Math CentralQuandaries & Queries


Question from daryl:

Looking for an accurate number to use when calculating barrels per inch in a a tank with the following dimensions:
Nominal diameter - 15'-6", nominal height - 16ft, nominal capacity - 500 barrels. These are commonly referred to as 500x16 tanks.
Currently we are using 2.6 barrels per inch. We need 180 barrels for a full load so I'm trying to figure out how many total inches I need to load 180 bbl. This has been a matter of debate for some time. Thanks for your help.

Hi Daryl,

The subject line of your email said barrels of oil and that is important as a barrel is a unit of volume in other situations also and barrels are not all the same size. A barrel of oil is 42 US gallons.

I used our volume calculator with a diameter of 15.5 feet and a height of 1 inch and got a volume of 117.63 US gallons. Since there are 42 gallons in a barrel of oil that is $\large \frac{117.63}{42} \normalsize = 2.801 \mbox{ barrels.}$ This means that $\large \frac{180}{2.801} \normalsize = 64.27$ inches would give 180 barrels.

I would check that the diameter of the tank is actually 15 feet 6 inches as a tank with this diameter and a height of 16 feet contains 537.7 barrels not 500.


In May 2014 Daryl sent his question again

Question from daryl:

I am trying to find out how many barrels of oil per inch of height in a 500 barrel tank that is 16 foot tall by fifteen foot six inches around. (Nominal diameter)
I'm positive about these are numbers. They are listed on the manufacturer data plate attached to the tank. One answer I've received is 500/(16x12)=2.604 in which case if I wanted to load 1800 barrels I'd need to pull 5ft 9in for 179.676 bbls.
Another formula says the tank must be 15ft 5in nominal diameter otherwise its 537 bbl not 500 and 2.8 bbl per inch. I'm positive about the 500 and the 15'6 around. I've seen many responses but none that are definitive. Thank you very much!


The confusion comes from the tank manufacture's use of the term nominal. According to the Merriam Webster online dictionary the term nominal means "existing as something in name only : not actual or real". If you scroll down the page on the Merriam Webster site for the full definition you will see 3b which says "of, being, or relating to a designated or theoretical size that may vary from the actual : approximate <the pipe's nominal size>".

In your original question you had "Nominal diameter - 15'-6", nominal height - 16ft, nominal capacity - 500 barrels". If that is what is printed on the manufacturer data plate then there is nothing I can do yo help as you don't know any of the actual dimensions.


Comment from Ben

In March of 2019 we received this comment from Ben.

This is not really a question. It's more of a direct answer for the hauler who wrote in, wondering about the number of inches for his 180 bbl load of oil. Because all oil tanks are slightly different, the nominal diameter he used (15' 6"), while a decent approximation, will not provide an answer across the board. However, in order to sell out of a tank, the tank must be strapped - that is, its volume must be calculated in increments of 1/4 inch of height. So to determine the number of inches for a 180 bbl load, the strapping table for that specific tank would be the best place to start. Also, it should be remembered that because oil is so volatile, its volume is very dependent on temperature, so the equivalent volume at standard temp decreases as temperature decreases (and vice versa). Point is: it's an involved problem, but the strapping table (or tank calibration table) is the best starting point.

Thanks for this Ben,


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