Ram Industries Inc. - Fluid Power Formulae

Ram Industries Inc.

PO Box 5007 33 York Road E Yorkton, SK S3N 3Z4 Canada
Phone: 306.786.2677	Toll Free: 1.877.799.1005
Fax: 306.786.2651	Email: estimating@ramindustries.com

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 behaviour 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 behaviour 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

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.

Formulae In SI Metric Units

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
Torque, HP, Speed Relations in 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 10 N = 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
Barlow's Formula - 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 A = 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.
Recommended Maximum 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

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