## Fluid Power Formulas

Torque and horsepower Relations:

T=HP×5252÷RPM

HP="T×RPM÷5252"

RPM="HP×5252÷T

Torque values are in foot pounds.

Hydraulic (fluid power) horsepower:

HP = PSI × GPM ÷ 1714

PSI is gauge pressure in pounds per square inch; GPM is oil flow in gallons per minute.

Velocity of oil flow in pipe:

V = GPM × 0.3208 ÷ A

V is oil velocity in feet per second; GPM is flow in gallons per minute;

A is inside area of pipe in square inches

Charles’ Law for behavior of gases:

T1V2 = T2V1, or T1P2 = T2P1 T1, P1,

and V1 are initial temperature, pressure,

and volume, and T2, P2, and V2 are final

conditions.

Boyle’s Law for behavior of gases:

P1V1 = P2V2

P1 and V1 are initial pressure and volume;

P2 and V2 are final conditions.

Circle formulas:

Area = πr 2 , or πD2 ÷ 4

Circumference = 2πr, or πD

r is radius; D is diameter, inches

Heat equivalent of fluid power:

BTU per hour = PSI × GPM × 1Z\x

Hydraulic cyl. piston travel speed:

S=CIM÷A

S is piston travel speed, inches per minute;

CIM is oil flow into cylinder, cubic inches

per minute;

A is piston area in square inches.

Force or thrust of any cylinder:

F=A×PSI

F is thrust or force, in pounds;

A is piston net area in square inches;

PSI is gauge pressure.

Force for piercing or shearing sheet metal:

F=P×T×PSI

F is force required, in pounds;

P is perimeter around area to be sheared, in inches;

T is sheet thickness in inches;

PSI is the shear strength rating of the material in pounds per square inch.

Side load on pump or motor shaft:

F = (HP × 63024) ÷ (RPM × R)

F is the side load, in pounds, against shaft;

R is the pitch radius, in inches, of sheave on pump shaft;

HP is driving power applied to shaft.

Effective force of a cylinder working at

an angle to direction of the load travel:

F = T × sin A

T is the total cylinder force, in pounds; F is

the part of the force which is effective, in

pounds; A is the least angle, in degrees,

between cylinder axis and load direction.

Heat radiating capacity of a steel reservoir:

HP=0.001×A×TD

HP is the power radiating capacity expressed in horsepower; A is surface area, in square feet; TD is temperature difference in degrees F between oil and surrounding air.

Burst pressure of pipe or tubing:

P = 2t × S ÷ O

P is burst pressure in PSI; t is wall thickness,

in inches; S is tensile strength of material in

PSI; O is outside diameter, in inches.

Relationship between displacement and

torque of a hydraulic motor:

T=D×PSI÷24π

T is torque in foot-lbs.; D is displacement in

cubic inches per revolution; PSI is pressure

difference across motor; π= 3.14.

## Rules-of-Thumb

Horsepower for driving a pump:

For every 1 HP of drive, the equivalent of 1

GPM @ 1500 PSI can be produced

Horsepower for idling a pump:

To idle a pump when it is unloaded will require about 5% of its full rated horsepower.

Compressibility of hydraulic oil:

Volume reduction is approximately 1/2% for every 1000 PSI of fluid pressure.

Compressibility of water:

Volume reduction is about 1/3% for every

1000 PSI pressure.

Flow velocity in hydraulic lines: Pump suction

lines 2 to 4 feet per second; pressure lines up

to 500 PSI, 10 to 15 feet per sec; pressure

lines 500 to 3000 PSI, 15 to 20 feet per sec.;

pressure lines over 3000 PSI, 25 feet per sec.;

all oil lines in air-over-oil system, 4 feet per

sec.

Wattage for heating hydraulic oil: Each watt

will raise the temperature of 1 gallon of oil by

1ºF per hour.