Problem #2 A Pinhole Leak
If a lyophilizer chamber had a volume of 8404 liters, already excluding the shelves, hoses, etc., and it had a measured leak rate of 0.5 mTorr/hr, what size would the leak hole be if it were a single simple pinhole through the wall?
Let
Let
Let
<= Molecular Wt for Air
Let
<Microscope view of pinhole.
A detailed calculation, allowing for all angles of approach of molecules to the surface and providing for the distribution of molecular veloities shows that with nm (the mean velocity in meters/sec), a correct velocity equation is where n' is the number of molecules per m3 and n is the number of collisions per m2 per second.

Thus the units of and the units of and the units of
From kinetic theory,
Thus or
<= EQU (1)
Separately, one can see that the mass (w) of molecules striking an opening per square meter per second is <= EQU (2) and units of
Now combining equations 1 and 2 we get

and
<= Ideal Gas Law
with a little algebra,
The mass that is striking the unknown area(of the pinhole) per sec can be determined from the DP/hr given in the problem.
First find the number of mole (n) per sec that are leaking through the pinhole.
Next, find "w", the that impinge on the opening.
<= Solve this for "Area" of the Pinhole
Then and