FLUID POWER FORMULAS

FLUID POWER FORMULAS

WEIGHT

OF. ONEFCUBIC

flUID

. - FOOT

- _ OF

F

THEORETICAl

TOROUE

TO

ORIVE GRAVITY

lllPUT

HORSEPO'NER

FORCE

(fXJUnds)

231

ACTUAl

TOROUE

TO

DRIVE

flOW

(GPM)

\JSPECIFIC

INTERNAl

AREA

(Square

Inches){GPMJ

UNIT

TIME

(Minute)

AREA

(Square

Inches)

THEORETICAl

FLOW

RATE

OUTPUT

"VOLUME

NEVI

SPEED

{RPM}

250,000

lapprox.)

(PSI)

FLOW

(GPM)

.3208

flOW

RATE

THROUGH

1.0.

(GPM)

1714

EFFICIE/ICY

(Ov-r:raU)

RPM

xRATE

DISPlACEMENT

(Cu.

In.lRev.)

=

1714 U/IIT

FlO'N

RATE

OUTPUT

(GFM)

x OF

PRESSURE

0

==~ .32080

1xpSI

TElf

231

AOf

4

8M

ADDITIONAL

A62.4283

SUS

4.635

=!!k~

100

OUTPUT

HORSEPOWER

100

.2253xSUS-~

SUS

pv

??

Approximately

=

.2193

VOLUMETRIC

xx PUMP

SUS

flOW

Elf.

_

xxR.I,TEOUTPUT

MECHANICAL

(GPMJ

Elf

x(psi)

100

A

1714

712

1714E1f

m

HP"

(psi)

VOLUME

Oil

UNDER

PRESSURE

= 2!!.¡ì.

PRESSURE

.!:.x

XACTUAL

DIAMETER'

RADIUS>

(psi)

(Inches)

xxx134.6

(Inches)

NET

(Square

Inct.es)

rPRESSURE

Elf",

F

=psixAorF=PA

EIf,'CL xx OF

EIf.EOt

TACT.

O",ro

A

EIf.EO!

=xAREA

TTHED

r[?

orASUS

=_ _.78S[?

VOLUME

FORCE

PRESSURE

P

V

AREA

SPECIAC

GRAVITY

BULK MODULUS

THE FLUID

=~(Gallons)

CElITISTOKES

OVERAll

EFACIENCY

SG

=

_W_

CEIITISTOKES

CS

=

.2253

0c.s

VA=

25O,ooolapprox.)

_O_P

or194.4

GPM

\/2%

x psi

Per 1000 psi

x 100 CIP) = VELOCITY

HORSEPOWER

MECHANICAL

EFFICIENCY

INPUT

HP

flOW

VOLUMETRIC

EFFICIENCY

.2193

134.6

CENTISTOKES

SUS

VALVE

--1- FACTOR

(e., X

) 100

Elfa,

EIf~.

c.,

= a VSG

AREA

=

=

WORD FORMULA

FORMULA:

B

HOURS OF BEARING LIFE

flEW PRESSURE (PSI)

=A

FORMULA:

===Y..

lETTER FORMULA

= IfiP= =

RPMM

PH

=

BASIC¡¤

FORMULAS

8'0

=

RATEDHAS.

x

RPM,

x

= RATED PUMP

LIFE HOURS x RATEDSPEED (RPM) x ( RATEDPRESSUREf-;:i

(PSI) J \

FORMULAS

J

3

FLUID POWER FORMULAS

ACTUATOR FORMULAS

. FORMULA

-

CONTINUED

WORD FORMULA

FOR:

CYLINDER VELOCITY or SPEED

LETTER FORMULA

=

VELOCITY

CYLINDER VOLUME CAPACITY

=

VOLUME

x

x

231

12

In FeetJSerond

x

60

flOW RATE

r X RADiUS'

(Inches)

231

In Gallons of Fluid

=

IIET AREA

(GP!.1)

=

y

x STROKE (Inches)

x

STROKE (Inches)

RATE

flOW

_

R~TE

12

x

x

60

VELOCITY (FeevSec)

flUID

MOTOR TOROUE

=

TOROUE

x

PRESSURE (psi)

o

= 720vA

231

231

NET AREA (Square InCl1es)

or

Length 01 Slroke

0 = 3.117yA

F.M. DISPLACEMENT (Cu. In.lRev.)

2r

In Inch Pounds

flUID

x

I=

=~

231

In Gallons Per Minute

A

v

231

CYlINDER flOW

.32080

I

= rf'

v

221

(Slrwe Inches)

=

2310 ory

72M

IIET AREA (Square Inches)

MOTOR TOROUE/100 psi

=

HORSEPOWER

RPM

=

FLOW RATE (GPM)

=

TOROUE/loo psi -

In Inch Pounds

FLUID MOTOR SPEED

FLUID MOTOR POWER

HORSEPOWER

63025

x

PRESSURE (psi)

RPM

x 36.77

n

HP

T,=

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

.0628

_

SPEED

In RevoIulions/Minule

x

T

= 63025 HP

n

T

=

--

36.770P or T = 36.770psi

n

n

=-d-63025

d

=

.0628

Tn

2310

231 flOW RATE (GPM)

-

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

=

TORQUE OUTPUT (Inch Pounds)

63025

In Horsepower Output

THERMAL

x

RPM

FORMULAS

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

HEAT (BTU/HR)

=

2

x

TEMPERATURE OJFFERENCEBffi'/EEN

RESERVOIRWAlLS AND AIR (oF)

x AREA OF RESERVOIR(SO. Ft)

BASED

ON ADEQUATE

HEAT IN HYDRAULIC OIL (approx.)

DUE TO SYSTEM

BTUIHR

=

2.0

BTU/HR

=

0

x

210

x

AT

BTU/HR

=

0

x

500

x

AT

x

x

AT

A

AIR CIRCULATION

INEFFICIENCY

(SG

=

I

.89

HEAT (BTU/HR)

=

Fl(J.'I1WE

(GPM)

x

210

x

TEMPERATURE DIFFERENCE(oF)

=

FLOW RATE (GPAt)

x

500

x

TEMPERATURE DIFFERENCE(OF)

-

.92)

HEAT IN FRESH WATER (approx.)

tHEAT

(BTU/HR)

PRESSURE

DROP FORMULAS

NOTE: SEE PAGES 79 THROUGH 84 FOR INFORMATION

ACCUMULATOR¡¤

FORMULAS

NOTE: SEE PAGES 130 AND 131 FORADDITIONAL INFORMATION

FORMULA

FOR:

PRESSURE OR VOLUME .

w/Constant

PRESSURE

"r

Where UP"

=

psia(ABSOLUTf}

x

psig (GAUGE PRESSURE)

lETTER

WORD FORMULA:

ORlGIIIAL PRESSURE

=

ORIGINAL VOLUME

=. FIfIAL

14.7 psi

FORMULA:

FINAL VOLUME

P, V,

=

X ORIG. TEMPERATURE

P, T,

= P, T, lsochoric

ORIGINAL TEMPERATURE

V, T,

=

x

PRESSURE

+

P, V,

lsothermic

(Temperature)

OR TEMPERATURE

. ORIGIIW: PRESSURE

x FIIJAi. m,IPERATURE

;; FlllAlPRESSURE

w/ Constant "V" (Volume)

VOLUME

OR TEMPERATURE

ORIGII/AL VOLUME X AI/AL TEI,IPERATURE

= FINAL VOLUME

x

V, T, Isobaric

w/Constant "P" (Pressure)

PRESSURE

OR VOLUME

ORIGINAL PRESSURE

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

w/Tempetalure Change Due

-

To Heat of Compression

FINAL TEMP.

TEMP.

ORIG.

U.S.

1

.037037

.0005787

.00002143

i,48052

28.317

.004329

.016384

146.656

1728

1.119825

.0160184

.004951

201.974

764.56

.001308

1.20032

.0353145

.160459

.264170

1.133681

4.54374

13.78543

27

.453592

2277.274

31

27.6798

61.0234

.0005929

.0059429

Liters

~~

.>

.....?.?.?...

i;,;

ORIG.

FIlIAL VOLUME\

VOLUMFj

l'"

",:,eINAL

ORIS. PRESSURE

PRESSURE

Gar:u.1S

VOLUME&CAPACITY

EQUIVALENTS

Water at Max. Oensity

39.2¡ã F 4¡ã C

~rams

. -\y.;;-.

.0036065

6.23210

168.266

I

¡¤of-Water

.0163872

.0361275

62.4283

1685.56

28.3170

764.559

.220083

2.20462

1

.833111

8.34545

3.78543

1

.0998281

10.0172

1

4.54373

.453593

To Convert

cms

Into

...

0.06102

0.001

0.02832

Liters

28.317

.0036065

feet

meters

.OF. Cms/sec

31.5

7.48052

448,83

0.01639

35,31

14.50

6.23210

7.481

28.32

264.2

0.5080

.00003521

.000001

.0002642

.0005787

.00001639

.004329

16.39

Fahrenheit

Gallons/min

Cu

cms/min

Gallons

Liters/min

inches

10,200

28,320

28,317

61,023

Pounds/sq

in...liquid)

Imperial

1,728

1,000,000

1,000

gallons

Multiply

by

Gallons

Kgs/sq

=9.5)

(tmeter

(U.S.

32)/1.8

tDegree

DC

Celsius

(COx

+32

Gallons/min

Liters

Liters/min

FeeVmin

Imperial

Kilograms/sq

Pascal

Pounds/sq

U.S,

U.S.

gallons

(Pa)

gallons

inch

cm

meter

To Convert

Into

...

277.274

4.54374

0.0353145

61.0234

0.001

3785

231

,160459

,00009807

.220083

1000

.069

.133681

.3785

Bar

Gallons/min

Bars

cms

meters

703.1

3.785

0.264170

3,785

.1337

1,20032

14.22

,001422

.035

.264

,00001

.000145

.83267

feet

Meters/min

Liters

Cu

feeVmin

inches

cm

0.3048

Liters/min

cms/min

2,048

3,785.412

6,895

1,000

Pounds/sq

Kgs/sq

meter

Multiply

byftin...liquid)

U.S.

gallons

Gallons

Imperial

(U.S.

gallons

Pascal

(Pa)

TABLE

6-E. CONVERSION

BETWEEN ENGLISH

UNITS AND SI UNITS

The "SI" (International

Standards) units shown below are adopted for use by the International

munity, and should be used on documents prepared for international circulation.

Conversion

Quantity

SI Unit for Fluid Power

"Customary"

Length .

Pressure*

Pressure**

Flow***

Flowt

Force

Mass .

Time ...

Volume*.**.

Temperature

Torque

.

Power

Shaft Speed

Frequency .

Displacement

Kinematic viscosity

Velocity.

millimeter (mm) .

bar (bar, g or bar, a) .

mm of mercury (mm Hg)

liters per minute (I/min)

cubic decimeters/see (dm3/sec)

Newton (N)

kilogram (Kg)

second (see)

liter (I) .

degrees Celcius (oC)

Newton-meters (Nm)

kilowat (kw)

revolutions per minute (rpm)

Hertz (Hz) .

millileters/revolution

(ml/rev)

centistokes (cSt) .

meter per second (m/s)

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) .

NOTES:

*Pressure above atmospheric

1 Horsepower

Gallon = 1.2 U.S. Gallons

7.48 Gallons

=

1728 Cubic Inches

=

Approx.

14.5 PSI (Approx.l Atmos.)

33.8 Foot Water Column

42 Foot Oil Column

II

29.92 Hg.

VzPSI Decrease Each 1000 Ft. Altitude

APPROXIMATE

1

1

1

1

1

1

-

32)

1 Hz = 1 cps

¡¤lml/rev = 0.061 cipr

cSt = (4.635)(SUS)tt

1 m/s = 3.28 fps

tGas

33,000 Ft. Lbs. per Minute

2545 BTU per Hour

746 Watts, or 0.746 Kilowatts

2.04161'Hg

27.71 "Water

Foot Column of Oil

1 Cubic Foot of Water Weighs 62.4 Pounds

=

(OF

1 Nm = 8.88 Ib(f)-in

1 kw = 1.34 HP

Foot Column of Water

=

1 Bar at Sea Level

1 U.S. gal = 3.791

¡ãC = 5/9

550 Ft. Lbs. per Second

42.4 BTU per Minute

lPSI=

1 Liter = 0.2642 U.S. Gallons

1 Cubic Foot

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)

***Liquid

4 Quarts; or 8 Pints

8.3356 Pounds

3.785 Liters

1 Imperial

Factor

MEASUREMENTS

231 Cu bic Inches

1 U.S. Ga lion

U.S. Unit

**Pressure below atmospheric

tt@38¡ãC;

Factor is 4.667 @ 99¡ãC

EQUIVALENT

Fluid Power Com-

Pint = 2 cups = 16 fluid ounces = 1 pound

Pint = 96 teaspoons = 32 tablespoons = 16 fluid ounces

Quart = 4 cups = 2 pints = 32 fluid ounces = 2 pounds

Quart = 192 teaspoons = 64 tablespoons = 32 fl. oz.

Gallon = 16 cups = 4 quarts = 8 pints

Gallon = 768 teaspoons = 256 tablespoons = 128 oz.

1 "Hg

=

=

= 0.433 PSI

= 0.390 PSI

0.491 PSI

1.132 Ft. Water

1 Barrel Oil = 42 Gallons

1 Micro-meter

25 Micro-meters

1 Millionth of a Meter (Micron)

= 1 Thousandth of a Meter

= 0.00004 Inch

=

= 0.001 Inch

MEASUREMENTS

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

1 Cubic inch = 330 drops

oil)

TABLE 6-F. EQUIVALENT VALUES

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

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

Example: To convert 25 horsepower

into BTU per minute, divide 25 by 0.02356 = 1061 BTU per minute.

.

Column 33.9

1

Column

Column

1per

144

745.7

0.01136

0.0005787

Column

Column

Feet

Column

of

Water

3Centimeters

2.Water

32per

Pounds

of

Water.

0.001341

Watts

.1.8+32

¡¤Atmospheres

550

.231

0.1337

Seconds

2.036

2.307

88

0.25

0.01745

0.004329

Gallons

Watts

Cubic

Foot

Fahrenheit

2.54

0.04167

1000

Inches.

0.005952

Hou

Hours

0.02356

1728

0.2931

Cubic

rs

lbs.

.nds

.of

.

7000

16

Pounds

0.6818

Inches.

U.S.

1.133

Inches

0.001

0.3937

Gallons

Meters

0.5

0.0001894

0.3048

2000

42.44

8.3453

Pou

29.92

Radians

5280

Quarts

0.001818

Feet

453.5924

0.00004

0.2642

1.467

liters

0.0000303

00.8826

oCx

778.3

0.4335

7.48052

Weeks.

Watts

14.7

Centimeters

Ounces

Grains.

Grams.

.001286

Inches.

Miles

liters

0.0625

1.805

0.4912

0.03342

Pints

0.0002642

Pounds

Quarts

Feet

.of

of

Inches.

0.5555

Tons

(U.SJ

86,400

Water

0.06804

Micro-meter

Inches.

(Micron)

0.03613

Ounces

0.0295

(Fluid)

BTU

Horsepower

per

Minute.

.Second

(Statute)

Horsepower

.Sq.(MPH)

33,000

Foot

Square

lbs.

Inches

per

Minute

Horsepower

U.S.Galions

Miles

Inches

per

of

Hour{MPH)

Hour

Minute

Mercury

.Sq.

...In.)

Inches

Gallons

Days

per

Hour

Mercury

(U.S.

liquid

liquid)

In)

("Hg)

PSI

(lbs.

Sq.

Temperature

(oC)

(oF)

- 32

Feet

.(Bars)*.

PSI

PSI

Feet

(lbs.

(lbs.perSq.ln).

(lbs.

per

per

Second.

In)

Inches

Atmospheres

of

(Weight)

Mercury

.in)

("Hg)

InJ

(Bars)*.

Please read instructions

in Column

3,

in Column

3.

above

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

This table is calculated

PSI

Bars

on the basis of 1 bar = 14.5 PSI, or, 1 PSI = .069 bar

? 10

??.....0.69

50

3.45

100

6.90

250

17.2

500

34.5

750

51.7

1000

69.0

1500

103.4

2000

137.9

2500

172.4

3000

206.9

5000

344.8

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

This table

GPM

.5

Liters/min~18.95

is calculated

on the basis of 1 U.S. GPM = 3.79 liters per min. (liquid)

8

30.32

12

45.48

15

56.85

20

75.80

25

94.75

30

113.7

35

132.7

or, 1 liter per min. = 0.2638

40

151.6

50

189.5

75

284.3

GPM.

100

379.0

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

This table

SCFM

~5

Dm3/sec~2.358

is calculated

on the basis of 1 SCFM = 0.4716

10

4.716

15

7.074

25

11.79

50

23.58

cubic decimeters

75

35.37

100

47.16

per second,

150

70.74

200

94.32

or 1 dm3/sec.

250

117.9

= 2.12 SCFM.

300

141.5

350

165.1

 ................
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