Open Channel Flow Part 2 (cont) ERT 349 SOIL AND WATER ENGINEERING ERT 349 SOIL AND WATER ENGINEERING Open Channel Flow Part 2 (cont) Non-uniform flow Open Channel Flow Siti Kamariah Md Sa’at PPK Bioproses, UniMAP Siti Kamariah Md Sa’at PPK Bioproses, UniMAP

Non-uniform flow i ≠ Sw ≠ So dy/dx ≠0 Changes in velocity or depth of unprismatic channel Causes of depth changes along channel: Changes of shape of channel Changes of discharge along the channel Avaibility of control structures Changes of base slope

Non-Uniform flow Two types: Rapidly varied flow (RVF) Gradually varied flow (GVF)

Open Channel Flow: Energy Relations velocity head energy grade line hydraulic grade line water surface Bottom slope (So) not necessarily equal to surface slope (Sf)

Non-Uniform flow i v2/2g H y Sw z So Datum

Specific Energy Bernoulli Equation H = Total Energy P/ρg = Pressure Head z = Measured from datum α = correction factor (assume as 1) v2/2g = kinetics head Bernoulli Equation

Specific Energy Total Energy = Height + flow depth + velocity energy If z =0, E = Specific Energy (Unit: m) = water energy at one section measured as distance from base slope to energy line

Specific Energy From v = Q/A

Specific Energy For rectangular channel (prismatic and straight channel), Where q= Q/B = flowrate/width A = By

Specific Energy From equation on previous slide, E, y and q relationship are: Relationship of E and y when q constant Relationship of q and y when E constant

Relationship of E and y when q constant

E-y curve when q constant Specific Energy Diagram q constant E = y y1 Sub-Critical Flow yc Critical Flow C y2 SuperCritical Flow Emin E

E-y curve when q constant At Point C, specific energy, E is minimum (Emin) and flow depth is critical, yc (critical depth) For E points, there are two value of flow depth: y1= subcritical flow (Fr < 1.0) y2=supercritical flow (Fr>1.0) y1 and y2 called alternate depth y>yc or v < vc  subcritical flow Y<yc or v > vc  supercritical flow

Relationship of q and y when E constant

Q-y curve when E constant Critical y2 q q qmax

Q-y curve when E constant Flow maximum when q=qmax when critical depth at yc For certain q value, there are 2 y which is: y1>yc = subcritical depth y2<yc = supercritical depth

Specific Energy: Sluice Gate q = 5.5 m2/s y2 = 0.45 m V2 = 12.2 m/s EGL 1 E2 = 8 m 2 Given downstream depth and discharge, find upstream depth. y1 and y2 are ___________ depths (same specific energy) Why not use momentum conservation to find y1? alternate

Specific Energy: Raise the Sluice Gate EGL 2 1 as sluice gate is raised y1 approaches y2 and E is minimized: Maximum discharge for given energy.

Specific Energy: Step Up Short, smooth step with rise Dy in channel Given upstream depth and discharge find y2 Dy Increase step height?

Critical Flow Emin dE/dy = 0, y=yc 2. Q max q=Qmax dq/dy = 0 3. Fr =1.0 Critical flow = unstable condition due to changes to E and changes of flow depth

Difficult to measure depth Critical Flow Characteristics Unstable surface Series of standing waves Occurrence Broad crested weir (and other weirs) Channel Controls (rapid changes in cross-section) Over falls Changes in channel slope,So from mild to steep Difficult to measure depth

Broad-crested Weir Hard to measure yc E H yc Broad-crested P weir E measured from top of weir Cd corrects for using H rather than E.

Critical Flow in any shape channel yc Arbitrary cross-section Find critical depth, yc & A=f(y) T=surface width dy A dA y P Hydraulic Depth

Changes in channel slope, So So = Sc Critical Slope (C) So < Sc Mild Slope (M) So > Sc Steep Slope (S)

Critical Slope, Sc Fr=1 (i) & (ii) (i) (ii)

Example 1: Water flowing with normal flow on rectangular channel width 5.0m and Manning, n = 0.017 with 150m3/s and depth 6.0m. Calculate critical depth and determine the types of flow critical slope Critical velocity Ans: yc=4.51 (subcritical) Sc=6.78 x 10-3 Vc=6.65 m/s

Example 2 Trapezoidal Channel, Q=28 m3/s with Manning, n=0.022, B=3.0 and side slope 1:2 Calculate: Critical depth Critical slope Critical velocity Ans: yc=1.5m (try and error method) Sc= 0.00523 Vc=3.11 m/s

Broad crested weir: Control Structure Total Energy Line Water Surface E1 Eo y1 yo h Base slope downstream upstream Eo = E1+h

Minimum dam height hmin= minimum dam/weir height cause the critical depth, yc hmin= hc There are 3 case will happen: 1. h<hmin = emergent dam 2. h=hmin = rare case 3. h>hmin = control dam

Gradually Varied Flow Can be divided to two: Backwater Drawdown Q dy/dx=+ve dy/dx=-ve Q

Example 3: Water flowing with normal flow 1.28m in a rectangular channel with 3.0m and Q=4.25m3/s. If the broad crested weir height 0.6m constructed across the channel, are the water depth upper the weir same with critical depth? Ans: ye=yc=0.589m

Example 4: Water flowing with normal depth 2.5m in rectangular channel 2.8m width with Q=10.4m3/s. If the broad crested weir with 1.2m height constructed across this channel, determine water depth above the weir and illustrate the water profile. Ans: 1. Calculate Eo= yo+q2/2gyo2=2.62 2. Calculate yc = 1.13 m 3. Calculate Emin=1.70 m 4. Calculate hmin=0.92m h=1.2>hmin, ye=yc=1.13m, yo=2.5m>yc

Hydraulic Jump Used for energy dissipation Occurs when flow transitions from supercritical to subcritical base of spillway We would like to know depth of water downstream from jump as well as the location of the jump

Examples of hydraulic jump: At downstream of sluice gate At upstream weir/dam At spillway

Types of hydraulic jump Undular Fr 1.0-1.7 Weak Fr 1.7-2.5 Oscillating Fr 2.5-4.5 Steady Fr 4.5-9.0 Strong Fr > 9.0