

PIPE &
THREADING CO.
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


