CFM at Different PSI: Understanding Compressed Air Systems

[stromark]

I have a compressed air system powered by a 25 HP reciprocating compressor giving 109 CFM @ 175 psi.
This system also provides air through a ball valve off the main system for vibrators totalling 186 cfm @ 80 psi.
Where does all this cfm come from that powers the vibrators when the pressure is stepped down via the ball valve from 175 to 80 psi?

 

[russ_watters]

I have a compressed air system powered by a 25 HP reciprocating compressor giving 109 CFM @ 175 psi.
This system also provides air through a ball valve off the main system for vibrators totalling 186 cfm @ 80 psi.
Where does all this cfm come from that powers the vibrators when the pressure is stepped down via the ball valve from 175 to 80 psi?

Welcome to PF!

Pressure and volume are inversely proportional; when you decrease the pressure, the volume(etric flow rate) goes up (there is also a temperature drop...).

 

[jack action]

You can find the power required for a desired flow with the following equation:

$$P = \frac{144\times 14.7\times CFM}{.287\times 33000} \left(\left(\frac{PSI}{14.7}\right)^{0.287} - 1\right)$$
Or:
$$P = \frac{CFM}{4.4742} \left(\left(\frac{PSI}{14.7}\right)^{0.287} - 1\right)$$
Plugging you numbers, you find that you need 25.2 hp for 109cfm@175psi and 26.0 hp for 186cfm@80psi, which are basically the same.

As @russ_watters said, when you decrease the pressure while keeping the same power input, the volumetric flow rate will increase. It's a similar phenomena as when you change gear ratio in a transmission: If you change the gear ratio (ball valve), you can decrease the torque (pressure), but the rpm (volumetric flow rate) will have to increase if the same power input is kept.

The energy produced has to go somewhere: If it is not in pressure, it will be in motion.