Electrical cost = HP x .746 x hours x Kw cost / motor efficiency
Example: 50 hp air compressor that runs 8 hours a day 5 days a week for a year with a $.06 Kw electric rate and a 90% efficient electric motor.
50 hp x .746 x 2080 hours x $.06 / .90 = $5,172.27 per year
Compressor RPM = motor pulley diameter x motor rpm / compressor pulley diameter.
Motor pulley diameter = compressor pulley diameter x compressor RPM / motor RPM
Compressor pulley diameter = motor pulley diameter x motor RPM / compressor RPM
Motor RPM = compressor pulley diameter x compressor RPM / motor pulley diameter
Gallons= cubic feet / .134
Cubic Feet = gallons x .134
Pump up time (minutes) =
V (tank size) x (final pressure – initial pressure)
Example: 7.5 hp compressor rated at 24 cfm with an 80 gallon tank – unit starts at 100 psi and turns off at 150 psi.
Pressure drop and horsepower: Every 1 psi of pressure drop equals 0.5% in horsepower
Heat and horsepower : Rejected heat from an air-cooled compressor is equal to total machine horsepower x 2,545 BTU per hour
Example: 50 hp compressor with 3 hp fan motor will produce…
Basic Formulas: Pressure (psi) = Force (pounds) / Area (in2)Force (pounds) = Area (in2) x Pressure (psi)Area (in2) = Force (pounds) / Pressure (psi) Fluid Power Horsepower (hp) = Pressure (psi) x pump flow (gpm) / 1,714 Torque (ft.lbs.) = Horsepower (hp) x 5,252 / Speed (rpm)Horsepower (hp) = Torque (ft.lbs.) x Speed (rpm) / 5,252Speed (rpm) = Horsepower (hp) x 5,252 / Torques (ft.lbs.)Cylinder Formulas:Piston cylinder area (in2) = Diameter squared x .7854
= 3.1416 x Radius squared
Rod-end cylinder area (in2) (Annulus end area)
= Cylinder area (in2) – Rod area (in2)
Cylinder force (pounds)
= Pressure (psi) x Area (in2)
Cylinder speed feet/minute)
= Area (in2) x Cylinder stroke (in.) x .26 /Flow rate (gpm)
Cylinder flow rate (gpm) = 12 x 60 x Cylinder speed (ft./sec.) x Area (in2) / 231Cylinder volume capacity (gallons)= 3.1416 x Radius squared (in.) x Cylinder stroke / 231Hydraulic Motor Formulas:Fluid motor torque(in.lbs.) = Pressure (psi) x Fluid motor displacement / 6.28
Fluid motor power (hp output)
= Torque output (in.lbs.) x Speed (rpm) / 63,025
Fluid motor torque / 100 psi (in.lbs.)= Fluid motor displacement (in3/rev.) /
Pump outlet flow (gpm)
= Speed (rpm) x Pump displacement (in3/rev.) / 231 Pump speed (rpm)
= 231 x Pump flow rate (gpm) /
= Flow rate output (gpm) x Pressure (psi) / 1,714 x Efficiency factor (overall %)
10 – 15 ft./sec.
Pressure lines of 500 to 3,000 psi 15 – 20 ft./sec. Pressure lines over 3,000 psi 25 ft./sec. Fluid velocity of oil flow in a pipe (ft./sec.)
= Flow rate (gpm) x 0.3208 / Inside area of pipe (in2)
Common Fluid Power Equivalents:One U.S. gallon = 231 in3
Approximately ½ psi decrease for each 1,000 feet of elevation change
One inch mercury (hg.) = 0.490 psi
One horsepower =
One atmosphere =
Calculating Bearing Requirements for Oil Lubricants:
V = A x T
V = Volume in terms of lube-oil replacement rate in cubic inches per hour (in3/hr)A = Bearing surface area in square inches (in2) (Sized differently based on bearing type)
T = Film thickness…generally .001 inch… but it may vary based on oil type and application
Calculating Bearing Requirements for Grease Lubricants: V = A x TV = Volume in terms of lube-grease replacement as cubic inches per four hour (in3/4 hrs) A = Bearing surface area in square inches (in2) (Sized differently based on bearing type)
T = Film thickness…generally .002 inches…but it may vary based on grease type and application
Note: Quite often requirements are expressed in metric terms.
Common Bearing Types:(Necessary to know for calculating areas.)Plain Bearings:
Sizing Example:Plain bearing with 6 inch shaft and 6 inch long bearing surface using oil.
Should this need to be converted to metric, the requirement for this single bearing application would be 1.85 cubic centimeters per hour.
Each and every bearing or lube point on a machine would be calculated in this fashion and when done, the replacement rates for all points would be added together to determine the total system lubrication requirement.
Air valves are sized for flow capacity (Cv) based on given cylinder piston size, stroke and travel time requirements. Cv is actually a flow coefficient that measures the amount of air a device can pass. The following formula can be used for air valve sizing:
Cv =Area (in2) x Length (ins.) x Compression factor
Area = Effective cylinder piston area in square inches
(A = 3.1416 x radius2 – or – diameter2 x .7854)
Note: For the rod end (annulus end) of the cylinder, the same area formulas apply, but to calculate accurately, one must take the cylinder area (in2) minus the rod area (in2) in using this valve sizing formula for determining return stroke Cv rating.
Length = Simply the total cylinder stroke length in inches
Compression factor = Taken from the table based on supply pressure rating.
Pressure drop factor = Taken from the table....10 or 15 psi drop is a good guideline for using in this formula
Time = Required cylinder stroke time in seconds
6 inch bore cylinder with 2 inch rod and 15 inch stroke.... 2 second travel time....100 psi supply pressure....and 15 psi pressure drop factor will be used:
1. Calculate piston area in square inches
(A = 6 ins. x 6 ins. x .7854 = 28.2 in2)
Note that this is the cylinder extend area, to calculate the cylinder return area, the rod area must be subtracted from
(A = 2 ins. x 2 ins. x .7854 = 3.14 in2)
Cylinder return area is then 28.2 in2 – 3.14 in2 = 25.06 in2
2. Simply apply application variables to the Cv sizing formula:
Cv = 28.2 in2 x 15 ins. x 7.8 = 3,299 = 1.52 Cv
3. Select a valve that meets this 1.52 Cv rating.
Air Flow Rates
Standard Cubic Feet Per Minute (SCFM)
Cubic Feet Per Minute (CFM): One cubic foot of gas (air) per minute at actual conditions...ie: at actual temperature and compressed or expanded pressure.
Free Air Flow: The volume of air at normal atmospheric conditions which enters a vacuum system due to the lower pressure caused by the pump or vacuum in a tank.
Expanded Air Flow: Air flow inside a vacuum system, same as CFM.
SCFM and Compressor Horsepower Requirements: To calculate pneumatic cylinder air consumption in SCFM and convert it to required air compressor horsepower, please request an RHM Fluid Power Data Book which includes quick reference charts for these purposes.
Note: This information is provided as a quick reference resource and is not intended to serve as a substitute for qualified engineering assistance. While every effort has been made to ensure the accuracy of this information, errors can occur. As such, neither RHM or its employees will assume any liability for damage, injury or misapplication tied to the use of this information.