1. 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

2. 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

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

4. 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)

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

6. 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

7. 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

8. Specific Energy
From v = Q/A

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

10. 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

11. Relationship of E and y when q constant

12. 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

13. 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

14. Relationship of q and y when E constant

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

16. 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

17. 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

18. 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.

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

20. 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

21. 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

22. 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.

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

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

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

26. Example 1:
Water flowing with normal flow on rectangular channel width 5.0m and Manning, n = 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

27. 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=
Vc=3.11 m/s

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

29. 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

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

32. 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

33. 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

34. 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

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

37. Types of hydraulic jump
Undular Fr
Weak Fr
Oscillating Fr
Steady Fr
Strong Fr > 9.0