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### Fluid Power Formulas

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 and the examples shown. However, it is possible that a typographical error or two has slipped in. Please double check any results that don't seem right.

Hydraulic Pump Calculations

Horsepower Required to Drive Pump

 GPM X PSI X .0007 (this is a 'rule-of-thumb' calculation) How many horsepower are needed to drive a 10 gpm pump at 1750 psi? GPM = 10 PSI = 1750 GPM X PSI X .0007 = 10 X 1750 X .0007 = 12.25 horsepower

Pump Output Flow (in Gallons Per Minute)
 RPM X Pump Displacement / 231 How much oil will be produced by a 2.21 cubic inch pump operating at 1120 rpm? RPM = 1120 Pump Displacement = 2.21 cubic inches RPM X Pump Displacement / 231 = 1120 X 2.21 / 231 = 10.72 gpm
Pump Displacement Needed for GPM of Output Flow
 231 X GPM / RPM What displacement is needed to produce 7 gpm at 1740 rpm? GPM = 7 RPM = 1740 231 X GPM / RPM = 231 X 7 / 1740 = 0.93 cubic inches per revolution

Hydraulic Cylinder Calculations

Cylinder Blind End Area (in square inches)

 PI X (Cylinder Radius) ^2 What is the area of a 6" diameter cylinder? Diameter = 6" Radius is 1/2 of diameter = 3" Radius ^2 = 3" X 3" = 9" PI X (Cylinder Radius )^2 = 3.14 X (3)^2 = 3.14 X 9 = 28.26 square inches

Cylinder Rod End Area (in square inches)

 Blind End Area - Rod Area What is the rod end area of a 6" diameter cylinder which has a 3" diameter rod? Cylinder Blind End Area = 28.26 square inches Rod Diameter = 3" Radius is 1/2 of rod diameter = 1.5" Radius ^2 = 1.5" X 1.5" = 2.25" PI X Radius ^2 = 3.14 X 2.25 = 7.07 square inches Blind End Area - Rod Area = 28.26 - 7.07 = 21.19 square inches

Cylinder Output Force (in Pounds)

 Pressure (in PSI) X Cylinder Area What is the push force of a 6" diameter cylinder operating at 2,500 PSI? Cylinder Blind End Area = 28.26 square inches Pressure = 2,500 psi Pressure X Cylinder Area = 2,500 X 28.26 = 70,650 pounds What is the pull force of a 6" diameter cylinder with a 3" diameter rod operating at 2,500 PSI? Cylinder Rod End Area = 21.19 square inches Pressure = 2,500 psi Pressure X Cylinder Area = 2,500 X 21.19 = 52,975 pounds

Fluid Pressure in PSI Required to Lift Load (in PSI)

 Pounds of Force Needed / Cylinder Area What pressure is needed to develop 50,000 pounds of push force from a 6" diameter cylinder? Pounds of Force = 50,000 pounds Cylinder Blind End Area = 28.26 square inches Pounds of Force Needed / Cylinder Area = 50,000 / 28.26 = 1,769.29 PSI What pressure is needed to develop 50,000 pounds of pull force from a 6" diameter cylinder which has a 3: diameter rod? Pounds of Force = 50,000 pounds Cylinder Rod End Area = 21.19 square inches Pounds of Force Needed / Cylinder Area = 50,000 / 21.19 = 2,359.60 PSI

Cylinder Speed (in inches per second)

 (231 X GPM) / (60 X Net Cylinder Area) How fast will a 6" diameter cylinder with a 3" diameter rod extend with 15 gpm input? GPM = 6 Net Cylinder Area = 28.26 square inches (231 X GPM) / (60 X Net Cylinder Area) = (231 X 15) / (60 x 28.26) = 2.04 inches per second How fast will it retract? Net Cylinder Area = 21.19 square inches (231 X GPM) / (60 X Net Cylinder Area) = (231 X 15) / (60 x 21.19) = 2.73 inches per second

GPM of Flow Needed for Cylinder Speed

 Cylinder Area X Stroke Length in Inches / 231 X 60 / Time in seconds for one stroke How many GPM are needed to extend a 6" diameter cylinder 8 inches in 10 seconds? Cylinder Area = 28.26 square inches Stroke Length = 8 inches Time for 1 stroke = 10 seconds Area X Length / 231 X 60 / Time = 28.26 X 8 / 231 X 60 / 10 = 5.88 gpm   If the cylinder has a 3" diameter rod, how many gpm is needed to retract 8 inches in 10 seconds? Cylinder Area = 21.19 square inches Stroke Length = 8 inches Time for 1 stroke = 10 seconds Area X Length / 231 X 60 / Time = 21.19 X 8 / 231 X 60 / 10 = 4.40 gpm

Cylinder Blind End Output (GPM)

 Blind End Area / Rod End Area X GPM In How many GPM come out the blind end of a 6" diameter cylinder with a 3" diameter rod when there is 15 gallons per minute put in the rod end? Cylinder Blind End Area =28.26 square inches Cylinder Rod End Area = 21.19 square inches GPM Input = 15 gpm Blind End Area / Rod End Area X GPM In = 28.26 / 21.19 * 15 = 20 gpm

Hydraulic Motor Calculations

GPM of Flow Needed for Fluid Motor Speed

 Motor Displacement X Motor RPM / 231 How many GPM are needed to drive a 2.51 cubic inch motor at 1200 rpm? Motor Displacement = 2.51 cubic inches per revolution Motor RPM = 1200 Motor Displacement X Motor RPM / 231 = 2.51 X 1200 / 231 = 13.04 gpm

Fluid Motor Speed from GPM Input

 231 X GPM / Fluid Motor Displacement How fast will a 0.95 cubic inch motor turn with 8 gpm input? GPM = 8 Motor Displacement = 0.95 cubic inches per revolution 231 X GPM / Fluid Motor Displacement = 231 X 8 / 0.95 = 1,945 rpm

Fluid Motor Torque from Pressure and Displacement

 PSI X Motor Displacement / (2 X PI) How much torque does a 2.25 cubic inch motor develop at 2,200 psi? Pressure = 2,200 psi Displacement = 2.25 cubic inches per revolution PSI X Motor Displacement / (2 x PI) = 2,200 X 2.25 / 6.28 = 788.22 inch pounds

Fluid Motor Torque from Horsepower and RPM

 Horsepower X 63025 / RPM How much torque is developed by a motor at 15 horsepower and 1500 rpm? Horsepower = 15 RPM = 1500 Horsepower X 63025 / RPM = 15 X 63025 / 1500 = 630.25 inch pound

Fluid Motor Torque from GPM, PSI and RPM

 GPM X PSI X 36.77 / RPM How much torque does a motor develop at 1,250 psi, 1750 rpm, with 9 gpm input? GPM = 9 PSI = 1,250 RPM = 1750 GPM X PSI X 36.7 / RPM = 9 X 1,250 X 36.7 / 1750 = 235.93 inch pounds second

Fluid & Piping Calculations

Velocity of Fluid through Piping

 0.3208 X GPM / Internal Area What is the velocity of 10 gpm going through a 1/2" diameter schedule 40 pipe? GPM = 10 Internal Area = .304 (see note below) 0.3208 X GPM / Internal Area = .3208 X 10 X .304 = 10.55 feet per second Note: The outside diameter of pipe remains the same regardless of the thickness of the pipe. A heavy duty pipe has a thicker wall than a standard duty pipe, so the internal diameter of the heavy duty pipe is smaller than the internal diameter of a standard duty pipe. The wall thickness and internal diameter of pipes can be found on readily available charts. Hydraulic steel tubing also maintains the same outside diameter regardless of wall thickness. Hose sizes indicate the inside diameter of the plumbing. A 1/2" diameter hose has an internal diameter of 0.50 inches, regardless of the hose pressure rating.

Suggested Piping Sizes

 Pump suction lines should be sized so the fluid velocity is between 2 and 4 feet per second. Oil return lines should be sized so the fluid velocity is between 10 and 15 feet per second. Medium pressure supply lines should be sized so the fluid velocity is between 15 and 20 feet per second. High pressure supply lines should be sized so the fluid velocity is below 30 feet per second.

Heat Calculations

Heat Dissipation Capacity of Steel Reservoirs

 0.001 X Surface Area X Difference between oil and air temperature If the oil temperature is 140 degrees, and the air temperature is 75 degrees, how much heat will a reservoir with 20 square feet of surface area dissipate? Surface Area = 20 square feet Temperature Difference = 140 degrees - 75 degrees = 65 degrees 0.001 X Surface Area X Temperature Difference = 0.001 X 20 X 65 = 1.3 horsepower Note: 1 HP = 2,544 BTU per Hour

Heating Hydraulic Fluid

 1 watt will raise the temperature of 1 gallon by 1 degree F per hour and Horsepower X 745.7 = watts and Watts / 1000 = kilowatts

Pneumatic Valve Sizing

Notes:

• All these pneumatic formulas assume 68 degrees F at sea level
• All strokes and diameters are in inches
• All times are in seconds
• All pressures are PSI

Valve Sizing for Cylinder Actuation

 SCFM = 0.0273 x Cylinder Diameter x Cylinder Diameter x Cylinder Stroke / Stroke Time x ((Pressure-Pressure Drop)+14.7) / 14.7 Cv Required = 1.024 x SCFM / (Square Root of (Pressure Drop x (Pressure-Pressure Drop+14.7))) Pressure 2 (PSIG) = Pressure-Pressure Drop

Air Flow Q (in SCFM) if Cv is Known

 Valve Cv x (Square Root of (Pressure Drop x ((PSIG - Pressure Drop) + 14.7))) / 1.024

Cv if Air Flow Q (in SCFM) is Known

 1.024 x Air Flow / (Square Root of (Pressure Drop x ((PSIG-Pressure Drop) + 14.7)))

Air Flow Q (in SCFM) to Atmosphere

 SCFM to Atmosphere = Valve Cv x (Square Root of (((Primary Pressure x 0.46) + 14.7) x (Primary Pressure x 0.54))) / 1.024 Pressure Drop Max (PSIG) = Primary Pressure x 0.54

Flow Coefficient for Smooth Wall Tubing

 Cv of Tubing =(42.3 x Tube I.D. x Tube I.D. x 0.7854 x (Square Root (Tube I.D. / 0.02 x Length of Tube x 12)

Conversions

 To Convert Into Multiply By Bar PSI 14.5 cc Cu. In. 0.06102 °C °F (°C x 1.8) + 32 Kg lbs. 2.205 KW HP 1.341 Liters Gallons 0.2642 mm Inches 0.03937 Nm lb.-ft 0.7375 Cu. In. cc 16.39 °F °C (°F - 32) / 1.8 Gallons Liters 3.785 HP KW 0.7457 Inch mm 25.4 lbs. Kg 0.4535 lb.-ft. Nm 1.356 PSI Bar 0.06896 In. of HG PSI 0.4912 In. of H20 PSI 0.03613

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