I have a vacuum chamber, connected to a vacuum pump with a pipe of diameter 50mm and need to create a high (0.0001mBar) vacuum.
I need to calculate the total suction time, and since I was not in the picture in the high vacuum area, I read some theories for example >here<.
The suction process starts at atmospheric pressure, and if I am right until about 0.001mBar the gas flow is viscous, after that the flow is molecular where less collision happens between particles.
In the continuous state I calculated the pressure drop by the time with iteration of this formula:
$$P=P_0 \mathrm{e}^{-Q \delta t/ V}$$
- $P_0$ - starting pressure
- $\mathrm{e}$ - euler number
- $Q$ - flow rate [L/min]
- $V$ - volume
- $\delta t$ - elapsed time
I've found some formulas in case of effusion but if I am right this is for the case if there is a pinhole in the system. However, I have a relatively big (50mm) hole on the side.
If I am right my case is a diffusion, but I don't find any formulas to calculate how many particles goes through the hole by the time.
I also have a formula to calculate the pressure based on number of outgoing particles in a given volume and temperature ($k_B$ = Boltzmann constant):
$P = n k_B T / V$
How can I calculate how many particles go through the hole by the time in the molecular state of suction?
Thank you
