--- title: "Locate control points and sketch profiles" subject: "Hydraulics" chapter: 8 key: "semester_4/hydraulics:sketch-profiles-three-slope-figures-control-points" source: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profiles-three-slope-figures-control-points site: BCT Engineering --- # Locate control points and sketch profiles Hydraulics · Chapter 8: Non-uniform gradually varied flow (GVF) - Asked in: 2076 Bhadra, 3+3+4 marks; 2071 Magh, 8 marks (asked 2 times) - Video: [Gradually Varied Flow Profiles](https://www.youtube.com/watch?v=cVmKkErbFeU) — CPPCivilEngLibrary - Page: https://www.bctengineer.com/q/semester_4/hydraulics/sketch-profiles-three-slope-figures-control-points - Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-8 ## Question Sketch possible water surface profiles for the channel in figure. First locate and mark the control points, then sketch the profiles, marking each profile with appropriate designation. Show any hydraulic jumps that occur. [Figure: three channels (a), (b), (c), each made of reaches of mild (M), steep (S) or horizontal (H) slope with sluice gates or free overfalls; normal depth and critical depth lines are shown] ## Short answer (a) Steep to mild: supercritical uniform flow, then M3 curve and hydraulic jump to mild normal depth. (b) Mild with gate: M1 curve upstream of gate, M3 downstream followed by a jump. (c) Mild free overfall: M2 drawdown curve from normal depth to critical depth at brink. ## Answer The figure is not available here, so the method is given first and then worked for the three arrangements that these figures normally show: (a) a steep reach joining a mild reach, (b) a mild reach with a sluice gate, (c) a mild reach ending in a free overfall. #### Method 1. Draw the NDL and CDL on every reach: mild $y_n > y_c$, steep $y_n < y_c$, horizontal $y_n = \infty$, adverse $y_n$ does not exist. 2. **Control points** (where depth is known): - critical depth at a break from mild to steep, and at a free overfall (taken as $y_c$ slightly upstream of the brink); - the depth set by a sluice gate (vena contracta downstream, backwater depth upstream); - the depth at a reservoir or pool. 3. Subcritical flow is controlled from **downstream**; supercritical flow from **upstream**. Build the profile from each control point, using the family M1, M2, M3, S1, S2, S3, H2, H3. 4. Where a supercritical profile must join a subcritical one, put a **hydraulic jump**, with the supercritical depth and subcritical depth conjugate. #### (a) Steep reach then mild reach - Control point: uniform supercritical flow upstream at $y_n$ (steep); uniform subcritical flow far downstream at $y_n$ (mild). - Profile: uniform flow on the steep reach, an **M3** curve rising on the mild reach, then a **hydraulic jump** to the mild normal depth. ```text STEEP MILD ---- NDL yn(steep) . M3 J ______ yn(mild) ____________________/'''' |-' (jump) ``` #### (b) Mild reach with a sluice gate - Control points: gate opening gives the depth $a C_c$ downstream (supercritical) and a deeper pool upstream; uniform subcritical flow far downstream. - Upstream of the gate: **M1** backwater curve (depth above $y_n$) rising towards the gate. - Downstream of the gate: **M3** curve from the vena contracta, ending with a **hydraulic jump** to the NDL. ```text M1 gate NDL ......___---'''''|G| J ___ NDL |_|__ M3 __/|--' ``` #### (c) Mild reach ending at a free overfall - Control point: depth $\approx y_c$ at the brink. - Profile: an **M2** drawdown curve from the NDL (asymptotic far upstream) falling to $y_c$ at the end. There is no jump. ```text NDL ......___ ''--.__ M2 CDL - - - - - - - - '--. (free overfall) ``` Every profile is tangent to the NDL where it approaches uniform flow, meets the CDL steeply (except at a jump or overfall), and a jump is shown wherever supercritical flow meets subcritical flow of greater depth. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which is a control point where depth is known? A. Any point on a mild slope B. Uniform flow far upstream only C. The channel centreline D. Critical depth at a free overfall or at a mild-to-steep break Answer: D. Overfalls and mild-to-steep breaks force yc; gates and pools also fix depths. (Key point: Control points) 2. On a mild reach with a sluice gate, the profile upstream of the gate is: A. M1 backwater rising towards the gate B. M2 drawdown C. M3 D. S2 Answer: A. The gate raises depth above yn upstream, giving an M1 curve. (Key point: Mild reach with gate) 3. A mild channel ending in a free overfall has which profile? A. M1 with a jump B. M2 drawdown falling to about yc at the brink C. M3 ending in a jump D. S1 Answer: B. The brink is a critical-depth control, so depth drops from yn toward yc along an M2 curve; no jump occurs. (Key point: Free overfall) 4. When is a hydraulic jump shown? A. Whenever slope changes B. At every gate C. Wherever the slope is mild D. Where supercritical flow must meet subcritical flow of greater (conjugate) depth Answer: D. A jump connects a supercritical depth to its conjugate subcritical depth. (Key point: Jump rule) ## 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× - [Surface profiles on mild slope](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Amild-slope-profiles-analytical) — Hydraulics, chapter 8, asked 2× - [Partial profile with possible jump at A](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Ahydraulic-jump-partial-profile-5m3s-point-a) — Hydraulics, chapter 8 - [Sketch profiles with upstream control and gate](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Asketch-profiles-slope-arrangement-uc-ac) — Hydraulics, chapter 8 - [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 ## Related in other subjects - [Control of sub-surface water and seepage](https://www.bctengineer.com/question.md?key=semester_6%2Ftransportation_engineering_i%3Asubsurface-drainage-measures) — Transportation Engineering I, chapter 4, asked 15× - [GSM traffic and control channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agsm-traffic-control-channels) — Wireless Communication, chapter 8, asked 4× - [GSM frame structure, traffic and control channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agsm-frame-traffic-control-channels) — Wireless Communication, chapter 8, asked 4× - [GSM control channels and their purposes](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Agsm-control-channels) — Wireless Communication, chapter 8, asked 2×