Technical Resources —
Pipe Related Formulas

1. CROSS SECTIONAL AREA (A):
The cross sectional area expressed in square inches is used in
various tubular goods equations. The formulas described below are
based on full sections, exclusive of corner radii.
{1a} Round Tube:
A = p/4 (D5  d5)
Where:
D = Outside Diameter, inches d = Inside Diameter,
inches
Example: Calculate the cross sectional area
of a 7" O.D. x .500" wall tube.
D = 7.000 d = 7.000  2(.500) = 6.000 inches
A = p/4 (D5  d5)
A = 3.1415/4 (7.0005
 6.0005)
A = 10.210 inches
{1b} Square Tube: A = D5  d5
Where:
D = Outside Length, inches d = Inside Length,
inches
Example: Calculate the cross sectional area
of a 7" O.D. x .500" wall tube.
D = 7.000 d = 7.000  2(.500) = 6.000 inches
A = D5  d5
A = 49  36 = 13
A = 13.00 inches5
{1c} Rectangular Tube: A = D^{1}D
 d^{1}d
Where:
D = Outside Length, long side, inches
D^{1}= Outside Length, short side, inches
d = Inside Length, long side, inches
d^{1}= Inside Length, short side, inches
Example: Calculate the cross sectional area
of a
4" x 6" rectangular tube with .500" wall
thickness.
D = 6.00" D^{1}= 4.00" d = 5.00" d^{1}=
3.00"
A = D^{1}D  d^{1}d
A = 4.00 (6.00)  3.00 (5.00) = 9.00
A = 9.00 inches5
2. PLAIN END WEIGHT (W_{pe}):
The plain end weight expressed in pounds per foot is used in
connection with pipe to describe the nominal or specified weight per
foot. This weight does not account for adjustments in weight due to
end finishing such as upsetting or threading.
{2} W_{pe} =
10.68 (D  t)t
Where:
W_{pe}
= plain end weight, calculated to 4 decimal places and rounded to 2
decimals, pounds/foot
D = Specified Outside Diameter of the Pipe,
inches
t = Specified Wall Thickness, inches
Example: Calculate the plain end weight of
pipe having a specified O.D. of 7 inches and a wall thickness of
.540 inches.
W_{pe}
= 10.68 (7.000  .540) .540
W_{pe}
= 37.2561
W_{pe}
= 37.26 pounds/foot
3. INTERNAL YIELD PRESSURE BURSTRESISTANCE
(P):
The internal yield pressure or burst resistance
of pressure bearing pipe is expressed in pounds/square inch (psi).
The .875 factor is to allow for minimum permissible wall based on
API criteria for OCTG and line pipe. This factor can be changed
based on other applicable specifications regarding minimum
permissible wall thickness.
{3} P = 0.875 [ 2 Y_{p}
t/D]
Where:
P = Minimum Internal Yield Pressure (Burst
Resistance) in pounds per square inch, rounded to the nearest 10 psi.
Y_{p}=
Specified Minimum Yield Strength, pounds per square inch.
t = Nominal (specified) Wall Thickness, inches
D = Nominal (specified) Outside Diameter, inches
Example: Calculate the burst resistance of 7"
O.D. x .540" wall API L80 casing.
P = 0.875 [ 2 Y_{p}
t/D]
P = 0.875 [ (2)(80,000)(.540)/7]
P = 10,800 psi
4. PIPE SPECIFICATIONS BASICS
Pressure Determinations:
Barlow's Formula is commonly used to determine:
1. Internal Pressure at Minimum Yield
2. Ultimate Bursting Pressure
3. Maximum Allowable Working Pressure
4. Mill Hydrostatic Test Pressure
This formula is expressed as P = 2St
where:
P = Pressure, psig
I = Nominal wall thickness, inches
D = Outside Diameter, inches
S = Allowable Stress, psi, which depends on the
pressure being determined
To illustrate, assume a piping systems 8 5/8" O.D.
x .375" wall has a specified minimum yield strength (SMYS) of 35,000
psi and a specified minimum tensile strength of 80,000 psi.
For 1. Internal Pressure of Minimum Yield
S = SMYS (35,000) psi and
P = 2St = (2)(35,000)(0.375)
D 8.625 = 3043 or 3040 psig (rounded to nearest
10 psig)
For 2. Ultimate Bursting Pressure
S = Specified Minimum Tensite Strength (60,000
psi) and
P = 2St = (2)(60,000)(0.375)
D 8.625 = 5217 or 5220 psig (rounded to nearest
10 psig)
For 3. Maximum Allowable Working Pressure (MAOP)
S = SMYS (35,000 psi) reduced by a design factor,
usually 0.72 and
P = 2St = (2)(35,000 x 2)(0.375)
D 8.625 = 2191 or 2190 psig (rounded to nearest
10 psig)
For 4. Mill Hydrostatic Test Pressure
S = SMYS (35,000 psi) reduced by a factor
depending on O.D. grade (0.60 for 8 5/8" O.D. grade B) and
P = 2St = (2)(35,000 x 0.60)(0.375)
D 8.625 = 1826 or 1830 psig (rounded to nearest
10 psig)
Wall Thickness
Barlow's Formula is also useful in determining
the wall thickness required for a piping system. To illustrate,
assume a piping system has been designed with the following
criteria:
1. A working pressure of 2,000 psi (P)
2. The pipe to be used is 8 5/8" O.D. (D)
specified to ASTM A53 grade B (SMYS  35,000 psi)
Rearranging Barlow's Formula to solve for wall
thickness gives:
t = PD = (2,000) (8.625) = 0.246"
wall
2S (2) (35,000)
Wall thickness has no relation to outside
diameter  only the inside diameter is affected. For example, the
outside diameter of a oneinch extra strong piece of pipe compared
with a oneinch standard weight piece of pipe is identical; however,
the inside diameter of the extrastrong is smaller than the inside
diameter of the standard weight because the wall thickness is
greater in the extrastrong pipe.
5. WATER DISCHARGE MEASUREMENTS:
To calculate the volume being displaced through a pipe or the amount
of volume of an irrigation well, the following formula is
applicable:
Q = 3.61 A H
%Y
Where:
Q = Discharge in Gallons per minutes
A = Area of the pipe, inches squared
H = Horizontal measurement, inches
Y = vertical measurement, inches
Example: Calculate the discharge of a 10"
pipe which has an area of 78.50 in^{2}, a horizontal
measurement of 12" and a vertical measurement of 12".
Q = 3.61 A H
%Y
Q = 3.61 (78.50) (12)
%12
Q = 3400.62
3.464
Q = 981.70 gallons per minute
This formula is a close approximation of the
actual measurement of the volume being displaced. The simplest
method is to measure a 12 inch vertical measurement as a standard
procedure, then measure the distance horizontally to the point of
the 12" vertical measurement.
GENERAL TECHNICAL INFORMATION
WATER
One miner's inch: 1 1/2 cubic feet per minute
= 11.25 U.S. gallons per minute = flow per minute through 1 inch
square opening in 2 inch thick plank under a head of 6 1/2 inches to
center of orifice in Arizona, California, Montana, Nevada and
Oregon. 9 U.S. gallons per minute in Idaho, Kansas, Nebraska, New
Mexico, North Dakota, South Dakota and Utah.
One horsepower: 33,000 ft. pounds per minute
Cubic feet per second: Gallons per minute
449
Theoretical water US GPM x head in feet x Sp. Gr.
horsepower: 3960
Theoretical water US GPM x head in pounds
horsepower: 1714
Brake horsepower: Theoretical water
horsepower
Pump efficiency
Velocity in feet .408 x US Gal Per Min
= .32 x GPM
per second: Pipe diameter in inches^{2}
pipe area
One acrefoot: 325,850 US gallons
1,000,000 US gallons per day: 695 US gallons
per minute
500 pounds per hour: 1 US gallon per minute
Doubling the diameter of a pipe or cylinder
increases its capacity four times
Friction of liquids in pipes increases as the
square of the velocity.
Velocity in feet per minute necessary to
discharge a given volume of water, in a given time =
Cubic Feet of water x 144
area of pipe in sq. inches
Area of required pipe, the volume and
velocity of water being given = No. cubic feet water x 144
Velocity in feet per min.
From this area the size pipe required may be
selected from the table of standard pipe dimensions.
Atmospheric pressure at sea level is 14.7
pounds per square inch. This pressure with a perfect vacuum will
maintain a column of mercury 29.9 inches or a column of water 33.9
feet high. This is the theoretical distance that water manu be drawn
by suction. In practice, however, pumps should not have a total
dynamic suction lift greater that 25 feet.
CRUDE OIL
One gallon: 58,310 grains
One barrel oil: 42 US gallons
One barrel per hour: .7 US gallons per minute
Gallons per minute: bbls. per day x .02917
Bbls. per hour: gallons per minute x .7
One barrel per day:
.02917 gallons per minute
Gallons per minute: bbls. per day x .02917
Bbls. per day: gallons per minute x .02917
Velocity in feet per second:
.0119 x bbls. per day x pipe dia. in inches^{2} x .2856 x
bbls. per hour x pipe dia. in inches^{2}
Net horsepower:
The theoretical horsepower necessary to do the work
Net horsepower: Barrels per day x pressure x
.000017
Net horsepower: Barrels per hour x pressure
x .000408
Net horsepower: Gallons per min. x pressure
x .000583
The customary method of indicating specific
gravity of petroleum oils in this country is by means of the Baume
scale. Since the Baume scale, for specific gravities of liquids
lighter than water, increases inversely as the true gravity, the
heaviest oil, i.e., that which has the highest true specific
gravity, is expressed by the lowest figure of the Baume scale; the
lightest by the highest figure.
MISCELLANEOUS
Areas of circles are to each other as the
squares of their diameters.
Circumference diameter of circle x 3.1416
Area circle diameter squared x .7854
Diameter circle circumference x .31831
Volume of sphere cube of diameter x .5236
Square feet square inches x .00695
Cubic feet cubic inches x .00058
Cubic yard cubic feet x .03704
Statute miles lineal feet x .00019
Statute miles lineal yards x .000568
1 gallon 8.33 pounds
1 liter .2642 gallons
1 cubic feet 7.48 gallons and/or 62.35 pounds
1 meter 3.28 feet
STATIC HEAD
Static head is the vertical distance between the
free level of the source of supply and the point of free discharge,
or to the level of the free surface of the discharged liquid.
TOTAL DYNAMIC HEAD
Total dynamic head is the vertical distance
between source of supply and point of discharge when pumping at
required capacity, plus velocity head friction, entrance and exit
losses.
Total dynamic head as determined on test where
suction lift exists, is the reading of the mercury column connected
to the suction nozzle of the pump, plus reading of a pressure gage
connected to discharge nozzle of pump, plus vertical distance
between point of attachment of mercury column and center of gage,
plus excess, if any, of velocity head of discharge over velocity
head of suction, as measured at points where the instruments are
attached, plus head of water resting on mercury column, if any.
Total dynamic head, as determined on tests where
suction head exists, is the reading of the gage attached to the
discharge nozzle of pump, minus the reading of a gage connected to
the suction nozzle of pump, plus or minus vertical distance between
centers of gages (depending upon whether suction gage is below or
above discharge gage), plus excess, if any, of the velocity head of
discharge over velocity head of suction as measured at points where
instruments are attached.
Total dynamic discharge head is the total dynamic
head minus dynamic suction lift, of plus dynamic suction head.
SUCTION LIFT
Suction lift exists when the suction measured at
the pump nozzle and corrected to the centerline of the pump is below
atmospheric pressure.
Static suction lift is the vertical distance from
the free level of the source of supply to centerline of pump.
Dynamic suction lift is the vertical distance
from the source of supply when pumping at required capacity, to
centerline of pump, plus velocity head, entrance and friction loss,
but not including internal pump losses, where static suction head
exists but where the losses exceed the static suction head the
dynamic suction lift is the sum of the velocity head, entrance,
friction, minus the static suction head, but not including internal
pump losses.
Dynamic suction lift as determined on test, is
the reading of the mercury column connected to suction nozzle of
pump, plus vertical distance between point of attachment of mercury
column to centerline of pump, plus bead of water resting on mercury
column, if any.
SUCTION HEAD
Suction head (sometimes called head of suction)
exists when the pressure measured at the suction nozzle and
corrected to the centerline of the pump is above atmospheric
pressure.
Static suction head is the vertical distance from
the free level of the source of supply to centerline of pump.
Dynamic suction head is the vertical distance
from the source of supply, when pumping at required capacity, to
centerline of pump, minus velocity head, entrance, friction, but not
minus internal pump losses.
Dynamic suction head, as determined on test, is
the reading of a gage connected to suction nozzle of pump, minus
vertical distance from center of gage to center line of pump.
Suction head, after deducting the various losses, many be a negative
quantity, in which case a condition equivalent to suction lift will
prevail.
VELOCITY HEAD
The velocity head (sometimes called "head due to
velocity") of water moving with a given velocity, is the equivalent
head through which it would have to fall to acquire the same
velocity: or the head necessary merely to accelerate the water.
Knowing the velocity, we can readily figure the velocity head from
the simple formula:
h = V^{2}
2g
in which "g" is acceleration due to gravity, or
32.16 feet per second; or knowing the head, we can transpose the
formula to:
V = %2
gh
and thus obtain the velocity.
The velocity head is a factor in figuring the
total dynamic head, but the value is usually small, and in most
cases negligible; however, it should be considered when the total
head is low and also when the suction lift is high.
Where the suction and discharge pipes are the
same size, it is only necessary to include in the total head the
velocity head generated in the suction piping. If the discharge
piping is of different size than the suction piping, which is often
the case, then it will be necessary to use the velocity in the
discharge pipe for computing the velocity head rather than the
velocity in the suction pipe.
Velocity head should be considered in accurate
testing also, as it is part of the total dynamic head and
consequently affects the duty accomplished.
In testing a pump, a vacuum gage or a mercury
column is generally used for obtained dynamic suction lift. The
mercury column or vacuum gage will show the velocity head combined
with entrance head, friction head, and static suction lift. On the
discharge side, a pressure gage is usually used, but a pressure gage
will not indicate velocity head and this must, therefore, be
obtained either by calculating the velocity or taking reading with a
Pitometer. Inasmuch as the velocity varies considerably at different
points in the cross section of a stream it is important, in using
the Pitometer, to take a number of readings at different points in
the cross section.
A table, giving the relation between velocity and
velocity head is printed below:
Velocity in feet per second 
Velocity head in feet 
Velocity in feet per second 
Velocity head
in feet 
1 
.02 
9.5 
1.40 
2 
.06 
10 
1.55 
3 
.14 
10.5 
1.70 
4 
.25 
11 
1.87 
5 
.39 
11.5 
2.05 
6 
.56 
12 
2.24 
7 
.76 
13 
2.62 
8 
1.00 
14 
3.05 
8.5 
1.12 
15 
3.50 
9

1.25 


NET POSITIVE SUCTION HEAD
NPSH stands for "Net Positive Suction Head". It
is defined as the suction gage reading in feet absolute taken on the
suction nozzle corrected to pump centerline, minus the vapor
pressure in feet absolute corresponding to the temperature of the
liquid, plus velocity head at this point. When boiling liquids are
being pumped from a closed vessel NPSH is the static liquid head in
the vessel above the pump centerline minus entrance and friction
losses.
VISCOSITY
Viscosity is the internal friction of a liquid
tending to reduce flow.
Viscosity is ascertained by an instrument termed
a Viscosimeter, of which there are several makes, viz. Saybolt
Universal; Tangliabue; Engler (used chiefly in Continental
countries); Redwood (used in British Isles and Colonies). In the
United States the Saybolt and Tangliabue instruments are in general
use. With few exceptions. Viscosity is expressed as the number of
seconds required for a definite volume of fluid under a arbitrary
head to flow through a standardized aperture at constant
temperature.
SPECIFIC GRAVITY
Specific gravity is the ratio of the weight of
any volume to the weight of an equal volume of some other substance
taken as a standard at stated temperatures. For solids or liquids,
the standard is usually water, and for gasses the standard is air or
hydrogen.
Foot pounds: Unit of work
Horse Power (H.P.): (33,000 ft. pounds per
minute  746 watts  .746 kilowatts) Unit for measurement of power
or rate of work
Voltamperes: Product of volts and amperes
KilovoltAmperes (KVA): 1000 voltamperes
Watthour: Small unit of electrical work 
watts times hours
Kilowatthour (KWHr): Large unit of
electrical work  1000 watthours
Horse Powerhour (HPHr): Unit of mechanical
work
To determine the cost of power, for any specific
period of time  working hours per day, week, month or year:
No. of working hrs, x .746 x H.P. motor =
KWHr consumed
Efficiency of motor at Motor Terminal
KWHr consumed at Motor Terminal x Rate per KWHr =
Total cost current for time specified
Torque is that force which produces or tends
to produce torsion (around an axis). Turning effort. It may be
thought of as a twist applied to turn a shaft. It can be defined as
the push or pull in pounds, along an imaginary circle of one foot
radius which surrounds the shaft, or, in an electric motor, as the
pull or drag at the surface of the armature multiplied by the radius
of the armature, the term being usually expressed in footpounds (or
pounds at 1 foot radius).
Starting torque is the torque which a motor
exerts when starting. It can be measured directly by fastening a
piece of belt to 24" diameter pulley, wrapping it part way round and
measuring the pounds pull the motor can exert, with a spring
balance. In practice, any pulley can be used for torque = lbs. pull
x pulley radius in feet. A motor that has a heavy starting torque is
one that starts up easily with a heavy load.
Running torque is the pull in pounds a motor
exerts on a belt running over a pulley 24" in diameter.
Full load torque is the turning moment
required to develop normal horsepower output at normal speed.
The torque of any motor at any output with a
known speed may be determined by the formula:
T = Brake H.P. x 5250
R.P.M.
With a known footpounds torque, the horsepower
at any given speed can be determined by the formula:
H.P. = T x R.P.M.
5250
H.P. = T x speed of belt on 24" pulley
in feet per minute 33000
COST OF PUMPING WATER
Cost per 1000 gallons pumped: .189 x power cost
per KWHr x head in feet
Pump eff. x Motor eff. x 60
Example: Power costs .01 per k.w.hour; pump
efficiency is 75%; motor efficiency is 85%; total head is 50 feet.
.189 x .01 x 50 = $ .0025 or 1/4 of a cent
.75 x .85 x 60
Cost per hour of pumping:
.000189 x g.p.m. x head in ft x power cost per
KWHr
Pump efficiency x Motor efficiency
Cost per acre foot of water:
1.032 x head in ft x power per KWHr
Pump efficiency x Motor efficiency
Pump efficiency: g.p.m. x head in feet
3960 x b.h.p. (to pump)
Head: 3960 x Pump eff. x b.h.p x g.p.m.
b.h.p. (Brake horsepower) to pump: Motor
efficiency x h.p. at motor
b.h.p.: g.p.m. x head in feet x 3960 x Pump eff.
g.p.m.: 3960 x Pump eff. x b.h.p. x head in feet
COMPUTING H.P. INPUT FROM REVOLVING WATT HOUR
METERS
(Disk Constant Method)
Kilowatts Input = KW in = K x R x 3.60 x t
HP Input = HP in = K x R x 3600 = 4.83 x K x R x
t x 746 t
K  constant representing number os watthours
through meter for on revolution of the disk. (Usually found on meter
nameplate or face of disk)
R  number of revolutions of the disk
t  seconds for R revolutions
Cost per 1000 gallons of water:
C = 746 x r x HP in x GPH
C  cost in dollars per 1000 gallons
r  power rate per kilowatt hour (dollars)
HP in  HP input measured at the meter (see
above)
H  total pumping head
GPH  gallons per hour discharged by pump
Cost per 1000 gallons of water
For each foot of head:
C = 746 x r x HP in x H x GPH
Cost per hour:
C = .746 x r x HP in 

