Valve exhaust ΔP, psi7.029.976.95Pressure 1, psia21.7224.6721.65Valve-fitting exhaust ΔP, psi2.392.981.16Pressure 2, psia24.1127.6522.82Air-line exhaust ΔP, psi1.111.380.57Pressure 3, psia25.2229.0323.39Flow-control exhaust ΔP, psiPressure 4, psia25.2229.0323.39Cylinder-fitting exhaust ΔP, psi9.6911.965.07Pressure 5, psia34.9140.9828.46Pressure 6, psia54.7963.8174.70Cylinder-fitting supply ΔP, psi6.237.592.34Pressure 7, psia61.0271.4077.04Flow-control supply ΔP, psi0.000.000.00Pressure 8, psia61.0271.4077.04Air-line supply ΔP, psi0.610.740.25Pressure 9, psia61.6372.1477.29Valve-fitting supply ΔP, psi1.171.420.48Pressure 10, psia62.8173.5777.76Valve supply ΔP, psi2.292.781.94


Check Sum pressure, psia65.1076.3579.70Maximum allowable pressure drop, psi11.9611.9611.96Cylinder force output, lb26.8533.9237.61Low-pressure force + friction force, lb69.9778.8328.62High-pressure force, lb96.82112.7566.23Calculated delay time, sec0.0540.0390.048Estimated total time, sec0.1760.1460.140
Tabulated results are for the example circuit lifting a 10-lb mass 3 in. in 0.170 sec or less. Cylinder ports are 1/8 NPT, valve ports are 1/4 NPT, and there are no flow controls in the system. Note that the 11.96-psi cylinder fitting exhaust pressure drop is the limiting factor with the larger cylinder, and the 79.70-psia Check Sum pressure limits the small-cylinder circuit.

Optimizing circuit design

Here are a few suggestions for optimum circuit design:

  • Make air-line lengths as short as possible.
  • Make air lines between the valve and cylinder as straight as possible with minimal bends.
  • Select cylinder bore sizes to handle the expected load plus a reasonable safety factor. Larger-than-necessary cylinders cost more money, waste energy, and add cycle time.
  • Cylinder stroke should be no more than required. Longer-stroke cylinders cost more, waste energy, and add cycle time.
  • A valve can be oversized without appreciably wasting energy. However, cycle time will increase if solenoid shift time increases.
  • Overpressurizing a circuit beyond a certain point -- the maximum pressure drop -- does not increase cylinder speed but does waste air and can increase delay time and total cycle time.
  • If the application calls for different loads or speeds for extend and retract motions, consider using different pressures or add flow controls.
  • Consider using quick-exhaust dump valves. The dumped air bypasses the exhaust circuit, possibly reducing cycle time and increasing speed.
  • Each application has an optimum air-line ID. Increasing the air-line diameter increases Cv but also increases the volume that must be filled and evacuated each cycle.
  • Components with the smallest Cvs and largest pressure drops limit circuit performance. Increase these Cvs first to have the greatest impact on circuit performance.
  • Components with the largest Cvs and smallest pressure drops are possibly oversized. Decreasing these Cvs could improve circuit performance.


Al = Air-line cross-sectional area, in.2
d = Cylinder diameter, in.
df = fitting ID, in.
dt = tubing ID, in.
fl = line-friction coefficient
l = line length, in.
Q = Flow rate at 1 atmosphere, 68°F, and 36% relative humidity, in scfm
Cv = Flow coefficient
G = Specific gravity of air at one atmosphere, 68°F, and 36% relative humidity. Usually, G = 1.
g = Acceleration of gravity
ks = Specific-heat ratio; ks = 1.4 for air.
n = Number of fittings
Pe = Exhaust pressure, psi
Ps = Supply pressure, psi
P1 = Upstream pressure at T1, psia
P2 = Downstream pressure, psia
qm = Mass flow rate
T1 = Upstream temperature, °R. Usually, T1 = 528°R.
Ve = Exhaust volume, in.3