Fluid Power Formulas
Torque and horsepower Relations:
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
Boyle’s Law for behavior of gases:
P1V1 = P2V2
P1 and V1 are initial pressure and volume;
P2 and V2 are final conditions.
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 is piston travel speed, inches per minute;
CIM is oil flow into cylinder, cubic inches
A is piston area in square inches.
Force or thrust of any cylinder:
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 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 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 is torque in foot-lbs.; D is displacement in
cubic inches per revolution; PSI is pressure
difference across motor; π= 3.14.
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
Wattage for heating hydraulic oil: Each watt
will raise the temperature of 1 gallon of oil by
1ºF per hour.