Hydraulic Formulas – FluidPower.Pro

Hydraulic Cylinder[ + ]
		Imperial	Metrical
Bore Area	##A_b=\frac{\pi}{4}\cdot D_b^{2}##	#A_b# – Bore Area, in² #D_b# – Bore Diameter, in	#A_b# – Bore Area, mm² #D_b# – Bore Diameter, mm
Annular Area	##A_a=\frac{\pi}{4}\cdot (D_b^{2}-D_r^{2})##	#A_a# – Annular Area, in² #D_b# – Bore Diameter, in #D_r# – Rod Diameter, in	#A_a# – Annular Area, mm² #D_b# – Bore Diameter, mm #D_r# – Rod Diameter, mm
Area Ratio	##CR=\frac{A_b}{A_b-A_r}:1##	#CR# – Area Ratio #A_b# – Bore Area, in² #A_r# – Rod Area, in²	#CR# – Area Ratio #A_b# – Bore Area, mm² #A_r# – Rod Area, mm²
Piston Velocity at the given flow	##v=\frac{Q\cdot K}{A\cdot 60}##	#v# – Velocity, in/sec #Q# – Flow, gpm #A# – Work Area, in² #K=231# in³/gal	#v# – Velocity, m/sec #Q# – Flow, lpm #A# – Work Area, mm² #K=1000# l/m³
Required Flow at the given time	##Q=\frac{s\cdot A\cdot 60}{t\cdot K}##	#Q# – Flow, gpm #s# – Stroke, in #A# – Work Area, in² #t# – Time, sec. #K=231# in³/gal	#Q# – Flow, lpm #s# – Stroke, m #A# – Work Area, mm² #t# – Ext./Ret. time, sec. #K=1000# l/m³
Force	##F=p\cdot A##	#F# – Force, lb #p# – Pressure, psi #A# – Work Area, in²	#F# – Force, N #p# – Pressure, MPa #A# – Work Area, mm²
Hydraulic Pump[ + ]
		Imperial	Metrical
Flow Rate	##Q=\frac{disp\cdot n}{K}\cdot \frac{E_v}{100}##	#Q# – Flow, gpm #disp# – Displacement, in.cu. #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#Q# – Flow, lpm #disp# – Displacement, cm³ #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Displacement	##disp=\frac{Q\cdot K}{n}\cdot \frac{100}{E_v}##	#disp# – Displacement, in.cu. #Q# – Flow, gpm #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#disp# – Displacement, cm³ #Q# – Flow, lpm #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Leakages (case drain flow)	##Q_L=\frac{disp\cdot n}{K} \cdot \frac{100-E_v}{100}##	#Q_L# – Drain Flow, gpm #disp# – Displacement, in.cu. #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#Q_L# – Drain Flow, lpm #disp# – Displacement, cm³ #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Required Torque to provide the given pressure	##T=\frac{disp\cdot p}{2\cdot \pi} \cdot \frac{100}{E_m}##	#T# – Torque, lb.-in. #disp# – Displacement, in.cu. #p# – Pressure, psi #E_{m}# – Mechanical Efficiency, %	#T# – Torque, Nm #disp# – Displacement, cm³ #p# – Pressure, MPa #E_{m}# – Mechanical Efficiency, %
Provided Pressure based on torque from engine	##p=\frac{2\cdot \pi\cdot T}{disp} \cdot \frac{E_m}{100}##	#p# – Pressure, psi #T# – Torque, lb.-in. #disp# – Displacement, in.cu. #E_{m}# – Mechanical Efficiency, %	#p# – Pressure, MPa #T# – Torque, Nm #disp# – Displacement, cm³ #E_{m}# – Mechanical Efficiency, %
Power required from the engine	##P_{in}=\frac{Q\cdot p}{K} \cdot \frac{100}{E}##	#P_{in}# – Power, hp #Q# – Flow, gpm #p# – Pressure, psi #E# – Overall Efficiency, % #K# = 1714	#P_{in}# – Power, kW #Q# – Flow, lpm #p# – Pressure, MPa #E# – Overall Efficiency, % #K# = 60
Hydraulic Motor[ + ]
		Imperial	Metrical
Required Flow to provide the given rpm	##Q=\frac{disp\cdot n}{K} \cdot \frac{100}{E_v}##	#Q# – Flow, gpm #disp# – Displacement, in.cu. #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#Q# – Flow, lpm #disp# – Displacement, cm³ #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Displacement to provide the given rpm	##disp=\frac{Q\cdot K}{n} \cdot \frac{E_v}{100}##	#disp# – Displacement, in.cu. #Q# – Flow, gpm #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#disp# – Displacement, cm³ #Q# – Flow, lpm #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Leakages (case drain flow)	##Q_L=\frac{disp\cdot n}{K} \cdot \frac{100-E_v}{E_v}##	#Q_L# – Drain Flow, gpm #disp# – Displacement, in.cu. #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 231	#Q_L# – Drain Flow, lpm #disp# – Displacement, cm³ #n# – Rotational speed, rpm #E_{v}# – Volumetric Efficiency, % #K# = 1000
Output Torque based on the motor inlet pressure	##T=\frac{disp\cdot p}{2\cdot \pi} \cdot \frac{E_m}{100}##	#T# – Torque, lb.-in. #disp# – Displacement, in.cu. #p# – Pressure, psi #E_{m}# – Mechanical Efficiency, %	#T# – Torque, Nm #disp# – Displacement, cm³ #p# – Pressure, MPa #E_{m}# – Mechanical Efficiency, %
Required Pressure to provide the given torque	##p=\frac{2\cdot \pi\cdot T}{disp} \cdot \frac{100}{E_m}##	#p# – Pressure, psi #T# – Torque, lb.-in. #disp# – Displacement, in.cu. #E_{m}# – Mechanical Efficiency, %	#p# – Pressure, MPa #T# – Torque, Nm #disp# – Displacement, cm³ #E_{m}# – Mechanical Efficiency, %
Power provided to the consumer	##P_{out}=\frac{Q\cdot p}{K} \cdot \frac{E}{100}##	#P_{out}# – Power, hp #Q# – Flow, gpm #p# – Pressure, psi #E# – Overall Efficiency, % #K# = 1714	#P_{out}# – Power, kW #Q# – Flow, lpm #p# – Pressure, MPa #E# – Overall Efficiency, % #K# = 60
Other generic formulas[ + ]
		Imperial	Metrical
Flow at the given velocity	##Q=\frac{v\cdot A\cdot 60}{K}##	#v# – Velocity, in/sec #Q# – Flow, gpm #A# – Work Area, in² #K=231# in³/gal	#v# – Velocity, m/sec #Q# – Flow, lpm #A# – Work Area, mm² #K=1000# l/m³
Torque	##T=\frac{P\cdot K}{n}##	#P# – Horse power, hp #T# – Torque, lb.-in. #n# – Rotational speed, rpm #K# = 63025	#P# – Horse power, kW #T# – Torque, Nm #n# – Rotational speed, rpm #K# = 9549
Power	##P=\frac{p\cdot disp\cdot n}{K}##	#P# – Power, hp #disp# – Displacement, in.cu. #p# – Pressure, psi #n# – Rotational speed, rpm #K# = 396000	#P# – Power, kW #disp# – Displacement, cc #p# – Pressure, MPa #n# – Rotational speed, rpm #K# = 60000
Efficiency	##\frac E{100}=\frac{E_v}{100}\cdot\frac{E_m}{100}##	#E# – Overall Efficiency, % #E_v# – Volumetric Efficiency, % #E_m# – Mechanical Efficiency, %	#E# – Overall Efficiency, % #E_v# – Volumetric Efficiency, % #E_m# – Mechanical Efficiency, %