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Fluid Power Formulas

Basic Fluid Power Formulas / Hydraulics / Pneumatics

Variable

Formula w/ Units

Simplified Formula

Fluid Pressure - P
(PSI) = Force (Pounds) / Area ( Sq. In.)
P  =  F / A
Fluid Flow Rate - Q
GPM= Flow (Gallons) / Unit Time (Minutes)
Q = V / T
Fluid Power in Horsepower - HP
Horsepower = Pressure (PSIG) × Flow (GPM)/ 1714
HP = PQ / 1714

Actuator Formulas

Variable

Formula w/ Units

Simplified Formula

Cylinder Area - A
( Sq. In.) = π × Radius (inch)2
A  =  π  × R2
(Sq. In.) = π × Diameter (inch)2 / 4
A  = π  × D2 / 4
Cylinder Force - F
(Pounds) = Pressure (psi)   × Area (sq. in.)
F  =  P × A
Cylinder Speed - v
(Feet / sec.) = (231 × Flow Rate (gpm)) / (12 × 60 × Area)
v   =  (0.3208 × gpm) / A
Cylinder Volume Capacity - V
Volume = π × Radius2 × Stroke (In.) / 231
V = π × R2 × L / 231 (L = length of stroke)
Cylinder Flow Rate - Q
Volume = 12 × 60 × Velocity (Ft./Sec.) × Net Area(In.)2 / 231
Q = 3.11688 × v × A
Fluid Motor Torque - T
Torque (in. lbs.) = Pressure (psi) × disp. (in.3 / rev.) / 6.2822
T  =  P × d / 6.2822
Torque = HP × 63025 / RPM
T = HP × 63025 / n
Torque = Flow Rate (GPM) × Pressure × 36.77 / RPM
T = 36.77 × Q × P / n
Fluid Motor Speed - n
Speed (RPM)  =  (231 × GPM) / Disp. (in.)3
n  =  (231 × GPM) / d
Fluid Motor Horsepower - HP
HP = Torque (in. lbs.) × rpm / 63025
HP  =  T × n / 63025

Pump Formulas

Variable

Formula w/ Units

Simplified Formula

Pump Output Flow - GPM
GPM = (Speed (rpm) × disp. (cu. in.)) / 231
GPM =  (n ×d) / 231
Pump Input Horsepower - HP
HP =  GPM × Pressure (psi) / 1714 × Efficiency
HP  =  (Q ×P) / 1714 × E
Pump Efficiency - E
Overall Efficiency = Output HP / Input HP
EOverall = HPOut / HPIn X 100
Overall Efficiency = Volumetric Eff. × Mechanical Eff.
EOverall = EffVol. × EffMech.
Pump Volumetric Efficiency - E
Volumetric Efficiency = Actual Flow Rate Output (GPM) / Theoretical Flow Rate Output (GPM) × 100
EffVol. = QAct. / QTheo. X 100
Pump Mechanical Efficiency - E
Mechanical Efficiency = Theoretical Torque to Drive / Actual Torque to Drive × 100
EffMech = TTheo. / TAct. × 100
Pump Displacement - CIPR
Displacement (In.3 / rev.) = Flow Rate (GPM) × 231 / Pump RPM
CIPR = GPM × 231 / RPM
Pump Torque - T
Torque = Horsepower × 63025 / RPM
T = 63025 × HP / RPM
Torque = Pressure (PSIG) × Pump Displacement (CIPR) / 2π
T = P × CIPR / 6.28

General Fluid Power Guidelines:


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 it's full rated power

Wattage for heating hydraulic oil:  
Each watt will raise the temperature of 1 gallon of oil by 1° F. per hour.

Flow velocity in hydraulic lines:  
Pump suction lines 2 to 4 feet per second, pressure lines up to 500 psi - 10 to 15 ft./sec., pressure lines 500 to 3000 psi - 15 to 20 ft./sec.; all oil lines in air-over-oil systems; 4 ft./sec.