## 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 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 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 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 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 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 inches^{2} 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 inches^{2} x .2856 x bbls. per hour x pipe dia. in inches^{2}

__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 = __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

__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**