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Resources - Useful Fluid Power Formulas
General Formulas:
Work, foot-pounds = force x distance
Horsepower = work/(time, seconds x 550)
Force, pounds = (pressure, lbs/sq-in)(area, sq-in)
Area of cylinder, square inches = (force, lbs)/(pressure, lbs/sq-in)
Pressure, lbs/square-inch = (force, lbs)/(area, sq-in)
Intensifier: P1 A1 = P2 A2 and P1 D12 = P2 D22
where: D1 is diameter of large piston; D2 is
diameter of small piston; P1 is pressure applied to large piston; P2 is pressure applied to small piston
Pump flow rate, gpm = DNEV/231
where: D = displacement, cu-in/rev; N = speed, rev/min: EV =
volumetric efficiency
Pump output horsepower = PQ/1714 =
TNEO/63025
where: T = torque, lb-in; Q = pump flow rate, gpm; P = pressure, psi; N =
speed, RPM; EO = overall efficiency
Lift pressure, pounds/square inch = (fluid column height, feet)(62.4)(SG)/144
Velocity of fluid in a tube, feet/second = 0.321 Q/A
Max fluid velocity allowed by
National Fluid Power Society = 20 feet/second for pressure lines
=
15 feet/second for return lines
= 5 feet/second for suction lines
Tube inside diameter, inches = 0.639(Q/Vmax)1/2
Maximum pressure for pipe threads = 200 psi Reference ANSI/(NFPA/JIC) T2.24.1 - 1991
Approximate tube stress, psi = P
ID/(2 T)
where: T = tube wall thickness, inch; P = pressure, psi; ID = inside diameter
of tube, inch
Factor of safety = ultimate tensile strength, psi/allowable stress, psi
Cylinder speed extending, inches/second = 3.85 Q/AE
Cylinder speed retracting, inches/second = 3.85 Q/AR
Hydraulic motor torque,
pound-inches = P D EM/(2 p)
where: P = pressure, psi; D = motor displacement, in3/rev; EM = mechanical efficiency
Hydraulic motor speed, rpm = Q EV 231/D
where: Q = flow rate, gpm; D = displacement, inches3/revolution; EV = volumetric efficiency
Hydraulic motor horsepower output =
P Q EO/1714
where: P = pressure, psi; Q = flow rate, gpm; EO = overall
efficiency
EO = EV x EM
where: EV, volumetric efficiency: EM, mechanical
efficiency: EO, overall efficiency
Oil flow rate across an orifice,
cu-in/sec = 100 AO (DP)1/2
where: AO = area of orifice, in2 ;DP = pressure differential across orifice,
psi
PSIA = PSIG + 14.7
Vacuum pressure, PSI =(0.491)(H, inches of mercury vacuum)
Compression ratio = (final pressure,
PSIA/initial pressure, PSIA)
Example: CR = (90 PSIG +14.7)/14.7
Time a receiver can deliver flow
between two pressures, minutes = (VR x (P1 – P2))/(14.7
x Q)
where: VR is volume of receiver, cu ft; Q is flow rate out, CFM; (P1-P2)
is starting pressure – ending pressure
Perfect gas law: P1 V1/T1 = P2 V2/T2
where: T = degrees Rankin; P1 & P2 = PSIA; units of
volume V unimportant
Constant temperature, P1 V1 = P2 V2
Constant volume, P1/T1 = P2/T2
Constant pressure, V1/T1 = V2/T2
DP
pressure loss in air line, psi = (0.1025 x L x (Q/60)2)/(CR x d 5.31)
where: L is length of pipe, feet; d is inside diameter of pipe, inches; Q is
air flow rate, SCFM; CR is compression ratio
Volume of free air required to
raise pressure in a receiver = (P2V2/P1) – V2
where: P1 =14.7 PSIA; P2 = final pressure, PSIA; V2 = receiver volume, ft3; V = volume of air that must be added by
compressor, ft3
Displacement of a compressor, in3/revolution = number of pistons x (p/4)(piston diameter2, in2)(stroke, inches)