# Re: Needle valves in CO2 systems

```zxcvbob <bob at a51web_net> wrote:
> As I've mentioned before, I use a homemade equivalent of a capillary
> tube to restrict the CO2 flow.  I adjust the flow rate by varying the
> output pressure of the CO2 regulator.  I don't know what its Cv is,
> but the flow rate is extremely nonlinear (in a good way).  I normally
> operate the regulator at about 3 psig, but to double the flow rate, I
> might have to increase it to 10 psig, and to double it again I might
> have to go to 40 psig.  The cross sectional area of the tube is
> non-uniform.  I suspect that at its most restrictive point, the gas
> velocity is approaching the speed of sound (thus establishing a
> maximum flow rate at any pressure).
>
> It's a very low-tech approach to rocket science ;-)

In practical terms, its not feasible to develop a reasonable
mathematical model for flow through restrictive devices such as valves
or crushed tubes because so many parameters come into consideration. I
expect that the flow in CO2 systems, particularly those with high
pressure, is at the speed of sound for that gas at that pressure and
temperature. This flow regime is called called "fully choked". To add to
the complications, the speed of sound is a function of temperature and
density of the fluid and these parameters are also affected by the
dynamics of the flow itself. Gas expanding absorbs energy and becomes
colder. If the flow is not fully choked, then it will be either laminar
or turbulent flow and these have different energy transfer mechanics.

The best solution that engineers use is to actually measure the flow
rates over the whole range of pressures and settings of interest and
then graph the results. Its never linear except when graphed on
logarithmic charts and only in the fully laminar or fully turbulent flow
regimes. You get nice graphs when you're dealing with orifices but I
don't believe they chart so nicely for valves.

For our purposes, its best to just fiddle the needle valve until you get
the right bubble rate and the temperature, pressure and flow have a
chance to stabilize.