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Hydraulic and Mechanical Presses
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Formulas and Conversion Factors Basic FormulasFluid Pressure =Force (Pounds)Unit Area (Square Inches)
Fluid Flow Rate=Volume (Gallons)Unit Time (Minute)
Fluid Power in Horsepower =Pressure (PSI) x Flow (GPM)1714
U.S. Gear Drive Formulas
Torque (in-lb) =hp x 63025 / rpm
Horsepower (hp)=in-lb x rpm / 63025
Pitch Dia=Teeth / Diametral Pitch
Thermal input (Watts) =hp x (1 - eff) x 745.7
Output Torque = Input Torque x Ratio x Gear Drive Efficiency
Output rpm = Input rpm / Ratio
Metric Gear Drive Formulas
Nm = kW x 9549RPM
kW = Nm x RPM9549
Thermal input (Watts) =kW x (1-eff)556.08
Output TQ = Input TQ x Ratio x Gear Drive Efficiency
Output rpm = Input rpm / Ratio
Back to Top U.S. Motor Formulas
hp =gpm x psi / 1714
hp = in-lb x rpm / 63025
in3 =(in-lb x 6.283) / (psi x eff)
in-lb = psi x in3 x eff / 6.283
in-lb =hp x 63025 / rpm
gpm =rpm x in3 / 231
rpm =gpm x 231 / in3
eff = (in-lb x 6.283) / (psi x in3)
in-lb =gpm x psi x eff x 36.77 / rpm
psi =(in-lb x 6.283) / (in3 x eff)
Back to Top Metric Motor Formulas
kW =L/min x bar / 70148.25
kW = Nm x rpm / 9549
cm3 = (Nm x 170.7) / (bar x eff)
Nm =bar x cm3 x eff / 170.7
Nm = kW x 9549 / rpm
L/min =rpm x cm3 / 125.25
rpm =L/min x 125.25 / cm3
eff =(Nm x 170.7) / (bar x cm3)
Back to TopPump Formulas
Pump Outlet Flow = RPM x Pump Displacement (Cu. In./Rev.)231
Pump Input Power in Horsepower = Flow Rate Output (GPM) x Pressure (PSI)1714 x Efficiency (Overall)
Overall Efficiency = Output HorsepowerInput Horsepowerx 100
Overall Efficiency = Volumetric Eff. x Mechanical Eff.
Volumetric Efficiency = Actual Flow Rate Output (GPM)Theoretical Flow Rate Output (GPM)x 100
Mechanical Efficiency = Theoretical Torque to DriveActual Torque to Drivex 100
Back to TopMetric to U.S. Conversion
kW = 1.341 hp
bar =14.5 psi
Nm = 8.8496 in-lb
daNm =88.496 in-lb
kg-m =86.796 in-lb
L/min =.2642 gpm
cm3 = .061 in3
L =2.114 Pints
C = (F - 32) / 1.8
Torque and horsepower relations:T = HP x 5252 RPMHP = T x RPM 5252RPM = HP x 5252 TTorque values are in foot pounds. Hydraulic (fluid power) horsepower:HP = PSI x GPM 1714PSI 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 AV 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 = T2P1T1, 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 = P2V2P1, V1 are initial pressure and volume; P2 and V2 are final conditions. Circle Formulae:Area = r2, or D2 4Circumference = 2r, or Dr is radius, D is diameter, inches; is 3.14 Heat equivalent of fluid power:BTU per hour = PSI x GPM x 1 Hydraulic Cylinder Piston travel speed:S = CIM AS 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 PSIT 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 PSIF 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 AT 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 TDHP 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 OP 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 24T is torque in foot pounds, D is displacement in cubic inches per revolution, PSI is pressure difference across motor, 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 RPMHP = T x RPM 5252RPM = HP x 5252 T T = Torque, foot-lbs.RPM = Speed, revs/minHP = HorsepowerT = Kw x 9543 RPMKw = T x RPM 9543RPM = Kw x 9543 T T = Torque, Nm (Newton-meters)RPM = Speed, revs/minKw = Power in kilowatts
Hydraulic Power Flowing Through the Pipes
HP = PSI x GPM 1714 HP = HorsepowerPSI = Gauge pressure, lbs/sq. InchGPM = Flow, gallons per minuteKw = Bars x dm3/min 600 Kw = Powers in kilowattsBars = System pressuredm3/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 inchesPSI = Gauge pressure, lbs/sq. inchN = A x Bars x 10 N = Cylinder force in NewtonsA = Piston area, sq. centimetersBars = Gauge pressure
Travel Speed of a Hydraulic Cylinder Piston
S = V A S = Travel speed, inches/minuteV = Vol. of oil to cyl., cu.in/minA = Piston area, square inchesS = V 6A S = Travel speed, meter/secV = Oil flow dm3/minuteA = Piston area, square centimeters
Barlow's Formula - Burst Pressure of Pipe & Tubing
P = 2t x S O P = Burst pressure, PSIt = Pipe wall thickness, inchesS = Tensile str., pipe material, PSIO = Outside diameter of pipe, inchesP = 2t x S O P = Burst pressure, barst = Pipe wall thickness, mmS = Tensile str., pipe material, barsO = Outside diameter of pipe, mm
Velocity of Oil Flow in Hydraulic Lines
V = GPM x 0.3208 A V = Velocity, feet per secondGPM = Oil flow, gallons/minuteA = Inside area of pipe, sq. inchesV = dm3/min 6A V = Oil velocity, meters/seconddm3/min = Oil flow, cu.dm/minuteA = Inside area of pipe, sq.cm.
Recommended Maximum Oil Velocity in Hydraulic Lines
fps = feet per secondPump suction lines - 2 to 4 fpsPres. lines to 500 PSI - 10 to 15 fpsPres. lines to 3000 PSI - 15 to 20 fpsPres. lines over 3000 PSI - 25 fpsOil lines in air/oil system - 4 fpsmps = meters per secondPump suction lines - .6 to 1.2 mpsPres. lines to 35 bar - 3 to 4 mpsPres. lines to 206.8 bar - 4 to 6 mpsPres. lines over 200 bar - 7 mpsOil lines in air/oil system - 1 mps
Material (common name)Density (in Kg/M^3)
Metals
Aluminum2,768
Beryllium1,868
Brass8,500
Cast Iron6,975
Chromium7,197
Copper8,940
Gold18,878
Lead11,349
Magnesium1,743
Molybdenum10,214
Nickel8,553
Phosphor Bronze8,858
Platinum21,452
Silver10,491
Stainless Steel7,861
Steel7,861
Tin7,308
Titanium4,512
Tungsten19,293
Zinc7,141
Woods (weight listed is average dried weight)
Acacia Blackwood660
Ash, White660
Balsa160
Basswood420
Beech, European720
Birch700
Bloodwood960
Bocote800
Brazilwood1,280
Bubinga880
Butternut450
Cedar, Western Red370
Chakte Kok640
Chechen850
Cherry, Black580
Cocobolo1,040
Douglas Fir520
Ebony, African1,000
Ebony, Gaboon1,193*
Ebony, Macassar1,090
Elm, American560
Goncalo Alves940
Hickory820
Holly800
Jarrah800
Jatoba900
Kiaat700*
Kingwood1,200
Koa660
Kwila963*
Lemonwood820
Lignum Vitae (Ironwood)1,310
Mahogany, Honduran640
Mahogany, Philippine (Lauan)382*
Makore620
Mango570
Maple, Hard720
Maple, Soft620
Oak, Red770
Oak, White770
Padauk720
Panga Panga930
Pink Ivory990
Poplar450
Purpleheart930
Redwood420
Rosewood, Brazilian850
Rosewood, East Indian830
Rosewood, Honduran940
Sapele620
Shedua748*
Snakewood1,295
Spruce, Sitka420
Teak640
Tulipwood960
Verawood1,218*
Walnut, Black640
Wenge880
Yellowheart860
Zebrawood740
Ziricote880
Plastics
ABS1,052
Acetal (Delrin)1,356
Acrylic1,163
Neoprene1,384
Polyamide (Nylon)1,100
Polycarbonate1,190
LDPE (Low-Density Polyethylene)913
HDPE (High-Density Polyethylene)941
Polypropylene913
PVC1,467
Teflon2,159
Other
Carbon Fiber1,743
Human Bone1,439
Water1,000
*Denotes my own measurements
Metal or AlloyDensity(kg/m3)
Actinium10070
Admiralty Brass8525
Aluminum2712
Aluminum - melted2560 - 2640
Aluminum - 11002720
Aluminum - 60612720
Aluminum - 70502800
Aluminum - 71782830
Aluminum bronze (3-10% Al)7700 - 8700
Aluminum foil2700 -2750
Antifriction metal9130 -10600
Antimony6690
Babbitt7272
Barium3594
Beryllium1840
Beryllium copper8100 - 8250
Bismuth9750
Brass - casting8400 - 8700
Brass - rolled and drawn8430 - 8730
Brass 60/408520
Bronze - lead7700 - 8700
Bronze - phosphorous8780 - 8920
Bronze (8-14% Sn)7400 - 8900
Brushed metal7860
Cadmium8640
Caesium1873
Calcium1540
Cast iron6800 - 7800
Cerium6770
Chemical Lead11340
Chromium7190
Cobalt8746
Constantan8920
Columbium8600
Constantan8880
Copper8940
Cupronickel8908 - 8940
Delta metal8600
Duralumin2790
Electrum8400 - 8900
Eroded metal7860
Europium5243
Gallium5907
Germanium5323
Gold19320
Hafnium13310
Hatelloy9245
Indium7310
Inconel8497
Incoloy8027
Iridium22650
Iron7850
Lanthanum6145
Lead11340
Light alloy based on Al2560 - 2800
Light alloy based on Mg1760 - 1870
Lithium534
Magnesium1738
Manganese7440
Manganese Bronze8359
Manganin8500
Mercury13593
Molybdenum10188
Monel8360 - 8840
Neodymium7007
Nichrome8400
Nickel8908
Nickel 208090
Nickel 2008890
Nickel silver8400 - 8900
Nickeline8770
Nimonic8100
Niobium8570
Osmium22610
Palladium12160
Phosphor bronze8900
Platinum21400
Plutonium19816
Red Brass8746
Silver10490
Sodium971
Solder 50/50 Pb Sn8885
Stainless Steel7480 - 8000
Steel7850
Tin7280
Titanium4500
Tungsten19600
Uranium18900
Vanadium5494
White metal7100
Wrought Iron7750
Zinc7135
Zirconium6570
Yellow Brass8470
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