I'm not sure I could calculate the throughput of a UF6 centrifuge from fundamental principles, but I have found a published figure for the efficiency of Pakistan's P-1 and P-2 centrifuges: about 2.5 SWU-kg per year for the P-1 (the kind Iran has today) and about double that for the faster P-2. To translate that into bomb-sized quantities here are some figures I posted elsewhere (OK, fark.com [blush])... WDK
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I can't calculate the throughput either hence trying to enlist my kid in this project.
I also went to the sizes.com site. There is also calculator at fas, federation of american scientists. While SWUs are probably the only way to figure out some kind of general idea of `time to HEU', there is a problem with using SWUs. They are separative work units and give a dimensionless number that represents a measure of work efficiency. This is a useful figure for measuring the relative energy costs of producing fuel grade, since the higher the SWU's per volume, the more costly the output is to produce. For example, the French use a gas diffusion method that consumes a very large amount of electricity to drive gas compressors and other production paraphernalia. Their consumption of electricity is very large accounting for something like 8% of any return energy production they might achieve in their nuclear reactors. The gas centrifuge system uses considerably less electricity and hence is much more `efficient' in this sense.
But I was contemplating several graphs and other materials and soon realized that there are literally no units of time anywhere.
The whole thrust of the USG's alarm bell on Iran depends on the scare of how little time there is between grinding out fuel grade which can take any where from next week until just short of infinity and using the same processing plants to produce weapons grade. In other words, if we use SWU's there is no measure of time as a physical quantity.
What struck me as rather dubious trickery with the FAS calculator is the assumption that centrifuges are added each day. So the time to the big afterglow can be speeded up or slowed down depending on what value the visitor chooses for the number added. There is no choice for `none', which implies to me, that a 164 unit cascade is incapable of producing weapons grade---or that it would take some impossible length of time, like a century. Here is the calculator:
http://www.fas.org/cgi-bin/ucountdown.pl
Plugging in (2) SWUs/yr, and (1) centrifuge addition per day, the time is 1791 days (4.91 years) to obtain 50 kg of U-235 at 90%.
So these thoughts forced me to think about the production rate of a single centrifuge. Production rate is not the same as SWU, since if you are going for weapons, you don't care about the cost of electricity, the huge amount of waste or anything else. The separative work units or efficiency of the system is irrelevant as long as it will produce HEU in some acceptible length of time.
There is also a paper on centrifuge technology that has equations for calculating the general throughput of centrifuges here:
http://www.urenco.com/im/uploaded/1086887106.pdf
The centrifuge design described above uses a counter-current gas flow. I suspect such a design requires a much taller centrifuge than the 1.8m Pakistan rigs the Iranians are using. So using the Urenco equations will give the highest possible result.
The problem included in the chem post on how much helium it takes to fill a balloon, might be adapted to help build up a mathematical model for a centrifuge as a cylindrical volumn with some guess-a-mated range of values of gas pumped in and out. From the wikipedia phase chart (and the one included in the Urenco paper) it looks like UF6 is a gas at one atmosphere and 125-150 f temperature. So I was wrong about extreme temperatures and pressures for this stage. However, there is probably an optimum intersection of values where some particular combination of temperature and pressure maximize the separation potential---probably based on the optimum diffusion rate.
Anyway, the Iranians were kind enough to supply the linear velocity (350 m/s), which can be turned into a value for radial velocity, which in turn gives some idea of the centripedal force on the two masses of gas particles within the rotating volumn.
Start with trying to find the rpm. Assume the diameter as .5m, with a radius of .25m, plugged into pi r^2 = pi (.25m^2) = 1.9634m the circumference. The circumference C travels L with the number of rotations L/C. 350m/1.934m = 178.262m/s, or 10695.72 rpm.
Once this ideal centrifuge is constructed as a mathematical model, then various quantities of UF6 can be plugged in and various other things can be played with to yield some kind of time line showing units of gas volumn processed per units of time. From the Urenco paper:
``According to this formula the separative power of a centrifuge increases proporitional to the length of the rotor and to the fourth power of the circumferential velocity of the rotor wall.
As a side note, Urenco built the G-1 centrifuges that were later slightly reworked by Pakistan and began the infamous P-1---the type that Nuke'm Khan was supposed to have sold the drawings for to Iran.
CG