**Chris Landis Valve/Vacuum Product Manager Parker Hannifin Corp. Richland, Mich. **

In recent years, much discussion has centered on *C _{v}* ratings (also known as capacity coefficients or flow factors) and whether or not American, European, and Japanese pneumatic-valve manufacturers rate valves the same way. With ANSI/NFPA, ISO, and JIS organizations all specifying slightly different test methods and rating criteria, the confusion is understandable.

Leaving that ongoing discussion to the respective standards organizations, here’s a look at the practical aspects of designing the most efficient and economical system without under or oversizing components. First, we’ll calculate *C _{vs}*for standard pneumatic cylinders and examine

*C*values for standard ISO valves, including 18 and 26 mm and ISO Sizes 1, 2, and 3. We’ll also chart average rod speed relative to cylinder bore size to pinpoint ISO valves that best match flow demands.

_{v}The approach is based on standard* C _{v}* calculations:

C=_{v} | Q | ## √ | GT |

22.48 | (P _{1}-P_{2})P_{2} |

where Q = volumetric flow rate in standard cubic feet per minute (scfm), based on 14.7-psi atmospheric pressure and 60°F air temperature.

To simplify the equation, experts typically assume a conservative pressure change between inlet and outlet ports (*P _{1} – P_{2}*) of 5 psi. For time or process-critical applications, reduce this to 2 psi. And, in many cases, a pressure drop of 10 psi is not detrimental to the application. A 10-psi pressure drop permits smaller valves that lower costs and require less mounting space.

To simplify calculations, let’s tabulate values for a portion of the equation for 2, 5, and 10-psi pressure changes. Here, we create a constant *A*, defined as

A= | 1 | ## √ | GT |

22.48 | (P _{1}-P_{2})P_{2} |

and list values for varying inlet gage pressures in the accompanying Basic Data table.

This reduces the flow-coefficient equation to *C _{v} = QA*. In terms of cylinder volume and time,

Q= | VP_{1} |

28.8 tP_{a} |

where atmospheric pressure, *P _{a}*, is assumed to be 14.7 psi.

Next, calculate values for compression ratio, *C _{r} = P_{1}/P_{a}*, for various inlet pressures and also list values in the Basic Data table.

Restating the volumetric flowrate equation in terms of compression ratio results in

Q=_{} | VC_{r} |

28 t |

Now examine the impact of cylinder volume and stroke time for known *C _{v}* values of ISO valves. Given that

*Cv = QA*; and

*V =*(π/4)

*d*

^{2}

*l,*we can restate the equation as:

C=_{v} | ## ( | (π/4)C _{r}A | ## )( | l | ## ) | (d)^{2} |

28.8 | t |

Here, l/t is a simplified representation of average rod velocity in inches per second.

This equation works well for NFPA cylinders. But because designers usually specify ISO cylinders in metric units, apply the conversion factor 1 in. = 25.4 mm and revise the equation:

C=_{v} | ## ( | (π/4)C _{r}A | ## )( | l | ## ) | (d)^{2} |

28.8(25.4) ^{3} | t |

Assuming 80 psig for inlet pressure — based on a typical plant operating at 100 psig with line losses — and using a conservative 5-psi pressure drop for the constant *A*, chart average cylinder rod speed versus cylinder diameter in terms of required C_{v}. The accompanying tables for two and threeposition valves highlight areas where each ISO valve meets C_{v} requirements.

**Nomenclature**

*d*= Cylinder diameter, in.

*G*= Specific gravity of the fluid (G = 1 for air)

*l*= Cylinder length, in.

*P*= Absolute pressure at inlet port (gage pressure + 14.7), psi

_{1}*P*= Absolute pressure at outlet port, psi

_{2}*P*= Atmospheric pressure, psi

_{a}*Q*= Volumetric flow rate, scfm

*T*= Absolute temperature of air, °R

*t*= Time to fill cylinder, sec

*V*= Cylinder volume, in.

^{3}