Design of Circular Pressurized Water Pipes |
Calculation uses Hazen-Williams friction loss equation (commonly used by Civil Engineers). Valid for water at temperatures typical of city water supply systems (40 to 75 ^{o}F; 4 to 25^{ o}C). |
LMNO Engineering home page LMNO@LMNOeng.com
phone: (740) 592-1890 (USA) |
Register to enable "Calculate" button.
Topics: Scenarios Equations Common Questions Hazen-Williams Coefficients Minor Loss Coefficients References
Introduction
This calculation is valid for water flowing at typical temperatures found in municipal
water supply systems. Our calculation is based on the steady state incompressible energy
equation utilizing Hazen-Williams friction losses as well as minor losses. The calculation
can compute flowrate, velocity, pipe diameter, elevation difference, pressure difference,
pipe length, minor loss coefficient, and pump head (total dynamic head).
Piping Scenarios
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 (H_{p}) as 0.
Steady State Energy Equation used for this page
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 heads. 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 h_{f} =... 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
conversions.
ft=foot, lb=pound, m=meter, N=Newton, s=second
A = Pipe cross-sectional area, ft^{2} or m^{2}.
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/s^{2} = 9.8066 m/s^{2}.
h_{f} = Major (friction) losses, ft or m.
h_{m} = Minor losses, ft or m.
H_{p} = 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
K_{m} = Sum of minor losses coefficients. See table
below.
Pump Power (computed by program) = SQH_{p}, lb-ft/s or N-m/s. Theoretical
pump power. Does not include an inefficiency term. Note that 1 horsepower = 550 ft-lb/s.
P_{1} = Upstream pressure, lb/ft^{2} or N/m^{2}.
P_{2} = Downstream pressure, lb/ft^{2} or N/m^{2}.
Q = Flow rate in pipe, ft^{3}/s or m^{3}/s.
S = Weight density of water = 62.4 lb/ft³ for English units = 9800 N/m³ for Metric
units
V = Velocity in pipe, ft/s or m/s.
V_{1} = Upstream velocity, ft/s or m/s.
V_{2} = Downstream velocity, ft/s or m/s.
Z_{1} = Upstream elevation, ft or m.
Z_{2} = 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
Calculation
Compiled from References
Material | C | Material | C |
Asbestos Cement | 140 | Copper | 130-140 |
Brass | 130-140 | Galvanized iron | 120 |
Brick sewer | 100 | Glass | 140 |
Cast-Iron: | Lead | 130-140 | |
New, unlined | 130 | Plastic | 140-150 |
10 yr. old | 107-113 | Steel: | |
20 yr. old | 89-100 | Coal-tar enamel lined | 145-150 |
30 yr. old | 75-90 | New unlined | 140-150 |
40 yr. old | 64-83 | Riveted | 110 |
Concrete/Concrete-lined: | |||
Steel forms | 140 | Tin | 130 |
Wooden forms | 120 | Vitrif. clay (good condition) | 110-140 |
Centrifugally spun | 135 | Wood stave (avg. condition) | 120 |
Table of Minor Loss Coefficients (Km
is unit-less) Back
to Calculation
Compiled from References
Fitting | Km | Fitting | Km |
Valves: | Elbows: | ||
Globe, fully open | 10 | Regular 90°, flanged | 0.3 |
Angle, fully open | 2 | Regular 90°, threaded | 1.5 |
Gate, fully open | 0.15 | Long radius 90°, flanged | 0.2 |
Gate 1/4 closed | 0.26 | Long radius 90°, threaded | 0.7 |
Gate, 1/2 closed | 2.1 | Long radius 45°, threaded | 0.2 |
Gate, 3/4 closed | 17 | Regular 45°, threaded | 0.4 |
Swing check, forward flow | 2 | ||
Swing check, backward flow | infinity | Tees: | |
Line flow, flanged | 0.2 | ||
180° 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 |
Re-entrant (pipe juts into tank) | 1.0 | Re-entrant (pipe juts into tank) | 1.0 |
Common Questions
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 P_{1}-P_{2}=0. Scenario B
automatically sets P_{1}-P_{2}=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 P_{2}=0 (relative to atmospheric pressure), P_{1}-P_{2}
that is input or output will be P_{1}.
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 (K_{m})
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
input box.
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. H_{p} is pump head (also known as total dynamic head).
References
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.
© 1998-2008 LMNO Engineering, Research, and
Software, Ltd. (All Rights Reserved)
September 2, 2008: added more discussion.
LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd. Athens, Ohio USA (740) 592-1890
LMNO@LMNOeng.com http://www.LMNOeng.com