Water Resources Engineering Slides - UWS

Slides for UWS Class of WResEng - 1

1. Water Resources Engineering
Module Code : ENGG09014
BEng (Hons) Civil Engineering
Dr Shakun Paudel

2. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
2
Open Channel Flow I (Revision)

3. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open Channel Flow
•Open-channel flow is a flow of liquid in a conduit with a free surface
•Free surface is a liquid-gas interface
•At free surface pressure is local atmospheric pressure
–Natural flows: rivers, creeks, floods, etc.
–Human-made systems: fresh-water aqueducts, irrigation, sewers, drainage
ditches, etc.
3

4. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open Channel Flow
4

5. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open Channel Flow
(www.sciencing.com)
5

6. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open channel flow vs pipe flow
6
Open channel flow Pipe flow
Have a free surface No free surface
Gravity is the main driving forcePressure is the main driving force
A free surface is subject to
atmospheric pressure
Not exposed to atmospheric pressure,
hydraulic pressure only
HGL coincides with the free surfaceHGL generally above the conduit
Flow area is determined by the channel
shape and changes with change in free
surface
Flow area is fixed by the pipe geometry,
usually circular

7. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open channels
7
Canal
Flume
Chute
(www.iku.edu.tr)

8. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open channels
8
Culvert
(www.iku.edu.tr)

9. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Prismatic Channel
9
A channel built with constant cross section
and constant bottom slope is called a
Prismatic Channel.

10. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Non-Prismatic Channel
10
If cross-section and bottom slope
are not constant along the length
then it is a non-prismatic channel

11. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Classification of Open Channel Flow
•Uniform flow
•Non-uniform flow
•Steady flow
•Unsteady flow
Gradually varying flow (GVF)
Rapidly varying flow (RVF)
11
Rapidly varied flow (RVF) occurs over a short distance near the obstacle, eg. Sluice gate
Gradually varied flow (GVF) occurs over larger distances and usually connects UF and RVF.

12. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Classification of Open Channel Flow
Reynolds number
•Flow conditions, if:
➢R
e < 500 Laminar flow
➢R
e = 500 to 2000 transitional flow
➢R
e > 2000 Turbulent flow
V = mean flow velocity
μ = dynamic viscosity
ρ = mass density
R = Hydraulic radius (=A/P)
12

13. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Classification of Open Channel Flow
Froude number
•Flow conditions, if:
➢F
r < 1.00 Subcritical flow
➢F
r = 1.00 Critical flow
➢F
r > 1.00 Supercritical flow
V = mean flow velocity
g = acceleration due to gravity
D = Hydraulic mean depth (=A/B)
13

14. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Definitions
•Wetted cross-sectional Area (A)
•Wetted perimeter (P)
•Depth of flow (y)
•Hydraulic radius (R or m = A/P)
•Hydraulic mean depth (D= A/B)
•Normal depth (d
n or d)
•θ is the channel bottom slope
d = ycosθ
For mild slope channels, d = y
b
φ°
d
B
14

15. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Uniform Flow
•Total Energy Line (TEL) = z+h+ v
2
/2g = H
•Hydraulic Grade Line (HGL) = Water Surface Line (WSL)
L
θ
1
1
2
2
h
1
h
2
Datum
Z
1
Z
2
h
f
15

16. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Uniform Flow
•In uniform flow, energy grade line is parallel to the water surface and
equal to the channel bottom slope
•The flow depth in uniform flow is called normal depth
16

17. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Equations for Uniform Flow
•Darcy-Weisbach
•Colebrook-White equation
•Chezy’s equation
•Manning’s equation
17
L
θ
1
1
2
2
h
1
h
2
Datum
Z
1
Z
2
h
f

18. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Darcy-Weisbach Equation
h
f = head drop
λ = friction factor
V = mean velocity
L = channel length
R = hydraulic radius = A/P
18

19. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Colebrook-White Equation
λ = friction factor
k = surface roughness
V = mean velocity
ν = Kinematic viscosity
R = hydraulic radius = A/P
19

20. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Chezy’s Equation
V = mean velocity
C = Chezy’s coefficient
R = hydraulic radius = A/P
S
o = channel bed slope
20
(1718-1798)
For uniform open channel flow:

21. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Manning’s Equation
V = mean velocity
n = manning’s coefficient for different types of surfaces
R = hydraulic radius = A/P
S
o = channel bed slope
21
(www.cmatc.cn)

22. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Typical Values for Manning’s n
22

23. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Example
A rectangular channel is 6.3 m wide and has a depth of flow of
1.7 m. The slope of the channel bed is 1/1000. Using the Chezy’s
equation with C = 49 m
1/2
/s, calculate the mean velocity and
discharge in the channel.
23
??????√ ??????
0
Q = AV
R = A/P

24. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Most Economical Channel Section
•The most economical channel section, or hydraulically efficient
section is the one which has maximum discharge for the given cross-
sectional area A, slope of the bed S
0, and resistance coefficient of a
channel
•The discharge is maximum, when the wetted perimeter is minimum
• Design a channel with resisting force as small as possible i.e. making
wetted perimeter as small as possible
24

25. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Most Economical Channel Section
r = 1 m
A = 3.142 m
2
P = 6.284 m
A = 3.142 m
2
a =1.7725 m
P = 7.090 m
a
a
A = 3.142 m
2
b = 2 m
d = 1.571 m
P = 7.142 m
b
d
25

26. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Most Economical Sections
d
b
b = 2d
R = d/2
b
d
B = b+2nd
θ°
n
1
nd nd
26
Top width = 2 x length of sides

27. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Example
A rectangular concrete lined channel (Manning’s n =0.015 s/m
1/3
) is to be constructed to
carry flood water. The slope of the ground surface is 1 in 500. The design discharge is 10
m
3
/s. Calculate the dimensions of the rectangular channel that will minimise excavation
and result in the optimum hydraulic section.
27

28. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
•Specific energy and critical depth
•Alternate or conjugate flow depths
•Subcritical and supercritical flow
•Hydraulic jump and specific force
•Gradually varying flow (GVF)
Non-uniform flow
28

29. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open Channel Flow
29

30. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Open Channel Flow
Froude number
•Flow conditions, if:
➢F
r < 1.00 Subcritical flow
➢F
r = 1.00 Critical flow
➢F
r > 1.00 Supercritical flow
V = mean flow velocity
g = acceleration due to gravity
D = Hydraulic mean depth (=A/B)
30

31. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Subcritical Flow
•Low velocity and relatively deep
•Froude number (F
r) less than 1
•Flow depth (y) greater than critical flow depth (y
c)
•Mean flow velocity (V) less than critical flow velocity (V
c)
•Bed slope (S
0) less than critical bed slope (S
c)
31

32. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
•Froude number (F
r) equal to 1
•Flow depth equal to critical depth
•Critical flow is the transition between subcritical and supercritical flow
•Critical depth represents minimum specific energy for the given flow
rate
•At critical depth, maximum possible discharge occurs for a given
specific energy
Critical Flow
32

33. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Supercritical Flow
•High velocity and shallow depth
•Froude number (F
r) greater than 1
•Flow depth (y) less than critical flow depth (y
c)
•Mean flow velocity (V) greater than critical flow velocity (V
c)
•Bed slope (S
0)
greater than critical bed slope (S
c)
33

34. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Definitions
•Specific flow rate (q)
•Critical depth (y
c)
•Critical velocity (V
c)
34

35. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Definitions
•Critical slope (S
c)
•Specific energy (E)
35

36. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
1
1
2
2
y
1 y
2
V
1
2
/2g
V
2
2
/2g
HGL
Specific Energy (E)
TEL
36

37. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Specific Energy (E)
For a particular flow rate in a channel with uniform flow with constant y and
V, the specific energy must be same at all cross sections along the channel,
i.e.
37

38. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Specific Energy Diagram
Depth (y)
Specific Energy (E)
y
c
E
min
Critical
depth
Supercritical
Subcritical
q
E
y
2
y
1
38??????
min= ??????
??????=
3
2
??????
??????

39. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Specific Force (Momentum)
39

40. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
40
Rapidly Varying Flow
Example: Flow over a weir

41. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Gradually Varying Flow (GVF)
•The water surface is not parallel to the bed
•Change in depth (D) with distance (L) along the channel
•Gradually varying flow equation:
where, F
r = Froude number, Fr
2
= αQ
2
T/ gA
3
α = velocity distribution coefficient
S
0 = bed slope
S
F = slope of total energy line
41

42. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
Gradually Varying Flow (GVF)
Water surface
S
0
Datum
Z
d
V
2
2g
S
F
d
c
d
N
42

43. 1.2.
Open Channel Flow
BEng (Hons) Civil Engineering | Water Resources Engineering
43
Gradually Varying Flow and Direct step method of flow profile calculation
to be continued in the next session.