Hydraulic Formulas
Welcome to the ultimate resource for engineers and technicians working with hydraulic systems. Whether you’re designing a new system or maintaining an existing one, this checklist of essential formulas and calculations will be your go-to guide.
Torque, HP, Speed Relations in Hydraulic Pumps & Motors
T = (HP x 5252) / RPM HP = (T x RPM) / 5252 RPM = (HP x 5252) / T
Definitions
T = Torque, foot-lbs
RPM = Speed, revs./minute
HP = Horsepower
Hydraulic Power Flowing Through the Pipes
HP = (PSI x GPM) / 1714
Definitions
HP = Horsepower
PSI = Gauge pressure, lbs/sq. inch
GPM = Flow, gallons per minute
Force Developed by an Air or Hydraulic Cylinder
F = A x PSI
Definitions
F = Force or thrust, lbs
A = Piston area, square inches
PSI = Gauge pressure, lbs/sq. inch
Inch & Millimeters (MM) Conversions
MM = inches x 25.4
Inches = MM x 0.03937
Fluid Dynamics
Flow Rate
Q = A * v
Where: Q = Flow Rate (ft3/s), A = Cross-sectional Area (ft2), v = Velocity (ft/s)
Pressure
P = f / A
Where: P = Pressure (PSI), f = force (pounds), A = area (square inches)
Pressure Drop
ΔP = [0.0668 * μv] / D^2
Where: ΔP = Pressure Loss Per 100 Feet, μ = Viscosity of Centipoises, v = Flow Velocity, D = Inside Diameter of Pipe (inches)
Hydraulic Cylinder Calculations
Cylinder Force
F = P * A
Where: F = Force (pounds), P = Pressure (PSI), A = Area (in2)
Pump Calculations
Pump Flow Rate
Q = [V_g * n] / 231
Where: Q = Flow Rate (GPM), V_g = Displacement per Revolution (in3/rev), n = Speed
(RPM)
Pump Efficiency
η = [P_out / P_in] * 100
Where: η = Efficiency (%), P_out = Output Power (HP), P_in = Input Power (HP)
Hydraulic Motor Calculations
Motor Torque
T = [P * V_g] / 6.28
Where: T = Torque (lb-ft), P = Pressure (PSI), V_g = Displacement per Revolution
(in3/rev)
Motor Speed
n = [Q * 231] / V_g
Where: n = Speed (RPM), Q = Flow Rate (GPM), V_g = Displacement per Revolution
(in3/rev)
System Design Calculations
Accumulator Sizing
V = Q * ΔP
Where: V = Volume (ft3), Q = Flow Rate (ft3/s), ΔP = Pressure Differential (PSI)
Heat Dissipation
Q = m * c * ΔT
Where: Q = Heat Energy (BTU), m = Mass (lb), c = Specific Heat Capacity (BTU/lb·°F),
ΔT = Temperature Change (°F)
Maintenance Calculations
Oil Viscosity Index
VI = (2 * [b – L] * g *a^2) / (9 * v)
Where: VI = Viscosity (lb·s/ft2), L = Liquid Density (lb/ft3), b = Ball Density (lb/ft3), g =
Acceleration Due to Gravity (ft/s2), a = Radius of Ball Bearing (ft), v = Velocity of Ball
Bearing through Liquid (ft/s)
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