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Mark Markham, P.E.
Gresham, Smith and Partners
September 14, 2017
Session 1
System Curves
Pumping Systems
�Session 1 - Components of a system
curve/hydraulics basic hydraulics/pipe
systems/system curve development
�Session 2 – Pump curves and pump selection
(centrifugal pumps)/duty points/efficiency/duplex &
triplex and series & parallel systems
�Session 3 – Pumping station wet well design - NPSH
and submergence
�Session 4 – Pumping station performance testing -
dry pit/wet pit, submersible, suction lift
Learning Objectives
�Review the elements/components of
pumping systems
�Review the basic hydraulics required to
design a pumping system
�Review basic equations for performing
system head calculations
�Develop a system curve
Terminology
�Pressure – driving force to move fluid
� psi
� feet
� atm
�Head - a measurement of liquid pressure above
a given reference point
� feet
� “Head pressure”
� Express Bernoulli Equation in terms of head (feet)
Pumps and Pumping Stations
�Pumping Systems add energy (provide sufficient pressure) to move fluid through a system at a desired flow rate
�Energy required by the system depends on:� Discharge/Flow rate needed
� Resistance to flow (head/pressure that the pump must overcome)
� Pump efficiency (ratio of power entering fluid to power supplied to the pump)
� Efficiency of the drive (usually an electric motor)
2 2
1 1 2 21 2
2 2pump L
v p v pz H z H
g gγ γ+ + + = + + +
2
2L f minor f i
vH h h h K
g= + = +∑ ∑ ∑ ∑
Elements of a Pumping System
�Convey a fluid that can’t be conveyed by gravity
�System network – pipes, fittings, valves
�Hydraulic Control Points (intake elevations, high
points, discharge elevations)
�Pump
�Motor
�Valves
�Instrumentation
�Controls
Information Needed
�Static Heads
� Min: Min discharge elev. minus max intake elev.
� Max: Max discharge elev. (not high pt.) minus min intake elev.
� Priming Head: Max high pt. minus min intake elev. (RARE)
�Fluid Characteristics
� Water at standard conditions (most of the time)
� Solids content
�System Components
� Pipe sizes, lengths, materials and conditions
� Fittings (elbow, tee, inlet, outlet, other (i.e. condenser, etc.))
� Valves (isolation, check and control)
Pumping System – Static Head� (Total) Static head – difference in head between suction
and discharge sides of pump in the absence of flow;
equals difference in elevation of free surfaces of the fluid
source and destination
�Static suction head – head on suction side of pump in
absence of flow, if pressure at that point is >0
�Static discharge head – head on discharge side of pump
in absence of flow
Total static
head
Static suction
head
Static
discharge
head
Pumping System – Static Head (Lift)
� (Total) Static head – difference in head between suction
and discharge sides of pump in the absence of flow;
equals difference in elevation of free surfaces of the fluid
source and destination
�Static suction lift – negative head on suction side of pump
in absence of flow, if pressure at that point is <0
�Static discharge head – head on discharge side of pump
in absence of flow
Total static
head Static suction
lift
Static
discharge
head
Pumping System – Static Head + Lift
Total static
head (both) Static suction
lift
Static
discharge
head
Static suction
head
Static
discharge
head
Static suction head
Static suction lif
Static discharge head
Static d t
Total static h
ischarge he d
ead
a
= −
= +
Note: Suction and discharge head / lift measured from pump centerline
Terminology
�Friction – force that resist fluid flow
� Pipe diameter & length
� Pipe materials & condition
�Darcy-Weisbach
�Hazen-Williams
� “C” – pipe roughness factor (≈140 new, ≤100 old)
� Typically used at GS&P
�Minor losses
� Valves, Pipe Bends
� “Km” – minor loss coefficient
Friction Head
�Losses dependent on flow rate
� Piping
� Valves/Fittings (“minor losses”)
� Equipment
�“Rule of Thumb” for Pipe velocities
� V > 2.0 fps and < 8 fps for “typical” pipe sizes
� Why – to minimize losses in “typical” systems
� V is not necessarily an indication of the rate of loss. For
example, Loss per 100’ pipe is ≈ 0.2’ in a:
� 24” @ 6,000 gpm (V=4.3 fps)
� 120” @ 425,000 gpm (V=12 fps)
Friction Head - Piping
� Darcy Weisbach
� �� = ��
�
�
�
� Hf = friction loss (ft)
� f = friction factor (Moody Diagram)
� L = pipe length (ft)� V = velocity
(ft/sec)� D = pipe diameter
(ft)� g = gravitational
acceleration = 32.2 ft/sec2
Friction Head - Piping
�Hazen-Williams equation
� �� =�.�
���.����
��.�����.���
� Hf = friction loss (ft)
� V = velocity (ft/sec)
� L = pipe length (ft)
� C = Hazen-Williams’ C-factor
� D = pipe diameter (ft)
Friction Head – Valves/Fittings
�Minor losses use “K”
value
� �� = ��
�
� Hm = minor loss (ft)
� K = resistance coefficient
� V = velocity (ft/sec)
� g = gravitational acceleration
= 32.2 ft/sec2
� Lots of references to find K
values—Cameron,
manufacturers, etc.
Pumping System – Total Dynamic Head (TDH)
� (Total) Dynamic head = dynamic suction head or lift + dynamic
discharge head – which includes static heads, frictional pipe losses
and minor losses
Total
Dynamic
Head
(TDH)Dynamic
suction lift
Dynamic
discharge
head
Energy Line
Energy Grade Line & Hydraulic Grade Line
Energy Grade Line = Energy Head = Velocity Head + Pressure
Head + Potential (Elevation) Head
Hydraulic Grade Line = Energy Head – Velocity Head = Water
Surface
Total System-Head Curve
Total System Head-Curve
Friction Head
(Total Head loss)
Static
Head
TDH
(Total Dynamic Head)
(ft)
Q, Flow
(ft3/s)
System Curve
The relationship
between the head
(pressure)
condition present
in a specific
system (pipe
network,
distribution
system, etc.) for a
specific flow
Determine the static head, total dynamic head (TDH), and total head (friction) loss in the system shown below
Total static head 730 ft 630 ft 100 ft= − =
pd =48 psig
ps =−6 psig
El = 630 ft
El = 640 ft
El = 730 ft
( ){ } 2.31 ftTDH 48 6 psi 124.7 ft
psi
= − − =
( )TDH Static head 124.7 100 ft 24.7 ftLH = − = − =
Example - TDH Calcs with Pressure Gauge Values
A booster pumping station is being designed to transport water from an
aqueduct to a water supply reservoir, as shown below. The maximum design
flow is 25 mgd (38.68 ft3/s). Determine the required TDH, given the following:
� H-W ‘C’ values are 120 on suction side and 145 on discharge side
� Minor loss coefficients are
0.50 for pipe entrance
0.18 for 45o bend in a 48-in pipe
0.30 for 90o bend in a 36-in pipe
0.16 and 0.35 for 30-in and 36-in butterfly valves, respectively
� Minor loss for an expansion is 0.25(v22 − v1
2)/2g
Short 30″ pipe w/30″butterfly valve
El = 6349
to 6357 ft
El = 6127
to 6132 ft
30″ to 48″expansion
4000′of 48″ pipe
w/two 45o bends
8500′of 36″ pipe w/one
90o bend and eight
butterfly valves
Example – TDH Calcs with Losses
Determine pipeline velocities from v =Q/A..
v30= 7.88 ft/s, v36= 5.47 ft/s, v48= 3.08 ft/s
Minor losses, suction side:2
30
2
30
2 2
30 48
2o 48
,minor
Entrance: 0.50 0.49 ft2
Butterfly valve: 0.16 0.16 ft2
Expansion: 0.25 0.21 ft2
Two 45 bends: 2* 0.18 0.05 ft2
0.91 ft
L
L
L
L
L
vh
g
vh
g
v vh
g
vh
g
h
= =
= =
−= =
= =
=∑
Example – TDH Calcs with Losses
Minor losses, discharge side:
2
36
2o 36
,minor
8 Butterfly valves: 8* 0.35 1.30 ft2
One 90 bend: 0.30 0.14 ft2
1.90 ft
L
L
L
vh
g
vh
g
h
= =
= =
=∑
Example – TDH Calcs with Losses
1.85
2.630.43f
Qh L
CD
=
( )( )( )
1.85
, 2.63
38.74000 2.76 ft
0.43 120 48 /12f suctionh
= =
Pipe friction losses (don’t use a conservative C):1.85
2.630.43
fh QS
L CD
= =
( )( ) ( )
1.85
, 2.63
38.78500 16.77 ft
0.43 145 36 /12f dischargeh
= =
Example – TDH Calcs with Losses
Loss of velocity head at exit:2
36Exit: 0.46 ft2
L
vh
g= =
( )Static head 6357 6127 ft 230 ft= − =
Total static head under worst-case scenario (lowest water level in
aqueduct, highest in reservoir):
[ ] [ ]( )
, ,TDH
230 0.91 1.90 2.76 16.77 0.46 ft
252.8 ft
static L minor f L exitH h h h= + + +
= + + + + +
=
∑ ∑Total dynamic head required:
Example – TDH Calcs with Losses
System Curve Development
�We’ve calculated TDH and head losses for a single flow condition
�A system curve represents a range of TDH and flow conditions
�DON’T use a conservative approach to calculate a system curve for a “new” system (use C ≈ 140). Try to be as accurate as possible.
�Only use C ≤ 100 as a check.
�To simplify system curve calcs, can either: � Sum K values for each pipe size
� Convert various pipe sizes, fitting and valves to one pipe size and lenght
Calculate System Curve
Summary
�Definition of a System Curve: � A graphical representation of a piping system’s energy
requirement response to a range of flows.
�References:� Crane Technical Paper No. 410 (Crane Valves)
� Cameron Hydraulic Data (Ingersoll-Rand)
� Hydraulic Handbook (Fairbanks Morse)
� Hydraulic Institute Engineering Data Book (HI)
� Handbook of Hydraulic Resistance (Idelchik)
� Component manufacturers (ℎ = ��
�)
�Programs:� AFT Fathom v9 (Applied Flow Technology)
� Flow of Fluids (Crane)
Next Steps
So we have a system curve – what next?
�Select a pump to meet the requirements of the
system
�Do you need to develop a composite system curve?
� Intermediate high point condition
�Bracket our system conditions (best case/worst case,
high head/low head/variable head, range of pipe
conditions/appropriate selection of C factor)
Questions/Discussion