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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
(7.000 5 - 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 =
D1D - d1d
Where:
D = Outside Length, long
side, inches
D1= Outside
Length, short side, inches
d = Inside Length, long
side, inches
d1= 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" D1=
4.00" d = 5.00" d1= 3.00"
A = D1D -
d1d
A = 4.00 (6.00) - 3.00
(5.00) = 9.00
A = 9.00
inches5
2. PLAIN END WEIGHT (Wpe): 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} Wpe
= 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 BURST-RESISTANCE (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 Yp 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 one-inch
extra- strong piece of pipe compared with a one-inch standard
weight piece of pipe is identical; however, the inside
diameter of the extra-strong is smaller than the inside
diameter of the standard weight because the wall thickness is
greater in the extra-strong 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 in2, 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
horse-power: 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.
horse-power:
3960
Theoretical
water US GPM x head in pounds
horse-power:
1714
Brake
horse-power: Theoretical water horse-power
Pump
efficiency
Velocity in
feet .408 x US Gal Per
Min = .32 x GPM
per
second: Pipe diameter in
inches2 pipe area
One
acre-foot: 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
inches2 x .2856 x bbls. per hour x pipe dia. in
inches2
Net
horse-power: The theoretical horse-power necessary to do the
work
Net
horse-power: Barrels per day x
pressure x .000017
Net
horse-power: Barrels per hour x
pressure x .000408
Net
horse-power: 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 = V2
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 |
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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
Volt-amperes:
Product of volts and amperes
Kilovolt-Amperes
(KVA): 1000
volt-amperes
Watt-hour: Small
unit of electrical work - watts times hours
Kilowatt-hour
(KWHr): Large unit of
electrical work - 1000 watt-hours
Horse Power-hour
(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 foot-pounds (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 horse-power 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 foot-pounds
torque, the horse-power 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
horse-power) 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 watt-hours 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
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