Pressure, Force and Horsepower Relationships:
Pressure (psi) = force (lbs) / area (in²)
Force (lbs) = area (in²) x pressure (psi)
Area (in²) = force (lbs) / pressure (psi)
Fluid Power Horsepower:
Fluid Power Horsepower (hp) = pressure (psi) x pump flow
(gpm) / 1,714
Torque and Horsepower Relationships:
Torque (ft lbs) = horsepower (hp) x 5,252 / speed (rpm)
Horsepower (hp) = torque (ft lbs) x speed (rpm) / 5,252
Speed (rpm) = horsepower (hp) x 5,252 / torque (ft lbs)
Basic Cylinder Calculations:
Piston Cylinder Area (in²) = diameter squared x .7854
(Can also use 3.1416 x radius squared (ins) )
Piston Rod End (annulus end) Area (in²) = piston cylinder area (in²) -
rod area (in²)
Cylinder Force (lbs) = pressure (psi) x area (in²)
Cylinder Speed (ft/min) = 19.25 x flow rate (gpm) / area (in²)
(Divide by 60 to convert speed to ft/sec)
Cylinder Speed (in/min) = flow rate (cu ins/min) / area (in²)
(Note that 1 US gallon = 231 cu ins)
Cylinder Time (secs) = area (in²) x cylinder stroke (ins) x .26 / flow
rate (gpm)
Cylinder Flow Rate (gpm) = 12 x 60 x cylinder speed (ft/sec) x area
(in²) / 231
Cylinder Volume Capacity (gals) = cylinder area (in²) x cylinder
stroke (ins) / 231
Basic Hydraulic Motor Calculations:
Motor Torque (in lbs) = pressure (psi) x motor displacement (cu
ins/rev) / 6.28
(Can also use horsepower (hp) x 63,025 / speed (rpm)
Motor Speed (rpm) = 231 x flow rate (gpm) / motor displacement
(cu ins/rev)
Motor Horsepower (hp) = torque (in lbs) x motor speed
(rpm) / 63,025
Motor Flow Rate (gpm) = motor speed (rpm) x motor displacement
(cu ins/rev) / 231
Motor Displacement (cu ins/rev) = torque (in lbs) x 6.28 / pressure
(psi)
Basic Pump Calculations:
Pump Outlet Flow (gpm) = pump speed (rpm) x pump displacement
(cu ins/rev) / 231
Pump Speed (rpm) = 231 x pump flow rate (gpm) / pump
displacement (cu ins/rev)
Pump Horsepower (hp) = flow rate (gpm) x pressure (psi) / 1,714 x
pump efficiency factor
(Can also use horsepower (hp) = torque (in lbs) x pump speed
(rpm) / 63,025)
Pump Torque (in lbs) = pressure (psi) x pump displacement (cu
ins/rev) / 6.28
(Can also use horsepower (hp) x 63,025 / pump displacement (cu
ins/rev)
Heat Generation Formulas: Converting heat into other units
1 hp = 2,545 BTU/hr = 42.4 BTU/min = 33,000 ft.
lbs./min = 746 watts
Horsepower (hp) = pressure (psi) x flow (gpm) / 1714 -or-
BTU/hr = 1½ x psi x gpm
1 BTU/hr = .0167 BTU/min = .00039 hp
Example: 10 gpm flow across a pressure reducing valve with a 300
psi drop = 1.75 hp of heat generated
1.75 hp of heat = 4,453 BTU/hr = 105 BTU/min = 57,750 ft.
lbs./min = 1,305 watts
Most of this heat will be carried back to the reservoir.
Note that heat is generated anytime no mechanical output work
is produced
General cooling capacity of a steel reservoir: HP (heat) = .001 x TD
xA
TD = temperature difference of the oil in the reservoir and the
surrounding ambient air
A = entire surface area of the reservoir in square feet (including the
bottom if elevated)
General Information and “Rules of Thumb”:
Estimating pump drive horsepower: 1 hp of input drive for each 1 gpm
at 1,500 psi pump output
Horsepower when idling a pump: an idle and unloaded pump will
require about 5% of its full rate hp
Reservoir capacity (GALS) = length (INS) x width (INS) x height
(INS) / 231
Oil compressibility: 1/2 % approximate volume reduction for every
1,000 psi of pressure
Water compressibility: 1/3 % approximate volume reduction for every
1,000 psi of pressure
Wattage to heat hydraulic oil: each 1 watt will raise the temperature of
1 gallon of oil by 1°F per hour
Guidelines for flow velocity in hydraulic lines:
2 to 4 ft/sec = suction lines
10 to 15 ft/sec = pressure lines up to 500 psi
15 to 20 ft/sec = pressure lines 500 – 3,000 psi
25 ft/sec = pressure lines over 3,000 psi
4 ft/sec = any oil lines in air-over-oil systems
Velocity of oil flow in a pipe: velocity (ft/sec) = flow (gpm) x
.3208 / inside area of the pipe (sq ins)
Circle area formulas:
Area (sq ins) = π x r² where π (pi) = 3.1416 and r = radius in
inches squared
Area (sq ins) = π x d² / 4 where π (pi) = 3.1416 and d =
diameter in inches
Circumference (ins) = 2 x π x r where π (pi) = 3.1416 and r is
radius in inches
Circumference (ins) = π x d where π (pi) = 3.1416 and d =
diameter in inches
Commonly Used Fluid Power Equivalents:
One US gallon equals:
231 cubic inches
3.785 liters (1 liter = .2642 US gals)
4 quarts or 8 pints
128 ounces liquid / 133.37 ounces weight
8.3356 pounds weight
One horsepower equals:
33,000 ft lbs per minute
550 ft lbs per sec
42.4 BTU per min
2,545 BTU per hour
746 watts
0.746 kw
On psi equals:
.0689 bar (1 bar = 14.504 psi)
6.895 kilopascal
2.0416 hg (inches of mercury)
27.71” water
One atmosphere equals:
14.696 psi
1.013 bar
29.921 hg (inches of mercury)
