Sciencemadness Discussion Board

Vacuum, pressure, and capillary diameter... wut

Nectarine - 16-1-2015 at 16:18

I've never done anything close to this, its a grad level course so he just dropped it on us. I don't need the answer, but I do need the equations:

"You are designing an electrospray system. You have a vacuum pump that displaces 37 m^3/h of air. You must purchase a capillary that is 7.8cm long. What should the inner diameter of the capillary bne fpr a [ressure of 1.3 torr in the first differential pumping region of your instrument. Consider only gas flow through the capillary to the pump (i.e. assume other gas flows are negligible).

So far, some equations I've found are

Conductance: C=(pi*d^4)/128nl * (P1+P2)/2 for 'large pressures'
C=(pi*v*d^3)/12l for kn>1 (knudsen #)

v = average velocity of the gas
l = length of tube
d = diameter
n = ?
P1 and P2 are the pressures outside and inside

Also Qout=PPSP
Pp= internal pressure (1.3 torr, I think in this case)
Sp = vacuum velocity (37 m^3/h I think in this case)

Then... I believe you can do Q = C(P2-P1)

..... I have no idea what the f*ck to do. :) Is 1.3 torr going to use a Kn > 1 or is this considered a large pressure??

Zombie - 16-1-2015 at 18:42

Copy/paste this into Google search box. The first link on the page is a Perdue University PDF w/ everything you need

Numerical Calculation of Mass Flow Rate in
Capillary Tubes Using ‘Art’, an Advanced
Simulation Softare

Also my second favorite site on the net. (after pornhub);)
http://www.engineeringtoolbox.com/

It's not that difficult. See the trees inside the forest. Take what you know, and apply that. The rest falls into place because it HAS to.:cool:

Nectarine - 19-1-2015 at 12:05

I ended up doing the problem and getting an answer that is at least 1 order of magnitude too high.

I used different equations, but I'm still unsure what mistake I've done. Everywhere I go rounds off different numbers and uses different conversion values (ending up with different sig figs and rounding).

Unsure, but since there is a r^3 value, any change in rounding can be substantial.

Zombie - 26-1-2015 at 13:22

It's over my head brother but like I said before... Take what you do know, and the rest has to fall into place.
That's how I approach everything.

Hopefully someone will know the formula that applies for you. If push comes to shove I have a friend I will see on Saturday that made a career in thin film tech. and high vacuum. Perhaps he will look at this thread with me.