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Pump operating point calculator units:
cfs=cubic foot per second, cm=centimeter, ft=foot, gal=U.S. gallon, gpd=U.S. gallon per day, gpm=U.S. gallon per mimute, hp=horsepower,
lb=pound, m=meter, min=minute, N=Newton, Pa=Pascal, psi=lb/inch^{2}, s=second
Topics: Scenarios Common Questions Equations
Variables HazenWilliams Coefficients
Minor Loss Coefficients Error Messages
Introduction
The HazenWilliams equation for major (friction) losses is commonly used by engineers for
designing and analyzing piping systems carrying water at typical temperatures of municipal
water supplies (40 to 75^{ o}F; 4 to 25^{ o}C). A pump curve is
incorporated into the pump operating point calculator to simulate flows containing centrifugal pumps or other
pumps that have a pump curve. To keep the pump operating point calculator's input relatively simple, we
only require you to enter two points on the pump curve  flow at zero head and head at
zero flow. A parabolic curve is then formed between the two points as shown in Equations below. The pump operating point calculator also asks for information
specifically about the pipe on the suction side of the pump. This information is
used to compute the net positive suction head available (NPSH_{A}). For a
pump to properly function, the NPSH_{A} must be greater than the NPSH required by
the pump (obtained from the pump manufacturer). If your system does not require a
pump or uses a pump that does not have a parabolically shaped pump curve, then our other HazenWilliams design calculation may be more
helpful.
Piping Scenarios
Pipe A is the pipe upstream from the pump (i.e. the suction side pipe).
Convention for Z_{1}Z_{2} and Z_{1}Z_{3}:
If location 1 is above location 2, then Z_{1}Z_{2} should be
entered as positive. If location 2 is above location 1, then Z_{1}Z_{2}
should be entered as negative. Likewise for Z_{1}Z_{3}.
Equations and Methodology
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Pump operating point calculator on this page uses the steady state energy equation. Minor losses
(due to valves, pipe bends, etc.) and major losses (due to pipe friction) are included.
The HazenWilliams equation for friction losses is used. The equations are
standard equations which can be found in most fluid mechanics textbooks (see References). A pump curve is included in the
calculation. Determination of the pump curve requires that the user enter the two
extreme points on the curve  head when capacity is zero, and capacity when head is
zero. Then, a parabola with a negative curvature is fit through the two
points. This parabola is used since it is a good approximation of a typical pump
curve and does not require users to enter a multitude of data points. And,
oftentimes, pump catalogs only give the two extreme points on the curve rather than a
graph showing the complete curve.
Pump Curve
To provide an example of a pump curve developed using the equation H=H_{max}[1(Q/Q_{max})^{2}],
let Q_{max}=1500 gpm (when head is zero) and H_{max}=900 ft (when Q is
zero). The pump curve used in the calculation will look like:
All of the calculations on this page have analytic (closed form) solutions except for
"Solve for V, Q", "Q known. Solve for Diameter", and "V known.
Solve for Diameter". These three calculations required a numerical
solution. Our solution utilizes a modified implementation of Newton's method that
finds roots of the equations with the result accurate to 8 significant digits. All
of the calculations utilize double precision, but results are shown to eight significant figures. "V known. Solve for
Diameter" may find two diameters which give the same velocity  if this is the case,
both diameters are shown.
Variables Units: L=length,
P=pressure, T=time
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A = Pipe area [L^{2}].
C = HazenWilliams coefficient. See table
below.
D = Pipe inside diameter [L].
DH = Driving Head [L] = left side of the first equation
above. Also equals the right side of the equation which is the sum of major and minor losses.
g = Acceleration due to gravity = 32.174 ft/s^{2} = 9.8066 m/s^{2}
h_{f} = Major losses for entire pipe [L].
h_{fA} = Major losses for pipe upstream of pump (pipe A) only [L].
h_{m} = Minor losses for entire pipe [L].
h_{mA} = Minor losses for pipe upstream of pump (pipe A) only [L].
H = Total dynamic head [L]. Also known as system head or head supplied by
pump.
H_{max} = Maximum head that pump can provide [L]. It is the head
when Q=0.
k = Unit conversion factor = 1.318 for English units = 0.85 for Metric units.
K = Sum of minor loss coefficients for entire pipe. See table below for values.
K_{A} = Sum of minor loss coefficients for pipe upstream of pump (pipe
A).
L = Total pipe length [L].
L_{A} = Length of pipe upstream of pump (pipe A) [L].
NPSH_{A} = Net positive suction head available [L].
P_{atm} = Atmospheric (or barometric) pressure [P]. Standard
atmospheric pressure = 14.7 psi = 29.92 inch Hg = 760 mm Hg = 1 atm = 101,325 Pa = 1.01
bar. Note that your local atmospheric pressure is different from standard
atmospheric pressure.
P_{v} = Vapor pressure of fluid [P]. Expressed as an absolute
pressure. This value is builtin to the program as 2000 N/m^{2} (absolute)
for water at 15^{o}C.
P_{1} = Gage pressure at location 1 of the system [P]. Location 1
could be the surface of a reservoir open to the atmosphere (thus P_{1}=0),
or the pressure in a supply main (same as a tank under pressure), or location 1 could
simply be a location in a pipe upstream of the pump.
P_{1}P_{3} = Pressure difference between locations 1 and 3 [P].
Q = Flowrate [L^{3}/T]. Also known as discharge or capacity.
Q_{max} = Maximum flowrate on pump curve [L^{3}/T].
Corresponds to point on pump curve where head is zero.
S = Specific Weight of Water (i.e. weight density; weight per unit volume)
= 62.4 lb/ft^{3} for English units = 9800 N/m^{3} for Metric units
V_{1} = Velocity of fluid at location 1. This is determined when
you select a scenario. If location 1 is a reservoir or main (Scenarios B, C, E, and
F), then V_{1} is automatically set to 0 because the velocity head of the
fluid in the reservoir or main (or pressure tank) is much smaller than in the attached
pipeline. This is a standard assumption in fluid mechanics. However, if
location 1 is inside the suction side pipeline, then V_{1} is
automatically computed as Q/A.
V_{3} = Velocity of fluid at location 3. This is determined when
you select a scenario. If location 3 is a reservoir or main (Scenarios B, D, E, and
G), then V_{3} is automatically set to 0 because the velocity head of the
fluid in the reservoir or main (or pressure tank) is much smaller than in the attached
pipeline. This is a standard assumption in fluid mechanics. However, if
location 3 is inside your discharge side pipeline, then V_{3} is
automatically computed as Q/A.
Z_{1}Z_{2} = Elevation of location 1 minus elevation of pump
[L]. If the pump is above location 1, then enter this value as negative.
Z_{1}Z_{3} = Elevation of location 1 minus elevation of location
3 [L].
Common Questions
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What is net positive suction head? It is the sum of the heads that push
fluid into the pump less the suction side losses. Most pumps have a minimum
requirement for NPSH, called NPSH_{R}. If the NPSH
available by the piping system (NPSH_{A}) is lower than NPSH_{R},
then the pump will not function properly and may overheat.
What is Driving Head? DH is the sum of heads supplied by the pump,
elevation, pressure, and velocity differences between the inlet and outlet system
boundaries. DH is equivalent to the sum of minor and major losses.
How is Total dynamic head different than Driving head? Total dynamic head, H,
is the head that the pump must provide to overcome major losses, minor losses, and
elevation, pressure, and velocity head differences between outlet and inlet. H
may be more or less than DH depending on whether the elevation, pressure, and/or
velocity head differences are beneficial or must be overcome.
Your program is great! What are its limitations? Pipes must all have
the same diameter. The fluid must be water. Our approximation for the pump
curve may not be close enough to your actual pump curve to give sufficiently accurate
results.
Do you have more common questions and answers somewhere else on your website?
Yes, see our HazenWilliams calculation
without pump curves.
Where can I find additional information? References
Table of HazenWilliams Coefficients (C is
unitless) Back
to Calculations
Compiled from References
Material 
C 
Material 
C 
Asbestos Cement 
140 
Copper 
130140 
Brass 
130140 
Galvanized iron 
120 
Brick sewer 
100 
Glass 
140 
CastIron: 

Lead 
130140 
New, unlined 
130 
Plastic 
140150 
10 yr. old 
107113 
Steel: 

20 yr. old 
89100 
Coaltar enamel lined 
145150 
30 yr. old 
7590 
New unlined 
140150 
40 yr. old 
6483 
Riveted 
110 
Concrete/Concretelined: 



Steel forms 
140 
Tin 
130 
Wooden forms 
120 
Vitrif. clay (good condition) 
110140 
Centrifugally spun 
135 
Wood stave (avg. condition) 
120 
Table of Minor Loss Coefficients (K
is unitless) Back
to Calculations
Compiled from References
Fitting 
K 
Fitting 
K 
Valves: 

Elbows: 

Globe, fully open 
10 
Regular 90^{o}, flanged 
0.3 
Angle, fully open 
2 
Regular 90^{o}, threaded 
1.5 
Gate, fully open 
0.15 
Long radius 90^{o}, flanged 
0.2 
Gate 1/4 closed 
0.26 
Long radius 90^{o}, threaded 
0.7 
Gate, 1/2 closed 
2.1 
Long radius 45^{o}, threaded 
0.2 
Gate, 3/4 closed 
17 
Regular 45^{o}, threaded 
0.4 
Swing check, forward flow 
2 


Swing check, backward flow 
infinity 
Tees: 



Line flow, flanged 
0.2 
180^{o} return bends: 

Line flow, threaded 
0.9 
Flanged 
0.2 
Branch flow, flanged 
1.0 
Threaded 
1.5 
Branch flow, threaded 
2.0 




Pipe Entrance (Reservoir to Pipe): 

Pipe Exit (Pipe to Reservoir) 

Square Connection 
0.5 
Square Connection 
1.0 
Rounded Connection 
0.2 
Rounded Connection 
1.0 
Reentrant (pipe juts into tank) 
1.0 
Reentrant (pipe juts into tank) 
1.0 
Error Messages
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Some or all values may be computed even with error messages, even though physically the situation cannot occur.
"An input is < 0." The following values must be entered as
≥ 0: K and K_{A}. One or more of them was
entered as <0.
"An input is ≤ 0." The following values must be entered as
positive: Q, V, D, L, C, Q_{max}, H_{max}, L_{A}.
One or more of them was entered as ≤0.
"K_{A} must be ≤ K." Minor loss coefficient for pipe
A cannot exceed the minor loss coefficient for the entire pipe system.
"L_{A} must be ≤ L". The length of pipe A
cannot exceed the length of the entire pipe.
"P_{1}+P_{atm} must be >0." The sum of P_{1}+P_{atm}
gives P_{1} in absolute pressure. It is physically impossible to
have an absolute pressure ≤ 0 since that implies a complete vacuum at location
1.
"Need P_{1}(P_{1}P_{3})+P_{atm} >0."
The absolute pressure at location 3 is less than 0 absolute. It is physically impossible to have a complete vacuum.
"Q must be ≤ Q_{max}." System flowrate cannot be
entered as greater than the maximum flow rate that the pump can deliver.
"Tanks open so P_{1}P_{3}=0 for B." This message
occurs if Scenario B (reservoir to reservoir) is selected and Solve for P_{1}P_{3}
is selected. Reservoirs are defined to be open to the atmosphere, so they have a
pressure difference of zero by default. If you have tanks that are under pressure,
select Scenario E (main to main) instead.
"Pump not needed. H will be ≤0." The system characteristics
that were entered result in a negative total dynamic head which means that a pump is not
necessary to deliver the flow. There are enough elevation, pressure, and/or velocity
head differences to overcome the major and minor losses without the need of a pump.
For this situation, it would be better to run our HazenWilliams
calculation that doesn't incorporate a pump curve.
"Infeasible Input. DH will be ≤0." Driving head (the left
hand side of the first equation shown above in Equations) must be
positive in order for fluid to flow. The system and pump characteristics entered
result in DH being ≤ 0.
"Infeasible Input. (DHh_{m})≤0." The difference (DHh_{m})
is ≤ 0 implying that major losses will also be ≤0 which is impossible for a
flowing fluid.
"Infeasible Input (DHh_{f} )<0." The difference (DHh_{f}
) is < 0 implying that minor losses will also be <0, which is impossible.
"Infeasible input." Driving head and/or major losses are ≤0;
or minor losses are < 0.
© 19992024 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
Please contact us for consulting or questions about water pipes and pump curves.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 7072614
LMNO@LMNOeng.com https://www.LMNOeng.com

To:
LMNO Engineering home page (more calculations)
Other single pipe calculators:
Pump curve calculator for liquids and gases (DarcyWeisbach friction)
Water pipe calculator without pump curve (HazenWilliams friction)
Pipe flow calculator for liquids and gases without pump curve (DarcyWeisbach friction)
Multiple pipes:
Bypass Loop
Pipe Network
Videos of experiment and analysis of friction loss
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