This presentation is review of fluid mechanics and hydraulics applicable to water supply engineering.

1. Water Pipeline or Channel
Hydraulics

2. Pipeline/channel hydraulics
Head (m of water column – 0.102 m WC = 1.0 kPa)
• Total energy per unit weight of the flowing fluid (water)
• Includes 3 components
– Kinetic head (V2/2g)
– Potential head (Z)
– Pressure head (p/ρg)
HGL (Hydraulic Grade Line)
• Imaginary line corresponding to the sum of the potential head and
the pressure head drawn for a pipeline/channel
• For pipe flow it corresponds to the height to which water will rise
vertically in a tube attached to a pipeline
EGL (Energy Grade Line)
• Imaginary line corresponding to the sum of the velocity head, the
potential head and pressure head drawn for a pipeline/ channel
• EGL line is above HGL line at a vertical distance equivalent to the
velocity head of the flowing fluid

3. Pipeline/channel hydraulics
Head loss (hL)
• Frictional head loss (major losses)
– Water flow in a pipe/channel results in the development of
shear stress between the flowing water and the wetted wall and
result in head loss
– Depends on
• flow rate
• roughness of the surface
• length of the channel/pipe
• hydraulic radius
– Head loss due to friction (major losses) is calculated by
• Darcy-Weisbach formula and Hazen-Williams formula
• Mannings formula - Chezy formula
• Minor losses
– Turbulence due to appurtenances and fittings on the
pipelines/channels cause head loss

4. ρ = density (kg/m3)
dh = hydraulic diameter (m)
u = velocity (m/s)
μ = Dynamic viscosity (Ns/m2)
ν = Kinematic viscosity (m2/s)

 hh
e
dudu
R 
Reynolds Number
dh = hydraulic diameter (m)
A = area section of the duct (m2)
p = wetted perimeter of the duct (m)p
A
dh
4

Hydraulic diameter
g
V
d
L
fhf
2
2

f is coefficient of friction
L is length of pipe (m)
d is diameter of pipe (m)
V is mean velocity (m/s)
Darcy-Weisbach equation

5. f = D'Arcy-Weisbach friction coefficient
Re = Reynolds Number
k = roughness of duct/pipe/tube surface (m)
dh = hydraulic diameter (m)









fRd
k
f eh
51.2
72.3
log2
1

7. 85.1
17.1 






KC
V
R
L
hf hf is frictional head loss
V is velocity (m/s)
L is length of pipe (m)
R is hydraulic radius (m)
K is conversion factor (0.849 for SI units)
C is Hazen-William’s roughness coefficient
Q is flow rate (m3/sec.)
D is pipe diameter (m)
S is slope
Hazen-Williams equation
85.1
87.4
7.10







C
Q
D
L
hf
For circular pipe flow
54.063.2
54.063.0
2785.0
849.0
SDCQ
SRCV


‘C’ value increases with increasing internal smoothness, and increasing
pipe diameter, but decreases with pipe age
Plastic pipes have higher ‘C’ value (140) than iron pipes (130)
‘C’ value to a negligible extent is affected by changes in flow rates
For open channel flow

9. f
g
C
n
R
CWhere
SRCV
8
6
1



Chezy formula
2
1
3
21
SR
n
V 
Manning formula
‘V’ is velocity (m/sec.)
‘R’ is hydraulic radius (m)
‘S’ is slope
‘n’ is Manning coefficient of roughness
‘C’ is Chezy coefficient (m1/2/Sec.)
‘f’ is Darcy-Weisbach friction factor

10. Equivalent pipe Length (minor loss
converted to pipe length equivalent)
g
V
Khm
2
2

K= minor loss coefficient
v = flow velocity (m/s)
hloss = head loss (m)
g = acceleration of gravity (m/s2)
f
DK
L
g
V
K
Dg
VL
f


22
22
‘f’= friction factor
‘L’ = equivalent pipe length (m)
‘D’ = pipe internal diameter (m)
Minor losses
And Equivalent pipe length

11. Pipes and pipe networks
Equivalent pipes
• A pipe is equivalent to another pipe when for a given head loss
same flow is produced
• Replacing a complex system of piping by a single equivalent pipe
Compound pipes
• pipes of several sizes in series
Branching pipes
• Two or more pipes branching out and not coming together again
downstream
Looping pipes
• Two or more pipes branching out and coming together downstream
(parallel pipes)
Pipe networks
• Flow analysis in pipe network for knowing flow rates – Hardy-Cross
method

12. Valves and gates for pipe flow
– Isolation or block valves; Flow control valves; Directional/Check
valves (non-return valves) and Pressure reducing valves
– Air release valves; Altitude valves and Float valves
Gates and sluice gates for open channel flow
Flow measurement devices for pipe flow
– Venturi meters and Orifice meters
– Current meters and Pitot tubes
– Electro-magnetic and sonic flow meters
Flow measurement devices for open channel flow
– V-notch, Rectangular weir, Proportional weir, Broad crested weirs
– Parshall flume, Venturi flume, and Palmer-Bolus flume
Pumps
– Centrifugal pumps; Reciprocating pumps; Open screw pumps
and Hydraulic ram pumps
Pumping stations

13. Best or most economic hydraulic cross
section for open channel flow
• Best or most economic hydraulic cross section for open channels
occur at the minimal wetted perimeter (or at the maximum
hydraulic radius) for a specific flow cross section
• For rectangular channels
widthdepthhas
channelgularrecfortioncrossfloweconomicmostandBest
giveszerotoderivativetheequating
y
yb
y
A
dy
dp
ytorespectwithderivativetaking
y
y
A
p
ybpperimeterwetted
byAtioncrossflow
2
1
tansec
2
.
2
2
2
.sec
22






14. Best or most economic hydraulic cross
section for open channel flow
For
..2 RP 






 
D
y
21cos2 1

Ry 
Ө is angle in radians

15. Scour velocity or Self cleansing velocity
• Self-cleansing velocity or scour velocity can be found by
Camp’s formula
• SG is specific gravity of the particle
• dp is particle size
• Ks is constant and its value is taken as 0.8
• Recommended self-cleansing velocity is 0.6 m/sec.
• Ensures transport of sand particles of 0.09 mm size and 2.65
specific gravity without allowing settling
• For preventing deposition of sand and gravel 0.75 m/sec.
velocity is recommended
• Velocity not exceeding 3.0 m/sec. is recommended for
avoiding damage channel damage from erosion
   2
1
6
1
1
1
pS dSGKR
n
V 

16. Water hammer
tCE
dk
C
g
VC
H


1
14250
.max
Hmax. Max. water hammer pressure (m)– occurs
when closure time is ≤ critical closure time
Increasing actual closure time decreases water
hammer pressure
C is velocity of the pressure wave/shock wave
(m/sec.)
High for rigid pipes- rigid pipes: 1370; steel
pipes: 850 and plastic pipes 200 m/sc.)
V0 is flow velocity prior to hammering (m/sec.)
‘k’ is bulk modulus of the water 2.07x108 kg/m2
‘d’ is pipe diameter (m)
Ct is pipe wall thickness (m)
E is modulus of elasticity of pipe material
(kg/m2)
Modulus of elasticity
of pipe material

17. Water supply system may require valves sized up to 900mm dia.
normal range is 25 - 300mm dia.
Plumbing utilizes float valves in 15 - 100mm dia. Range.
Valves installed in applications outside their design limits give rise to problems such as
non shut-off, premature seat wear, high noise, water hammer or seat chatter
Selection, sizing and installation of the most appropriate float valve is very important
Design considerations include
•Providing high flow rates at low head loss (low running pressure at valve inlet)
•Designing the valve seat to minimize cavitation and noise
•Minimize valve’s internal frictional resistance
•Shut off loads whilst ensuring the float / lever mechanism is always in control

19. Altitude and Level Control Valves
– These are employed at the point where pipeline enters a tank
– When tank level rises to a specified upper limit, the valve closes
to prevent any further flow eliminating overflow
– When the flow trend reverses, the valve reopens and allows the
tank to drain or to supply the usage demands of the system.
When valve inlet (system)
pressure falls below tank head
pressure, the altitude valve
opens to feed the system
When system pressure recovers
above tank head, the tank begins
to refill
When the high level set point is
reached, the valve will close

20. Air Release Valves
Used to release air trapped in pipelines (and to allow air into
empty pipelines under vacuum/negative gage pressure)
– Usually provided on both sides of an isolation valve, at the
system high points (summits), and at the points of pipeline
grade change (where negative pressures are possible)
Free air (air pockets) can be found in the pipelines (at high
points) and fittings
– Pressure change can cause release of dissolved air
– Air can enter pipelines by vortex action of pumps, at the intake
– Any openings, connections, and fittings can allow air to enter
What if air pockets are left in pipelines?
– Affect pipeline efficiency and intensify water hammering –
cause pressure surges and increase cavitation hazards
– Air in the water lines speeds up the corrosion process
– Air trapped at bends, tees and other fittings can reduce and
even stop flow
– Air can result in improper reading of customers’ meters

21. Air Release Valves
Valve Locations
• on rising mains after the pumps for both releasing and admitting air
• at high points throughout pipeline systems
• at pipeline slope transition points (before & after steep slopes)
• At every 500m distance on the long pipeline of uniform slope
Valve size: Air valve to conduit size is 1:12 for air release type
and 1:8 for air release as well as air admission
Valve operation
• Entry of the pipeline air into the valve body drops down the float
and allows the air to escape through the valve opening
• With the release of air, the pipeline water rises into the valve body
and lifts the float to its limit – pressing of the float against the seat
closes the valve opening and prevents the liquid escape
• When there is no flow in the pipeline, negative pressure developed
in the pipeline extends into the valve body and drops down the
float – this allows air entry through the valve into the pipeline

23. Flow measurement
Rectangle Weirs:
• Contracted: Flow, Q = 3.33 (L - 0.2H) H1.5
• Suppressed: Flow, Q = 3.33 L(H1.5)
Q = Flow, cubic feet per second
L = Length of crest, feet
H = Upstream head, feet
Cipoletti Weirs: Flow, Q = 3.367 L(H1.5)
Q = Flow, cubic feet per second
L = Length of crest, feet
H = Upstream head, feet
V-Notch Weirs:
• 90' V-notch: Flow, Q = 2.50 H2.50
• 60' V-notch: Flow, Q = 1.443 H2.50
• 45' V-notch: Flow, Q = 1.035 H2.50
• 30' V-notch: Flow, Q = 0.685 H2.45
Q = Flow, cubic feet/second
H = Upstream head, feet

24. θ = v-notch angle
q = flow rate (m3/s)
h = head on the weir (m)
b = width of the weir (m)
g = 9.81 (m/s2) - gravity
cd= discharge constant for the weir - must be
determined
Rectangular Weir
q = 2/3 cd b (2 g)1/2 h3/2
Triangular or V-Notch Weir
q = 8/15 cd (2 g)1/2 tan(θ/2) h5/2
Broad-Crested Weir
q = cd h2 b ( 2 g (h1 - h2) )1/2
Common weir constructions are
rectangular weir (sharp-crested thin metal plate)
triangular or v-notch weir (sharp-crested thin metal plate)
broad-crested weir
trapezoidal (Cipolletti) weir
Sutro (proportional) weir
compound weirs (combination of the weirs of different shapes)
Weirs for flow measurement

25. Sluice gates for flow measurement
h = elevation height
ρ = density
v = flow velocity
According to Bernoulli Equation
1/2 ρ v1
2 + ρ g h1 = 1/2 ρ v2
2 + ρ g h2 -1
q = flow rate
A = flow area
b = width of the sluice
h1 = upstream height
h2 = downstream height
cd = discharge coefficient
ho = height sluice opening
According to the Continuity Equation:
q = v1 A1 = v2 A2 -2
q = v1 h1 b = v2 h2 b -3
 
  1/2
12
2
1
12
21
2
1
1
2
21
2
]h[2 gv2
1
2

















ghbhcq
hhfor
h
h
hhg
bhq
d
Combining equations -1 and -3
Used to measure flow rate in open channels
Pressures on the upstream and on the downstream are the same
cd is a function of opening height and vena
contracta height (cd = ho / h1 )
Its value is taken as ~ 0.61 for ho / h1 < 0.2

26. Q Flow rate
μ Out flow coefficient (0.985)
b1 is throat width & b2 is channel width
h1 is liquid depth in the stream side
a is height of the constriction
C is coefficient for constriction (read from graph)
Venturi Flume
1
1
1
2
2
3
12
h
ah
t
b
b
m
hCgbQ


 

27. Parshall Flume
A commonly used fixed hydraulic structure to measure flows in
channels
An improved venturi flume developed in 1915 by Ralph L. Parshall of
the U.S. Soil Conservation Service
A drop in elevation through the throat produced supercritical flow
through the throat of the flume and made only one head
measurement necessary to determine the flow rate
Parshall flume consists of a uniformly converging upstream section, a
short parallel throat section, and a uniformly diverging downstream
section
Floor of the flume is flat in the upstream section, slopes downward in
the throat, and then rises in the downstream section, ending with a
downstream elevation below that of the upstream elevation
Parshall flumes are constructed to the dimensions specified
22 sizes of Parshall flumes have been developed, covering flows from
0.1416 to 92,890 l/s (throat width, indicated as the flume size,
range from 1” to 50’)

28. Parshall Flume
Parshall flumes may operate under two conditions
• Free Flow condition: hydraulic jump is induced on the downstream
side and back water does not restrict flow through the flume –only
one depth (upstream) measurement is needed for flow calculation
• Submerged Flow condition: back water restricts flow through a
flume – for flow calculation depth measurement both upstream
and downstream is needed
When free-fall conditions exist for all flows, the throat and
downstream diverging sections of the flume may be left off
(Montana flume, a modified style of Parshall flume)
Parshall and Montana flume of the same throat width use the same
discharge tables and equations
When used in submerged flow applications, two head measurements,
one in the converging section and the other in the throat section,
are needed
Due to the added instrumentation costs and operational complexity of
operating under submerged flow conditions, operating flumes
under free-flow conditions is recommended

29. Q is flow rate
C is free-flow coefficient
Ha is head at the uptream
n varies with flume size
Free-flow discharge for the Parshall flume
Throat
Width
Coefficient
(C)
Exponent
(n)
1 in .338 1.55
2 in .676 1.55
3 in .992 1.55
6 in 2.06 1.58
9 in 3.07 1.53
1 ft 3.95 1.55
1.5 ft 6.00 1.54
2 ft 8.00 1.55
3 ft 12.00 1.57
4 ft 16.00 1.58
5 ft 20.00 1.59
6 ft 24.00 1.59
7 ft 28.00 1.60
8 ft 32.00 1.61
10 ft 39.38 1.60
12 ft 46.75 1.60
15 ft 57.81 1.60
20 ft 76.25 1.60
25 ft 94.69 1.60
30 ft 113.13 1.60
40 ft 150.00 1.60
50 ft 186.88 1.60
Flume Size St=Hb/Ha
1" - 3" 0.5
6" - 9" 0.6
1' - 8' 0.7
10' - 50' 0.8
For submerged flow
Hb/Ha is ≥ St - flow is submerged flow
Qnet = Q – Qcor.
Qcor. = M (0.000132 Ha
2.123 e9.284 (Hb/Ha))
M = multiplying factor
Q values are in ft3/s
Ha and Hb are in feet
Flume
Size
Factor,
M
1' 1
1.5' 1.4
2' 1.8
3' 2.4
4 3.1
5 3.7
6 4.3
7 4.9
8 5.4
Parshall Flume

33. Pumps

34. pump
tH
mdH
msH
g
Vd
2
2
g
Vs
2
2
dh
 mdfd hh
sh
.enth
statH
 mSfS hh
datum
Pump System

35. Analysis of pump systems
Conducted to
– Select the most suitable pumping unit(s)
– Define operating point(s) of the pump(s)
Involves calculating the system head – capacity curves for the pumping
system and using these in conjunction with the head-capacity
curves of the available pumps
System head – capacity curve
– Graphical representation of the system head
– Developed by ploting total dynamic head over a range of flows from
zero to the maximum expected value
Pump head – capacity curve (pump characteristic curves)
– Illustrate relationship between head, capacity, efficiency and break
horse power over a wide range of possible operating conditions
Operating point:
– Plot pump head-capacity curve on the system head-capacity curve
– Intersection point of these two curves is operating point

39. Pumping Stations
Components of a typical pumping station
• Wet well (sump)
• Dry well (pumping station!)
• Pumps and drives, piping with fittings (valves, gauges, etc.)
• Priming pumps, and seepage pump
• Electrical power control panels
• Crane or overhead girder
• Proper access to the pumps and drives
• Aisle space
• DG sets (for power backup!)
Pumping stations (types)
• Stations with only wet well (sump) and no dry well
– Using submersible (non-clog) pumps
– Using ground level (self-priming!) pumps (with a priming pump!)
• Stations with both wet well and dry well
– factory built dry well and non-clog pumps with top mounted drives
– Built on-site dry wells with pumps installed at the bottom