Late Update: TPM Reader MR responds:
I am an engineer, and the math is not hugely difficult - especially with the computer models to help you out. However, the assumptions are not. You have a pipe diameter, and you can do some particle velocity estimates based on the video. But the oil:gas ratios and viscosity of the mixture can throw some pretty big variables in there.
So, for instance the numbers that I heard on NPR 20,000-100,000 barrels/day compared to 5,000 barrels/day estimate from BP and the coast guard - could reflect total volume flow (gas+oil) vs flow of oil only. The professors that NPR were doing velocity estimates - but they didn't make it clear if they were talking about the flow of the mixture vs the flow of the oil.
BP could get the information - but clearly they seem to think they have other priorities at the moment. Or maybe they are using the data, or their low-balling to keep the disaster looking less disastrous. I can't tell you that. But I can tell you that there are plenty of variables that mean you'd have to spend some time at the well head taking measurements in order to get the real number.