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Units in pipe design using Hazen-Williams friction loss equation:
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/inch2, s=second
Topics: Scenarios Equations Common Questions
Minor Loss Coefficients
Introduction to Pipe Design using Hazen-Williams Friction Losses
This calculation is valid for water flowing at typical temperatures found in municipal
water supply systems (40 to 75 oF; 4 to 25 oC). Our calculation is based on the steady state incompressible energy
equation utilizing Hazen-Williams friction losses as well as minor losses. The Hazen-Williams friction loss equation is commonly used by civil engineers
for municipal water distribution system design. Our pipe flow calculation
can compute flowrate, velocity, pipe diameter, elevation difference, pressure difference,
pipe length, minor loss coefficient, and pump head (total dynamic head).
Since boundary conditions affect the flow characteristics, our calculation allows you to
select whether your locations 1 and 2 are within pipes, at the surface of open reservoirs,
or in pressurized mains (same as pressurized tank). If there is no pump between locations
1 and 2, then enter the pump head (Hp) as 0.
Steady State Energy Equation used for Water Flow Through a Pipe
Back to Calculation
The first equation shown is the steady state energy equation for incompressible flow. The
left side of the equation contains what we call the driving head. These heads include
heads due to a pump (if present), elevation, pressure, and velocity. The terms on the
right side are friction loss and minor losses. Friction losses are computed using the
Hazen-Williams friction loss equation. The energy equation is well-accepted in the field
of fluid mechanics and can be found in many references such as Cimbala and Cengel (2008),
Munson et al. (1998), and Streeter et al. (1998), while the Hazen-Williams equation for
friction losses is well-established in the water supply literature and can be found in
references such as Viessman and Hammer (1998) and Mays (1999).
The Hazen-Williams equation (the hf =... equation) is empirical and requires
that you use particular units as noted below. Though the other equations are dimensionally
correct, only units that can be used in all of the equations are shown below. Our
calculation allows you to enter a variety of units and automatically performs the unit
ft=foot, lb=pound, m=meter, N=Newton, s=second
A = Pipe cross-sectional area, ft2 or m2.
C = Hazen-Williams pipe roughness coefficient. See
table below for values.
D = Pipe diameter, ft or m.
Driving Head (DH) = left side of the first equation (or right side of the equation), ft.
This is not total dynamic head.
g = acceleration due to gravity = 32.174 ft/s2 = 9.8066 m/s2.
hf = Major (friction) losses, ft or m.
hm = Minor losses, ft or m.
Hp = Pump head (also known as Total Dynamic Head), ft or m.
k = unit conversion factor = 1.318 for English units = 0.85 for Metric units
Km = Sum of minor loss coefficients. See table
L = Pipe length, ft or m.
Pump Power (computed by program) = SQHp, lb-ft/s or N-m/s. Theoretical
pump power. Does not include an inefficiency term. Note that 1 horsepower = 550 ft-lb/s.
P1 = Upstream pressure, lb/ft2 or N/m2.
P2 = Downstream pressure, lb/ft2 or N/m2.
Q = Flow rate in pipe, ft3/s or m3/s.
S = Weight density of water = 62.4 lb/ft3 for English units = 9800 N/m3 for Metric
V = Velocity in pipe, ft/s or m/s.
V1 = Upstream velocity, ft/s or m/s.
V2 = Downstream velocity, ft/s or m/s.
Z1 = Upstream elevation, ft or m.
Z2 = Downstream elevation, ft or m.
All of the calculations on this page have analytic (closed form) solutions except for
"Solve for V, Q" and "Q known. Solve for Pipe Diameter." These
two 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.
Table of Hazen-Williams Coefficients (C is
unit-less) Back to
Compiled from References
|10 yr. old
|20 yr. old
||Coal-tar enamel lined
|30 yr. old
|40 yr. old
||Vitrif. clay (good condition)
||Wood stave (avg. condition)
Table of Minor Loss Coefficients (Km
is unit-less) Back
Compiled from References
|Globe, fully open
||Regular 90o, flanged
|Angle, fully open
||Regular 90o, threaded
|Gate, fully open
||Long radius 90o, flanged
|Gate 1/4 closed
||Long radius 90o, threaded
|Gate, 1/2 closed
||Long radius 45o, threaded
|Gate, 3/4 closed
||Regular 45o, threaded
|Swing check, forward flow
|Swing check, backward flow
||Line flow, flanged
|180o return bends:
||Line flow, threaded
||Branch flow, flanged
||Branch flow, threaded
|Pipe Entrance (Reservoir to Pipe):
||Pipe Exit (Pipe to Reservoir)
|Re-entrant (pipe juts into tank)
||Re-entrant (pipe juts into tank)
Back to Calculation
I took fluid mechanics a long long time ago. What is head? Why does it have
units of length? Head is energy per unit weight of fluid (i.e. Force x
Length/Weight = Length).The program on this page solves the energy equation (shown below);
we call energy "head."
Why is Pressure=0 for a reservoir? A reservoir is open to the atmosphere, so its
gage pressure is zero.
Why is Velocity=0 for a reservoir? This is a common assumption in fluid
mechanics and is based on the fact that a reservoir has a large surface area. Therefore,
the water level drops very little even if a lot of water flows out of the
reservoir. A reservoir may physically be a lake or a large diameter tank.
What is a "main" and a "lateral"? A "main" is
a large diameter water supply pipe that has many smaller diameter "laterals"
branching off of it to supply water to individual residences, businesses, or
sub-divisions. In fluid mechanics, we set V=0 for the main since it has a large diameter
(relative to the lateral) and thus a very small velocity. To further justify the V=0
assumption, the main's pressure is typically high, so the velocity head in the main is
negligible. The main is drawn such that it is coming out of your computer monitor.
Can I model flow between two reservoirs using either Scenario B or E? Yes,
you can. If using Scenario E, just set P1-P2=0. Scenario B
automatically sets P1-P2=0.
Can I model flow between two mains using either Scenario B or E? Only if the
pressure is the same in both mains.
How do I model a pipe discharging freely to the atmosphere? Use Scenario A,
C, or F. Since P2=0 (relative to atmospheric pressure), P1-P2
that is input or output will be P1.
What are minor losses? Minor losses are head (energy) losses due to valves,
pipe bends, pipe entrances (for water flowing from a tank to a pipe), and pipe exits
(water flowing from a pipe to a tank), as opposed to a major loss which is due to the
friction of water flowing through a length of pipe. Minor loss coefficients (Km)
are tabulated below. For our program, all of the pipes have the same diameter, so you can
add up all your minor loss coefficients and enter the sum in the Minor Loss Coefficient
I'm confused about pumps. Only input Pump Head if the pump is between points
1 and 2. Otherwise, enter 0 for Pump Head.
Your program is great! What are its limitations? Pipes must all have
the same diameter. Pump curves cannot be implemented. The fluid must be water.
Where can I find additional information? References
What is Driving Head? See above definitions of variables. It is not total
dynamic head. Hp is pump head (also known as total dynamic head).
Back to Calculation
Cimbala, John M. and Yunus A. Cengel. 2008. Essentials of Fluid Mechanics: Fundamentals
and Applications. McGraw-Hill.
Mays, Larry W, ed. 1999. Hydraulic Design Handbook. McGraw-Hill.
Munson, Bruce R. Donald F. Young, and Theodore H. Okiishi. 1998.
Fundamentals of Fluid Mechanics. John Wiley and Sons. Inc. 3ed.
Streeter, Victor L., E. Benjamin Wylie, and Keith W. Bedford. 1998. Fluid
Mechanics. McGraw-Hill. 9ed.
Viessman, Warren and Mark J. Hammer. 1998. Water Supply and Pollution
Control. Addison Wesley. 6ed.
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Software, Ltd. All rights reserved.
Please contact us for consulting or questions about design of circular pressurized water pipes.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio 45701 USA Phone: (740) 707-2614
LMNO Engineering home page (more calculations)
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Videos of experiment and analysis of friction loss