When you do back-of-the-envelope calculations in oil well drilling, half the job is just keeping track of the units. In the old days, it was all “american units” in the north sea, but today, reports and logs sports a colourful mix of metric and imperial units for all aspects of the well.
For instance, you may want to calculate the pressure down in a well filled with a specific drilling mud. If the mud isn’t moving around and is not very compressible, the pressure is approximately p = ρgh where ρ is the fluid density, g the gravitational constant and h the height. We want the pressure in bar, we’ve got g in m/s² but mud density might be given in ppg or “pounds per gallon”. The experts may have the conversion factors memorized, but for the rest of us it’s a lot quicker to visit wolframalpha.com and simply write:
12 ppg * gravitational acceleration * 3000 m in bar
which outputs 423 bars as well as the value in atmospheres, pascal and psi in case you’r interested.
Similarly, when you’r extending the well you may want to know how much mud you need to fill the extra volume. We may state the length we drill in meters, but the diameter of the well depends on the size of the drillbit, which is always given in inches. So will this volume be given in cubic metres, litre or perhaps gallons? Here’s where one of the famous locals enter the scene, the “barrels of oil” (bbl) as a standard measure of volume. It’s the natural unit if you ship or store your drilling mud in oil barrels I guess. Again, the calculations are not really complicated, but the more units we juggle the larger the chance of a mistake. After all, you’r probably just doing a quick calculation as a reality-check for your computer simulation, right? Typing:
volume of cylinder with length 23m and diameter 8 inches
tells you that the extra length of hole needs 745.9 L of mud, which via 745.9 L in barrels of oil concludes with a need for 4.7 barrels of your finest drilling mud.
Wolfram Alpha seems weak on nested evaluation and won’t accept these two queries formulated as one sentence. (Or I might be missing something?) but it sure is a lot faster than looking up the conversion factors every time. So with Wolfram Alpha, you save ten minutes checking and double-checking your results or a whole day searching for bugs in your simulation, depending on which you check first ;-)