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Reference Tables -- Fluid Power Formulas

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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) � Flow (GPM)/ 1714	HP = PQ / 1714
Actuator Formulas
Variable	Word Formula w/ Units	Simplified Formula
Cylinder Area - A	( Sq. In.) = π � Radius (inch)²	A = π � R²
Cylinder Area - A	(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	Word 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	E_Overall = HP_Out / HP_{In X 100}
Pump Efficiency - E	Overall Efficiency = Volumetric Eff. � Mechanical Eff.	E_Overall = Eff_Vol. � Eff_Mech.
Pump Volumetric Efficiency - E	Volumetric Efficiency = Actual Flow Rate Output (GPM) / Theoretical Flow Rate Output (GPM) � 100	Eff_Vol. = Q_Act. / Q_Theo. X 100
Pump Mechanical Efficiency - E	Mechanical Efficiency = Theoretical Torque to Drive / Actual Torque to Drive � 100	Eff_Mech = T_Theo. / T_Act. � 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
Pump Torque - T	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.

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