Open channel flow

1. OPEN CHANNEL FLOW
(Uniform Flow)

2. Types of Channels
 Open channel flow is a flow which has a free surface and
flows due to gravity.
 Pipes not flowing full also fall into the category of open
channel flow
 In open channels, the flow is driven by the slope of the
channel rather than the pressure

3. Types of Channels
 Open channel flow is a flow which has a free
surface and flows due to gravity.
 Pipes not flowing full also fall into the
category of open channel flow
 In open channels, the flow is driven by the
slope of the channel rather than the pressure

4. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
4. Sub-critical, Critical and Super-critical Flow

5. 1. Steady and Unsteady Flow
 Steady flow happens if the conditions (flow rate,
velocity, depth etc) do not change with time.
 The flow is unsteady if the depth is changes with
time

6. 2. Uniform and Non-uniform Flow
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
 If for a given length of channel, the velocity of flow,
depth of flow, slope of the channel and cross section
remain constant, the flow is said to be Uniform
 The flow is Non-uniform, if velocity, depth, slope and
cross section is not constant

7. 2. Non-uniform Flow
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
Types of Non-uniform Flow
1. Gradually Varied Flow (GVF)
If the depth of the flow in a channel changes gradually over a
length of the channel.
2. Rapidly Varied Flow (RVF)
If the depth of the flow in a channel changes abruptly over a
small length of channel

9. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow

10. 3. Laminar and Turbulent Flow
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
Both laminar and turbulent flow can occur in open channels
depending on the Reynolds number (Re)
Re = ρVR/µ
Where,
ρ = density of water = 1000 kg/m3
µ = dynamic viscosity
R = Hydraulic Mean Depth = Area / Wetted Perimeter

11. TURBULENT
LAMINAR

12. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow

13. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
4. Sub-critical, Critical and Super-critical Flow
4. Sub-critical, Critical and Super-critical Flow

14. Types of Flows
1. Steady and Unsteady Flow
2. Uniform and Non-uniform Flow
3. Laminar and Turbulent Flow
4. Sub-critical, Critical and Super-critical Flow

15. TYPES OF FLOWING WATER AND ITS CONTROL
Critical Section (In uniform and non-uniform flow)
1) If So < Sc, y > yc : Subcritical flow
2) If So = Sc, y = yc : Critical flow
3) If So > Sc, y < yc : Supercritical flow

16. Velocity Distribution
 Velocity is always vary across channel
because of friction along the boundary
 The maximum velocity usually found just
below the surface

17. Velocity Distribution
 Velocity is always vary across channel
because of friction along the boundary
 The maximum velocity usually found just
below the surface

18. Type of
channel
TOP WIDTH,
T
AREA, A WETTED
PERIMETER, P
RECTANGULAR B By B + 2y
TRAPEZOIDAL B+2my By + my2 B+2y √ 1+m2
GEOMETRIC PROPERTIES OF OPEN CHANNELS
Where,

19. Discharge through Open Channels
1. Chezy’s C
2. Manning’s N
3. Bazin’s Formula
4. Kutter’s Formula

20. Discharge through Open Channels
1. Chezy’s C
2. Manning’s N
3. Bazin’s Formula
4. Kutter’s Formula
Forces acting on the water between sections 1-1 & 2-2
1. Component of weight of Water = W sin i 
2. Friction Resistance = f P L V2 
where
W = density x volume
= w (AL) = wAL
Equate both Forces:
f P L V2 = wAL sin i

21. Chezy’s Formula, miCV 
3ConstantsChezy'C
f
w
2RadiusHydraulicm
P
A
1isin
P
A
f
wV




22. Chezy’s Formula, miCV 
im.CV
iitanisini,ofvaluessmallfor
isinm.CV
1,Eqn.in3&2Eqn.substitute




23. 1. Manning’s N
Chezy’s formula can also be used with Manning's Roughness
Coefficient
C = (1/n) R1/6
where
R = Hydraulic Radius
n = Manning’s Roughness Coefficient

24. 2. Bazin’s Formula
1. Manning’s N
2. Bazin’s Formula
Chezy’s formula can also be used with Bazins’ Formula
where
k = Bazin’s constant
m = Hydraulic Radius
m
k1.81
157.6C



25. Most Economical Sections
1. Cost of construction should be minimum
2. Discharge should be maximum
Types of channels based on shape:
1. Rectangular
2. Trapezoidal
3. Circular

26. Most Economical Sections
1. Cost of construction should be minimum
2. Discharge should be maximum
Types of channels based on shape:
1. Rectangular
2. Trapezoidal
3. Circular

27. maximumbewillQminimum,isPIf
iACAKwhere
P
1
KQ
imCAVAQ



28. Rectangular Section
0
d(d)
dP
minimumbeshouldP
section,economicalmostfor


29. Rectangular Section
0
d(d)
dP
minimumbeshouldP
section,economicalmostfor

222
2d
2
A
m
b/2dor2db
2dbd2dA02
d
A
0
)(
2
0
)(
minimumbeshouldPseciton,economicalmostfor
222
1
2
22
2
d
dddb
bd
P
dd
d
d
A
d
dd
dP
d
d
A
dbP
d
A
bbdA


















30. Circular Section
0
d
P
A
3
d
Discharge,Max.for
0
d
P
A
d
Velocity,Max.for

















31. Circular Section
0
d
P
A
3
d
Discharge,Max.for
0
d
P
A
d
Velocity,Max.for
















0.95Dd,154θ0
dθ
P
3A
d
discharge,max.for
constantsareiandC,i
P
A
Ci
P
A
ACimACQ
0.3Dm0.81D,d,45128θ0
dθ
dm
velocity,max.for
3)
2
2θsin
-(θ
2θ
R
P
A
m
22RθP
1)
2
2θsin
-(θRA
0
3
'0
2















32. Trapezoidal Section
0
d(d)
dP
minimumbeshouldP
section,economicalmostfor


33. 600θand
2
d
m
1nd
2
2ndb
0
d(d)
12n2dnd
d
A
d
0
d(d)
dP
minimumbeshouldPseciton,economicalmostfor
21n2dnd
d
A
1n2dbP
1nd
d
A
bnd)d(bA
2
22















34. Problems
1. A trapezoidal channel has side slopes of 1 horizontal and 2
vertical and the slope of the bed is 1 in 1500. The area of
cross section is 40m2. Find dimensions of the most
economical section. Determine discharge if C=50

35. Problems
1. A trapezoidal channel has side slopes of 1 horizontal and 2
vertical and the slope of the bed is 1 in 1500. The area of
cross section is 40m2. Find dimensions of the most
economical section. Determine discharge if C=50

36. Specific Energy
EnergySpecificascallediswhich
2g
v2
hEs
datum,astakenisbottomchanneltheIf
datus,abovechannelofbottomofHeightzwhere
2g
v2
hzEfluid,flowingofEnergyTotal




37. Specific Energy
h22g
q
h
2g
V
hEs
h
q
bh
Q
V
constant
b
Q
q,unit widthperdischargeIf
bh
Q
A
Q
VVAQ
22





38. Specific EnergyPotential Energy (h)
Es= h + q2/2gh2
hcgVc
1Eqn.inVchc
b
vbh.
b
Q
qvaluesubsitute
q
2
hc
g
q
2
hc
g
q
2 3
1
hc
h
22g
q
2
hEwhere,
0
dh
dE
Depth,Criticalfor













1.
33
g

39. Specific EnergyPotential Energy (h)
Es= h + q2/2gh2
hcgVc
1Eqn.inVchc
b
vbh.
b
Q
qvaluesubsitute
q
2
hc
g
q
2
hc
g
q
2 3
1
hc
h
22g
q
2
hEwhere,
0
dh
dE
Depth,Criticalfor













1.
33
g

40. 3
Emin2
or
hc
g
q
criticalisflowofDepthminimum,isenergyspecificwhen
hc
2
3hc
2
hc
hc2
2g
hc
3
hcEmin
hc
3
or
g
q
2 3
1
hcsubstitute
hc
2
2g
q
2
hcE
2












41. Specific Energy Curve
Alternate Depths 1 & 2
Hydraulic Jump

44. THANK YOU