Fluid Power Formulas: Horsepower, Pressure, and Volume Conversions, Schemes and Mind Maps of Chemistry

Various formulas and conversions for horsepower, pressure, and volume in the context of fluid power systems. It covers topics such as horsepower calculation, pressure conversion, and volume conversion. The document also includes notes on British thermal units (BTU), reservoir capacity, and pressure drop formulas.

Typology: Schemes and Mind Maps

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FLUID POWER FORMULAS
BASIC· FORMULAS
FORMULA FOR:
WORD FORMULA: lETTER FORMULA:
FLUID PRESSURE
PRESSURE
_ FORCE (fXJUnds) P
F . F
In P/JUnds/Square Inch
U/IIT AREA (Square Inches)
=AOf pSI = A
FLUID FlOW RATE
=VOLUME (Gallons)=Y..
.-
FLaN RATE
0
In Gal/ollS/Minule
UNIT TIME (Minute)
T
FLUID POWER IN HORSEPOWER
HORSEPOWER
= PRESSURE (PSI) x FLOW (GPM) HP =~
1714
1714
FLUID FORMULAS
VELOCITY THROUGH PIPING
VELOCITY
= .3208 x flOW RATE THROUGH 1.0. (GPM) V
= .32080
tn Feet/Second ~
INTERNAl AREA (Square Inches)
A
COMPRESSIBILITY OF Oil
ADDITIONAL
PRESSURE (psi) x VOLUME OF Oil UNDER PRESSURE pv •• Approximately
=VA= 25O,ooolapprox.) \/2% Per 1000 psi
In Additional Required Or7 To Reach Pressure
VOLUME
250,000 lapprox.)
COMPRESSIBILITY OF A FLUID
1
-
CIP) = --1-
COMPRESSIBILITY =
BULK MODULUS OF THE FLUID 8M
SPECIFIC GRAVITY OF A FLUID
SPECIAC GRAVITY
=
WEIGHT OF ONE CUBIC FOOT OF flUID
SG = _W_
WEJGHT OF ONE CUBIC FOOT OF WATER
62.4283
VALVE Ie. ) FLOW FACTOR
VALVE FACTOR(e., )
_ flOW RATE (GPM) x \JSPECIFIC GRAVITY
c., =a VSG
VPRESSURE DROP(PS!)
IfiP
FOR VISCOSITIES OF 32 TO 100 SAYBOlT UNIVERSAl SECONDS:
VISCOSITY IN CENnSTOKES CEIITISTOKES
= .2253xSUS-~ CS = .2253 SUS _ 194.4
SUS
SUS
FOR VISCOSITIES OF 100 TO 240 SAYBOLT UNIVERSAl SECONDS:
VISCOSITY IN CENTISTOKES CElITISTOKES
=.2193 x SUS _ 134.6 c.s = .2193 SUS _ 134.6
SUS
SUS
FOR VISCOSITIES GREATERTHAN 240 SAYBOLT UNIVERSAL SECONDS:
VISCOSITY IN CENTISTOKES CENTISTOKES
=2!!.§. c.s =SUS
4.635
4.635
NOTE: SAYBOlT UNIVERSAL SECOIIDS IS OFTEN ABBREVIATED AS SSU. SEE PAGE120 FOR ADDITlONAl VISCOSITY INFORMATION. PUMP FORMULAS
PUMP OUTlET FLOW
flOW
= RPM x PUMP DISPlACEMENT (Cu. In.lRev.) 0
=~
In Gallons/Minute
231
231
PUMP INPUT POWER
HORSEPOWERINPUT
= FlO'N RATEOUTPUT (GFM) x PRESSURE (psi) HP =_O_P _ or GPM x psi
In HOrsepD!!fr Required
1714 x EFFICIE/ICY (Ov-r:raU)
m1714 Elf 1714E1f
PUMP EFACIENCY
OVERAll EFACIENCY
= OUTPUT HORSEPOWER x 100 Elfa,
=!!k x 100
OVERALL IN PERCENT
lllPUT HORSEPO'NER
HP"
OVERAll EFACIENCY
=VOLUMETRIC Elf. x MECHANICAL Elf Elf",
=EIf,'CL x EIf.EOt
PUMP EffiCIENCY
VOLUMETRIC EFFICIENCY
= ACTUAL flOW R.I,TEOUTPUT (GPMJ x 100 EIf~.
= ~ x 100
VOLUMETRIC IN PERCENT
THEORETICAl FLOW RATEOUTPUT {GPMJ
O",ro
PUMP EFACIENCY
MECHANICAL EFFICIENCY
THEORETICAl TOROUE TO ORIVE
x 100 EIf.EO! = TTHED X100
=MECHANICAL IN PERCENT
ACTUAl TOROUETO DRIVE
TACT.
PUMP LIFE B HOURS OF BEARING LIFE =RATED LIFE HOURS x RATEDSPEED (RPM) x ( RATEDPRESSURE (PSI) \3
8'0 = RATEDHAS. x RPM, x f-;:i J
B,o BEARING LIft
" NEVI SPEED {RPM} flEW PRESSURE (PSI) J
RPMM PH
ACTUATOR FORMULAS
FORMULA FOR:
WORD FORMULA lETTER FORMULA
CYLINDER AREA
AREA
= r XRADIUS> (Inches) A=712
In Squiire Inches
AREA
= .!:.x DIAMETER' (Inches) A=r[» orA = .78S[»
4
4
CYLINOER FORCE
FORCE
=PRESSURE (psi) x NET AREA (Square Inct.es) F =psixAorF=PA
In P/JUnds, Push or Pull
pf3
pf4
pf5

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FLUID POWER FORMULAS

WORD FORMULA:PRESSURE (^) BASIC· FORMULASlETTER FORMULA: _ FORCE (fXJUnds) P

F. F (^) U/IIT (^) =AREA AOf (Square pSI = A Inches) = VOLUME =Y.. (Gallons)

. - UNIT TIMET (Minute) 0 HORSEPOWER

= PRESSURE (PSI) x FLOW (GPM) VELOCITY^1714 HP =~ = .32080 =^ PRESSURE.3208^ x^ flOW (psi)^ ADDITIONAL RATE THROUGH 1.0.x VOLUME OF Oil UNDER PRESSURE (GPM)^ V INTERNAlA pv •• AREA^ (Square^ Approximately Inches) VOLUME VA= 25O,ooolapprox.) /2% Per 1000 psi

  • 250,000 lapprox.) (^1) CIP) = --1- BULK MODULUS OF THE FLUIDWEIGHT OF ONE CUBIC FOOTOF flUID^ == SPECIAC GRAVITY 8M VALVE FACTOR (e., ) SG^ =^ _W_62.

_ flOW RATE (GPM) x \JSPECIFIC GRAVITY c., = a VSG

===^ .21932!!.§..2253xSUS-~ x SUS (^) CEIITISTOKESCElITISTOKES_CENTISTOKES 134.6 (^) IfiPSUSCSc.sc.sSUS 4.635=== .2253.2193SUS SUSSUS _ _ 194.4134.

PUMP FORMULAS

flOW

= RPM x PUMP DISPlACEMENT (Cu. In.lRev.) 0

=~ 231 231 = FlO'N RATE OUTPUTHORSEPOWER INPUT (GFM) x PRESSURE (psi) (^) HP = _O_P _ or GPM x psi m 1714 Elf^1714 x^ EFFICIE/ICY1714E1f^ (Ov-r:raU) =!!k x 100 = OUTPUT HORSEPOWER xOVERAll EFACIENCY (^100) Elfa, = EIf,'CL x EIf.EOt =^ VOLUMETRIC Elf.^ x^ MECHANICAL^ Elf^ lllPUTElf",^ HORSEPO'NERHP" = ~ x 100 = ACTUAL flOWVOLUMETRIC EFFICIENCY R.I,TEOUTPUT (GPMJ x (^100) EIf~. THEORETICAl O",ro FLOW RATE OUTPUT {GPMJ MECHANICAL EFFICIENCY

THEORETICAl TOROUE TO ORIVE x 100 EIf.EO!^ =^ TTHED^ X^100

ACTUAlTACT. TOROUE TO DRIVE

B HOURS OF BEARING LIFE = RATED LIFE HOURS x RATEDSPEED 8'0 (RPM)^ =^ xRATEDHAS. x ( RATEDPRESSURE^ RPM,^ x^ f-;:i (PSI)^ J\ 3

WORD FORMULA^ "^ NEVI SPEED^ {RPM} lETTER^ FORMULAflEW PRESSURE RPMM (PSI) PH^ J AREA

=== r.!:.xPRESSURE (psi) X RADIUS>DIAMETER' (^) AREAFORCE (Inches) x (Inches) NET AREA (Square Inct.es) AAF^ ===psixAorF=PA^4 712 r[» orA = .78S[»

. FORMULA FOR:

FLUID POWER FORMULAS

ACTUATOR FORMULAS - CONTINUED WORD FORMULA (^) LETTER FORMULA CYLINDER VELOCITY or SPEED In FeetJSerond CYLINDER VOLUME CAPACITY In Gallons of Fluid

CYlINDER flOW RATE In Gallons Per Minute flUID MOTOR TOROUE In Inch Pounds

flUID MOTOR TOROUE/100 psi In Inch Pounds FLUID MOTOR SPEED In RevoIulions/Minule FLUID MOTOR POWER In Horsepower Output

VELOCITY

VOLUME

flOW R~TE

TOROUE

TOROUE/loo psi -

SPEED

HORSEPOWER

= 231 x flOW RATE (GP!.1) 12 x 60 x IIET AREA (Square Inches)

= r X RADiUS' (Inches) x STROKE (Inches)

231

= IIET AREA (Slrwe Inches) x STROKE (Inches) 231

_ 12 x 60 x VELOCITY (FeevSec) x NET AREA (Square InCl1es) 231

= PRESSURE (psi) x F.M. DISPLACEMENT (Cu. In.lRev.) 2r

= HORSEPOWERx 63025 RPM

= FLOW RATE (GPM) x PRESSURE (psi) x 36. RPM

= F.M. DISPLACEMENT (Cu. Inches/RevotuDon) .

_ 231 flOW RATE (GPM)

  • F.M. DISPLACEMENT (Cu. Inches/Revolution)

= TORQUE OUTPUT (Inch Pounds) x RPM 63025

THERMAL FORMULAS

y = (^2310) 72M ory = .32080A

v = rf' I

221

v = ~ 231 I= Length 01 Slroke

o = 720vA or 0 = 3.117yA 231

T = (^63025) n HP

T = 36.770Pn or T = 36.770psin

T,= (^) = .0628d

n 2310 =-d-

HP (^) Tn = 63025

NOTE: ONE BRITISH THERMAL UNIT (BTU) IS THE AMOUNT OF HEAT REOUIREDTO RAISE THE TEMPERATURE OF ONE POUND OF WATER OIlE OEGREEF.AHRENHBT.ONE HORSEPOWER= 2545 BTU/HR. RESERVOIR COOUNG CAPACITY BASED ON ADEQUATE AIR CIRCULATION

HEAT (BTU/HR) = 2 x TEMPERATURE OJFFERENCEBffi'/EEN RESERVOIRWAlLS AND AIR (oF) x AREA OF RESERVOIR(SO. Ft) BTUIHR^ =^ 2.0^ x^ AT^ x^ A

HEAT IN HYDRAULIC OIL (approx.) I HEAT (BTU/HR)

DUE TO SYSTEM INEFFICIENCY (SG = .89 - .92) HEAT IN FRESH WATER (approx.) tHEAT (BTU/HR)

NOTE: SEE PAGES 79 THROUGH 84 FOR INFORMATION

= Fl(J.'I1WE (GPM) x 210 x TEMPERATURE DIFFERENCE(oF)

= FLOW RATE (GPAt) x 500 x TEMPERATURE DIFFERENCE(OF)

PRESSURE DROP FORMULAS

BTU/HR = 0 x 210 x AT

BTU/HR = 0 x 500 x AT

NOTE: SEE PAGES 130 AND 131 FORADDITIONAL INFORMATION

ACCUMULATOR· FORMULAS Where UP" = psia(ABSOLUTf} = psig (GAUGE PRESSURE) + 14.7 psi

FORMULA FOR: PRESSURE OR VOLUME. w/Constant "r (Temperature) PRESSURE OR TEMPERATURE w/ Constant "V" (Volume) VOLUME OR TEMPERATURE w/Constant "P" (Pressure) PRESSURE OR VOLUME w/Tempetalure Change Due To Heat of Compression

WORD FORMULA:

ORlGIIIAL PRESSURE x ORIGINAL VOLUME =. FIfIAL PRESSURE x FINAL VOLUME

. ORIGIIW: PRESSURE x FIIJAi. m,IPERATURE ;; FlllAlPRESSURE X ORIG. TEMPERATURE

ORIGII/AL VOLUME X AI/AL TEI,IPERATURE = FINAL VOLUME x ORIGINAL TEMPERATURE

ORIGINAL PRESSURE x ORIGIIIAL VOLUME" ...= FINAL PRESSURE x FINAL VOLUME"

FINAL TEMP.ORIG. TEMP. .> .....•.•.•... i;,; ORIG. VOLUME\FIlIAL VOLUMFj ",:,eINALORIS. PRESSURE PRESSURE l'"

lETTER FORMULA: P, V, = P, V, lsothermic

P, T, = P, T, lsochoric

V, T, = V, T, Isobaric

Water at Max. Oensity 39.2° F 4° C

~rams. -\y.;;-. I ·of-Water

VOLUME&CAPACITY EQUIVALENTS

Liters .0005787.037037.00002143 1 764.56201.974.0353145.001308.004951.00594291.20032.0160184.0005929.11982528.317i,48052 U.S..004329 1 .264170.133681.160459 1 4.543743.78543 27 .016384 1 .45359246.656^1728 231 277.274 61.023427.6798^1 Gar:u.1S

.

. . 1 .

.

1

.

1

.

TABLE 6-E. CONVERSION BETWEEN ENGLISH UNITS AND SI UNITS

The "SI" (International Standards) units shown below are adopted for use by the International Fluid Power Com- munity, and should be used on documents prepared for international circulation.

"Customary" U.S. Unit

inch (in). Ibs/sq in (psig or psia). inches of mercury (in Hg) U.S. gallons per minute (U.S. GPM). cubic feet per minute (cfm) pound(f) or Ib(f) (force). pound(m) or Ib(m) (mass). second (see) gallon (U.S. gal). degrees Fahrenheit (0 F) pounds(f)-inches Ibs(f)-in horsepower (HP). revolutions per minute (rpm) cycles per second (cps). cubic inches per revolution (cipr). Saybolt Universal Seconds (SUS) feet per second (fps). **Pressure below atmospheric tt@38°C; Factor is 4.667 @ 99°C

Quantity SI Unit for Fluid Power

Length. millimeter (mm). Pressure* bar (bar, g or bar, a). Pressure** mm of mercury (mm Hg) Flow*** liters per minute (I/min) Flowt cubic decimeters/see (dm3/sec) Force Newton (N) Mass. kilogram (Kg) Time ... second (see) Volume.*. liter (I). Temperature degrees Celcius (oC) Torque. Newton-meters (Nm) Power kilowat (kw) Shaft Speed revolutions per minute (rpm) Frequency. Hertz (Hz). Displacement millileters/revolution (ml/rev) Kinematic viscosity centistokes (cSt). Velocity. meter per second (m/s) NOTES: *Pressure above atmospheric ***Liquid

Conversion Factor

1 in = 25.4 mm

1 bar = 14.5 psi

1 in Hg = 25.4 mm Hg
1 U.S. GPM = 3.79 I/min

1 dm3 /sec = 2.12 cfm 1 Ib(f) - 4.44N 1 Kg = 2.20 Ib(m)

1 U.S. gal = 3.

°C = 5/9 (OF - 32)

1 Nm = 8.88 Ib(f)-in 1 kw = 1.34 HP

1 Hz = 1 cps ·lml/rev = 0.061 cipr

cSt = (4.635)(SUS)tt
1 m/s = 3.28 fps

tGas

EQUIVALENT MEASUREMENTS

1 Liter = 0.2642 U.S. Gallons

1 Imperial Gallon = 1.2 U.S. Gallons

1 Cubic Foot = 7.48 Gallons = 1728 Cubic Inches 1 Cubic Foot of Water Weighs 62.4 Pounds

1 Bar at Sea Level = 14.5 PSI (Approx.l Atmos.) 33.8 Foot Water Column 42 Foot Oil Column II 29.92 Hg. Approx. VzPSI Decrease Each 1000 Ft. Altitude

1 Horsepower = 33,000 Ft. Lbs. per Minute 550 Ft. Lbs. per Second 42.4 BTU per Minute 2545 BTU per Hour 746 Watts, or 0.746 Kilowatts

lPSI= 2.04161'Hg 27.71 "Water Foot Column of Water = 0.433 PSI

Foot Column of Oil = 0.390 PSI

1 "Hg = 0.491 PSI = 1.132 Ft. Water

1 Barrel Oil = 42 Gallons

1 Micro-meter = 1 Millionth of a Meter (Micron)

= 1 Thousandth of a Meter

= 0.00004 Inch 25 Micro-meters = 0.001 Inch

231 Cu bic Inches 4 Quarts; or 8 Pints 8.3356 Pounds 3.785 Liters

1 U.S. Ga lion

APPROXIMATE MEASUREMENTS

1 Pint = 2 cups = 16 fluid ounces = 1 pound
1 Pint = 96 teaspoons = 32 tablespoons = 16 fluid ounces
1 Quart = 4 cups = 2 pints = 32 fluid ounces = 2 pounds
1 Quart = 192 teaspoons = 64 tablespoons = 32 fl. oz.
1 Gallon = 16 cups = 4 quarts = 8 pints
1 Gallon = 768 teaspoons = 256 tablespoons = 128 oz.

1 Gallon = 231 cubic inches = 76,800 drops 1 Cup = 16 tablespoons = 48 teaspoons 1 Tablespoon = 3 teaspoons

2 Tablespoons = 1 fluid ounce
1 Fluid ounce (volume) = 600 drops (hydraulic oil)

1 Cubic inch = 330 drops

TABLE 6-F. EQUIVALENT VALUES

To convert units appearing in Column 1 into equivalent values of units in Column 2, multiply by factor in Column 3,

Example: To convert 7 gallons into cubic inches, multiply 7 x 231 = 1617 cubic inches.

To convert units appearing in Column 2 into equivalent values of units in Column 1, divide by factor in Column 3.

Example: To convert 25 horsepower into BTU per minute, divide 25 by 0.02356 = 1061 BTU per minute.

Column 1 ColumnColumnFeet of WaterColumnColumnColumn^32 1 32 Please^ read^ instructions^ above

. 33.9 SecondsWattsHorsepowerCubic Inches.Cubic FeetU.S.GalionsMetersMilesAtmospheresInches of MercuryPSI (lbs.453.5924Miles per HourMiles per HourBTUHorsepowerHorsepower···BTU per Minute.0.001341Inches of MercuryPSI (lbs.perSq.ln).FootFahrenheitInches.U.S. GallonslitersU.S.Galions0.26420.00004^528088 Radians0.06250.5^7000 2.3072.0360.25Cubic FeetCubic Inches.0.5555Pounds^2000 Horsepower33,000Horsepower^550 Horsepower745.7Hours0.04167Hou rs .0.005952Inches.2.54Inches of Mercury0.03342Inches of Mercury1.133Inches of Mercury0.4912Inches of Water0.03613liters^1000 liters1.4671.805PintsPoundsPounds^16 PSI (lbs.0.06804PSI (lbs.PSI (lbs.^144 WattsMicro-meterMiles (Statute)Miles per Hour (MPH)Miles per Hour{MPH)OuncesOuncesPoundsQuarts.231778.3oCx0.017450.88260.0012860.00003030.0018180.13378.345342.4429.92Watts0.2931Weeks.0.023560.39370.00026420.001^1728 7.480520.00057870.00432986,4000.30480.00018940.02950.43350.011360.6818Foot14.7DaysCentimetersAtmospheresPSI (lbs.Cubic CentimetersGallons (U.S. liquid)Inches.PoundsAtmospheresFootFeet of WaterPSI (lbs.FeetFeet per MinuteFeet per Second.Cubic Inches.QuartsGrains.Grams.OuncesFeet of WaterInches of MercuryGallonsSquareSquareTemperatureTemperatureTonsPou ndsHorsepower^ lbs.^.^ ... .. .. 1.8+32 of Water. lbs.lbs.(Weight) .(Fluid) (U.SJ ..per Sq. In)per Sq. In)per Sq. In)per Sq. in) (^) FeetInches (^) liquidliquidper Sq. InJper Sq. In.)per Second(Micron).per Minute.(Bars)... (oF) - 32(oC)(Bars).(Bars)*... ("Hg)("Hg)("Hg)("Hg)("Hg)^ ....

TABLE 6-G. PSI GAUGE PRESSURE CONVERTED TO METRIC PRESSURE UNITS

This table is calculated on the basis of 1 bar = 14.5 PSI, or, 1 PSI = .069 bar PSI 10 50 100 250 500 750 1000 1500 2000 2500 3000 5000 Bars ••.....0.69 3.45 6.90 17.2 34.5 51.7 69.0 103.4 137.9 172.4 206.9 344.

TABLE 6-H. GPM OIL FLOW CONVERTED TO METRIC UNITS

This table is calculated on the basis of 1 U.S. GPM = 3.79 liters per min. (liquid) or, 1 liter per min. = 0.2638 GPM.

GPM .5 8 12 15 20 25 30 35 40 50 75 100 Liters/min~18.95 30.32 45.48 56.85 75.80 94.75 113.7 132.7 151.6 189.5 284.3 379.

TABLE 6-1. SCFM AIR FLOW CONVERTED TO METRIC UNITS

This table is calculated on the basis of 1 SCFM = 0.4716 cubic decimeters per second, or 1 dm3/sec. = 2.12 SCFM.

SCFM ~5 10 15 25 50 75 100 150 200 250 300 350 Dm3/sec~2.358 4.716 7.074 11.79 23.58 35.37 47.16 70.74 94.32 117.9 141.5 165.