Water Surface Profiles](https://www.youtube.com/watch?v=vLmIyw57_to) — WIT Solapur - Professional Learning Community - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profile-mild-steep-mild-sluice-gate - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-8 ## Question Sketch the flow profile. [Figure: a channel with a mild slope (NDL above CDL) changing to a steep slope carrying a sluice gate, then changing back to a mild slope; NDL = normal depth line, CDL = critical depth line] ## Short answer Upstream mild reach: M2 drawdown to critical depth at break. Steep reach: S2 curve, hydraulic jump, then S1 backwater to gate; downstream of gate S3 curve. Final mild reach: M3 curve rising to a jump to normal depth. ## Answer **Terms:** NDL = normal depth line ($y_n$); CDL = critical depth line ($y_c$). On a mild slope $y_n > y_c$ (NDL above CDL); on a steep slope $y_n < y_c$ (NDL below CDL). Subcritical flow is controlled from downstream; supercritical flow is controlled from upstream. **Step by step** 1. **Mild reach (upstream).** The flow far upstream is uniform at $y_n$ (subcritical). At the break to the steep slope the flow must pass through critical depth. The profile is a drawdown, **M2**, falling from the NDL to the CDL at the break. 2. **Steep reach, before the gate.** Flow leaves the break at $y_c$ and falls towards the steep NDL as an **S2** curve (supercritical, accelerating). The sluice gate is an artificial control: it holds the water behind it at a depth above $y_c$. Supercritical flow at $y_n$ cannot meet this deeper water smoothly, so a **hydraulic jump** forms and the deep water behind the gate is an **S1** curve rising to the gate. 3. **Steep reach, after the gate.** The jet from the gate (vena contracta) is shallower than $y_n$, so the depth increases gradually towards the NDL as an **S3** curve. 4. **Steep to mild break.** The supercritical flow at $y_n$ (steep) enters a mild slope where the uniform depth is the deeper $y_n$ (mild). It rises gradually as **M3** and then a **hydraulic jump** raises it to the mild normal depth, after which flow is uniform. (If the mild tailwater is high enough, the jump moves up to the break and the M3 curve disappears.) ```text MILD | STEEP (gate) | MILD -----+---- NDL1 ....................... NDL3 (high) \ | gate _____ \M2| S2 J S1 |G| S3 J/ M3 CDL..\._________ /'''''' |_|__ / NDL2 yn ..\_/...... yn_/_/ ``` | Reach | Profile | |---|---| | Mild (upstream of break) | M2 | | Steep, before jump | S2 then uniform flow at $y_n$ | | Steep, jump to gate | jump, then S1 | | Steep, after gate | S3 | | Mild (downstream) | M3, jump, then uniform flow | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. On a steep slope, the NDL lies: A. Above the CDL B. Coinciding with the CDL C. Below the CDL (yn < yc) D. At infinity Answer: C. Steep slope means yn < yc; mild means yn > yc. (Key point: Slope classification) 2. At the break from mild to steep slope, the upstream profile is: A. M1 rising B. M2 drawdown falling to yc at the break C. M3 D. S1 Answer: B. Flow must pass through critical depth at the break, so the mild reach has an M2 drawdown. (Key point: Profile at mild-to-steep break) 3. Why does a hydraulic jump form upstream of the sluice gate on the steep reach? A. Supercritical flow meets deeper water held behind the gate (S1) B. The gate makes flow supercritical C. The slope becomes mild D. The gate removes energy only Answer: A. The gate holds depth above yc behind it, so supercritical flow cannot join smoothly and jumps to the S1 curve. (Key point: Gate effect on steep slope) 4. What happens where supercritical flow at steep yn enters the mild reach? A. It continues as S2 B. It drops via M2 C. It becomes uniform immediately D. It rises as M3 and then a hydraulic jump to the mild normal depth Answer: D. The depth is below mild yn, so M3 rises until a jump brings it to subcritical normal depth. 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