# Bernoulli

A project log for MultiBot CNC v2

A low cost 3D printed CNC that can be built with minimal tools yet is capable of great things.

David Tucker 04/21/2021 at 03:350 Comments

Bernoulli's equation can help us understand a bit more about what is going on between pressure and velocity with our compressor.  In its simplest form (ignoring the gravity term) it is:

Where P is fluid pressure, ρ is fluid density, and v is fluid velocity.  Assuming the density is a constant then this can be simplified into approximately:

This basically says that cutting the pressure in half gives us a 4x increase in velocity.  You would think we would need an increase in pressure to get an increase in velocity but that is thinking about it backwards.  We are releasing the pressure, it is at some psi in the line but when it exits the line then pressure drops to 1 psi or standard pressure.  If there was no drop in pressure then there would be no velocity (no air would move).

I'm not exactly sure how this relates back to CFM, I guess cfm is just velocity over time.

Anyway the idea is that a doubling of supply line pressure results in a 4x increase of velocity at the outlet.  Since area of a circle basically grows with the square of diameter then a halving of the diameter also results in a doubling of the exit velocity.  Of course this is all in an ideal environment, there is a limit to how much we can increase the line pressure or reduce the nozzle diameter.  There are line losses and turbulence at the nozzle that will sap energy.

Not quite related but here is an interesting graph I found that compares line pressure to flow rates (liters per hour I think) for several of those metal aquarium air pumps you can get from AlliExpress and Amazon.  You can see that increasing the line pressure results in a reduction of flow in the compressor.  This does not follow Bernoulli's principle because the air does not flow cleanly through the pump. Turbulence through the pump causes things to behave differently and that in turn gives us more of a linear relationship rather than an exponential one.