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
<= 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 **n**_{m} (the mean velocity in meters/sec), a correct velocity equation is
where n' is the number of molecules per m^{3}^{ }and **n** is the number of collisions per m^{2} 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