Common Pneumatic Formulas
Air Valves help to regulate pressure in the cylinder and are sized for flow capacity (Cv). Cv is based on the specific cylinder stroke & travel time requirements, as well as piston size. Cv is a coefficient that measures the quantity of air a device can pass.
Cv= Area (in²) x Length (ins.) x Compression Factor
Pressure Drop Factor x Time (secs) x 29
Area= Effective cylinder piston area (square inches)
A= πr² (3.14 x radius²)
PLEASE NOTE: The same formulas apply for the rod end of the cylinder. However, to make precise calculations, one must take the cylinder area (in²) minus the rod end area (in²) when utilizing this valve sizing formula to determine return stroke Cv rating.
Length= The total cylinder stroke length in inches (in.)
Compression Factor= Taken from the table (based on supply pressure rating).
Pressure drop factor= 10 or 15 psi drop is a good guideline for using this formula (refer to Table 20 for further details)
Time= Required cylinder stroke time (in seconds)
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| Pressure Drop Factor PD for Various Pressure Drops | ||||||
| Supply Pressure | Compression Factor | 2 | 5 | 10 | 15 | 20 |
| 40 | 3.7 | 9.9 | 15.3 | 20.5 | 23.6 | N/A |
| 50 | 4.4 | 10.8 | 16.7 | 22.6 | 26.4 | 29 |
| 60 | 5.1 | 11.7 | 18.1 | 24.6 | 29 | 32 |
| 70 | 5.8 | 12.5 | 19.3 | 26.5 | 31.3 | 34.8 |
| 80 | 6.4 | 13.2 | 20.5 | 28.2 | 33.5 | 37.4 |
| 90 | 7.1 | 13.9 | 21.6 | 29.8 | 35.5 | 39.9 |
| 100 | 7.8 | 14.5 | 22.7 | 31.3 | 37.4 | 42.1 |
| 110 | 8.5 | 15.2 | 23.7 | 32.8 | 39.3 | 44.3 |
| 120 | 9.2 | 15.8 | 24.7 | 34.2 | 41 | 46.4 |
| 130 | 9.8 | 16.4 | 25.6 | 35.5 | 42.7 | 48.4 |
| 140 | 10.5 | 16.9 | 26.5 | 36.8 | 44.3 | 50.3 |
| 150 | 11.2 | 17.5 | 27.4 | 38.1 | 45.9 | 52.1 |
Table 20
Compression Factor= Taken from Table 20 (based on supply pressure rating).
Sizing Example
- 6 inches bore cylinder with 2-inch rod thickness and 15-inch total stroke
- Travel time=2 seconds
- 100 psi supply pressure
- 15 psi pressure drop factor to be used
Calculate the 6” diameter piston bore area (in square inches) for extend calculations
A= 6 ins. x 6 ins. x .7854 = 28.27 (in²)
PLEASE NOTE: This is for the cylinder extend area. To calculate the cylinder return area, the rod area must be calculated (in²) and then this value must be subtracted from the piston bore area (in²).
Calculate the 2” diameter rod end area in square inches
A= 2 ins. x 2 ins. x .7854 = 3.1416 (in²)
Thus, Cylinder Return Area is 28.27 in² – 3.1416 in² = 25.12 in²
Apply these application variables to the Cv sizing formula:
| Cv= | 28.27 in² x 15 ins. X 7.8 | = | 3,307 | 1.52 Cv (to extend) |
| 37.4 x 2 secs. X 29 | 2,169 |
| Cv= | 25.12 in² x 15 in x 7.8 | = | 2,939 | 1.52 Cv (to extend) |
| 37.4 x 2 secs x 29 | 2,169 |
Select a valve that meets this 1.52 Cv rating
Air Flow Rates
SCFM – Standard Cubic Feet per Minute – One cubic foot of gas (air) per minute at conditions of:
14.69 Pounds per Square Inch (psi)
68 degrees F
Relative humidity of 36%
Cubic Feet Per Minute (CFM): A particular unit of measurement for airflow volume. It’s determined by how many cubic feet of air passes by a stationary point per minute.
Free Air Flow: How much flow is actually generated (in standard condition).
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