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# Formulas

Torque and horsepower relations:
T = HP x 5252 ÷ RPM
HP = T x RPM ÷ 5252
RPM = HP x 5252 ÷ T
Torque values are in foot pounds.

Hydraulic (fluid power) horsepower:
HP = PSI x GPM ÷ 1714
PSI is gauge pressure in pounds per square inch, GPM is oil flow in gallons per minute.

Velocity of oil flow in pipe:
V = GPM x 0.3208 ÷ A
V is oil velocity in feet per second, GPM is flow in gallons per minute, A is inside area of pipe in square inches.

Charles’ Law for behavior of gases:
T1V2 = T2V1, or T1P2 = T2P1
T1, P1 and V1 are initial temperature, pressure and volume, and T2, P2 and V2 are final conditions.

Boyle’s Law for behavior of gases:
P1V1 = P2V2
P1, V1 are initial pressure and volume; P2 and V2 are final conditions.

Circle Formulae:
Area = pr2, or pD2 ÷ 4
Circumference = 2pr, or pD
r is radius, D is diameter, inches; p is 3.14

Heat equivalent of fluid power:
BTU per hour = PSI x GPM x 1½

Hydraulic cylinder piston travel speed:
S = CIM ÷ A
S is piston travel speed, inches per minute, CIM is oil flow into cylinder, cubic inches per minute, A is piston area in square inches.

Thrust or force of any cylinder:
T = A x PSI
T is thrust or force, in pounds, A is piston area in square inches, PSI is gauge pressure.

Force for piercing or shearing sheet metal:
F = P x T x PSI
F is force required, in pounds, P is perimeter around area to be sheared, in inches, T is sheet thickness in inches; PSI is the sheer strength rating of the material in pounds per square inch.

Side load on pump or motor shaft:
F = (HP x 63024) ÷ (RPM x R)
F is the side load, in pounds, against shaft; R is the pitch radius of sheave on pump shaft, in inches; HP is driving power applied to shaft.

Effective force of a cylinder working at an angle to direction of the load travel:
F = T x sin A
T is the total cylinder force, in pounds; F is the part of the force which is effective, in pounds, A is the least angle, in degrees, between cylinder axis and load direction.

Heat radiating capacity of a steel reservoir:
HP = 0.001 x A x TD
HP is the power radiating capacity expressed in horsepower; A is surface area, in square feet; TD is temperature difference in °F between oil and surrounding air.

Burst pressure of pipe or tubing:
P = 2t x S ÷ O
P is burst pressure in PSI, t is wall thickness, in inches; S is tensile strength of material in PSI; O is outside diameter, in inches.

Relationship between displacement and torque of a hydraulic motor:
T = D x PSI ÷ 24p
T is torque in foot pounds, D is displacement in cubic inches per revolution, PSI is pressure difference across motor, p is 3.14

## Familiar fluid power formulae in English units are shown in the left column. When the industry converts to SI (International) units, these formulae will take the form shown in the right column.

English Units Metric Units

## Hydraulic Pumps and Motors

T = HP x 5252 ÷ RPM
HP = T x RPM ÷ 5252
RPM = HP x 5252 ÷ T
T = Torque, foot-lbs.
RPM = Speed, revs/min
HP = Horsepower
T = Kw x 9543 ÷ RPM
Kw = T x RPM ÷ 9543
RPM = Kw x 9543 ÷ T
T = Torque, Nm (Newton-meters)
RPM = Speed, revs/min
Kw = Power in kilowatts

## Hydraulic Power Flowing Through the Pipes

HP = PSI x GPM ÷ 1714 HP = Horsepower
PSI = Gauge pressure, lbs/sq. inch
GPM = Flow, gallons per minute
Kw = Bars x dm3/min ÷ 600 Kw = Powers in kilowatts
Bars = System pressure
dm3/min = Flow, cu. dm/minute

## Force Developed by an Air or Hydraulic Cylinder

T = A x PSI
T = Force or thrust, in lbs.
A = Piston area, square inches
PSI = Gauge pressure, lbs/sq. inch
N = A x Bars x 10N = Cylinder force in Newtons
A = Piston area, sq. centimeters
Bars = Gauge pressure

## Travel Speed of a Hydraulic Cylinder Piston

S = V ÷ A S = Travel speed, inches/minute
V = Vol. of oil to cyl., cu.in/min
A = Piston area, square inches
S = V ÷ 6A S = Travel speed, meter/sec
V = Oil flow dm3/minute
A = Piston area, square centimeters

## Burst Pressure of Pipe & Tubing

P = 2t x S ÷ O P = Burst pressure, PSI
T = Pipe wall thickness, inches
S = Tensile str., pipe material, PSI
O = Outside diameter of pipe, inches
P = 2t x S ÷ O P = Burst pressure, bars
T = Pipe wall thickness, mm
S = Tensile str., pipe material, bars
O = Outside diameter of pipe, mm

## Velocity of Oil Flow in Hydraulic Lines

V = GPM x 0.3208 ÷ A V = Velocity, feet per second
GPM = Oil flow, gallons/minute
Velocity of an oil flow in pipe
“GPM is oil flow in gallons per minute”.= Inside area of pipe, sq. inches
V = dm3/min ÷ 6A V = Oil velocity, meters/second
dm3/min = Oil flow, cu.dm/minute
A = Inside area of pipe, sq.cm.

## Oil Velocity in Hydraulic Lines

fps = feet per second
Pump suction lines – 2 to 4 fps
Pres. lines to 500 PSI – 10 to 15 fps
Pres. lines to 3000 PSI – 15 to 20 fps
Pres. lines over 3000 PSI – 25 fps
Oil lines in air/oil system – 4 fps
mps = meters per second
Pump suction lines – .6 to 1.2 mps
Pres. lines to 35 bar – 3 to 4½ mps
Pres. lines to 206.8 bar – 4½ to 6 mps
Pres. lines over 200 bar – 7½ mps
Oil lines in air/oil system – 1¼ mps

At RAM, we’re 100% committed to our customers and to their satisfaction.

### OUR PLEDGE IS SIMPLE:

“The job’s not done right until you say it’s done right.”

### Rules of Thumb:

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 its full rated horsepower.

Compressibility of hydraulic oil:
Volume reduction is approximately 0.5% for every 1000 PSI pressure.

Compressibility of water:
Volume reduction is about 0.3% for every 1000 PSI pressure.

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/second; pressure lines up to 500 PSI, 10 to 15 feet/second; pressure lines 500 to 3000 PSI, 15 to 20 feet/second; pressure lines over 3000 PSI, 25 feet/second; all oil lines in air-over-oil system, 4 feet/second.

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