C O N T R O L L E D
M O T I O N   I N C .
              
   ~ INTELLIGENT FLUID POWER ~

The following formulas are readily available in many engineering textbooks, fluid power design guides, and hydraulic handbooks. Every effort has been made to insure the accuracy of the formulas however, it is possible that a typographical error or two has slipped in. Please double check any results that don't seem right.

Basic Fluid Power Formulas / Hydraulics / Pneumatics
Variable
Word 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) x Flow (GPM)/ 1714 HP = PQ / 1714
Actuator Formulas
Variable
Word Formula w/ Units
Simplified Formula
Cylinder Area - A ( Sq. In.) = pi  x Radius (inch)2 A  =  pi  x R2
(Sq. In.) =  pi  x Diameter (inch)2 / 4 A  =  pi x D2 / 4
Cylinder Force - F (Pounds) = Pressure (psi)  x Area (sq. in.) F  =  P x A
Cylinder Speed - v (Feet / sec.) = (231 x Flow Rate (gpm)) / (12 x 60  x Area) v   =  (0.3208 x gpm) / A
Cylinder Volume Capacity - V Volume = pi  x Radius2  x Stroke (In.) / 231

V = pi x R2 x L / 231

(L = length of stroke)

Cylinder Flow Rate - Q Volume = 12 x 60 x Velocity (Ft./Sec.) x Net Area(In.)2 / 231                          Q = 3.11688 x v x A
Fluid Motor Torque - T Torque (in. lbs.) = Pressure (psi) x disp. (in.3 / rev.) / 6.2822 T  =  P x d / 6.2822

Torque = HP x 63025 / RPM T = HP  x 63025 / n
Torque = Flow Rate (GPM) x Pressure x 36.77 / RPM T = 36.77 x Q x P / n
Fluid Motor Speed - n Speed (RPM)  =  (231 x GPM) / Disp. (in.)3 n  =  (231 x GPM) / d
Fluid Motor Horsepower - HP HP = Torque (in. lbs.) x rpm / 63025 HP  =  T x n / 63025
Pump Formulas
Variable
Word Formula w/ Units
Simplified Formula
Pump Output Flow - GPM GPM = (Speed (rpm) x disp. (cu. in.)) / 231 GPM =  (n x d) / 231
Pump Input Horsepower - HP HP =  GPM x Pressure (psi) / 1714 x Efficiency HP  =  (Q x P) / 1714 x E
Pump Efficiency - E Overall Efficiency = Output HP / Input HP EOverall = HPOut / HPIn X 100
Overall Efficiency = Volumetric Eff. x Mechanical Eff. EOverall = EffVol. x EffMech.
Pump Volumetric Efficiency - E Volumetric Efficiency = Actual Flow Rate Output (GPM) / Theoretical Flow Rate Output (GPM) x 100 EffVol. = QAct. / QTheo. x 100
Pump Mechanical Efficiency - E Mechanical Efficiency = Theoretical Torque to Drive / Actual Torque to Drive x 100 EffMech = TTheo. / TAct. x 100
Pump Displacement - CIPR Displacement (In.3 / rev.) = Flow Rate (GPM) x 231 / Pump RPM CIPR = GPM x 231 / RPM
Pump Torque - T Torque = Horsepower x 63025 / RPM T = 63025 x HP / RPM
Torque = Pressure (PSIG) x Pump Displacement (CIPR) / 2 pi T = P x CIPR / 6.28
General Fluid Power Guidelines:

Horsepower Guideline for driving a pump: 

For every 1 hp of drive, the equivalent of 1 gpm @ 1500 psi can be produced.

Horsepower Guidline for idling a pump: 

To idle a pump when it is unloaded will require about 5% of it's full rated power

Wattage Guideline 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.