What is the approximate weight of the water in a full vertical cylindrical tank that is approximately six feet (two meters) in diameter and 20 feet (six meters) high? Use π (pi) = three for estimating purposes.

A. 33,700 pounds

B. 134,800 pounds

C. 18 metric tons

D. 72 metric tons

E. None of the above

Commentary

The solutions to this problem are relatively straightforward. The volume of a full tank of water is π (pi) times the square of the radius times the tank height (3 ● 3^{2} ● 20) or approximately 540 cubic feet. The density of water is approximately 62.4 pounds per cubic foot so the water in the tank weighs approximately 33,700 pounds.

The solution to the example in metric units is (3 ● 1^{2} ● 6) or approximately 18 tons (18,000 kilograms) because the density of water is approximately one metric ton per cubic meter. Therefore, Answer A and Answer C are correct.

As mentioned, this problem is relatively straightforward from a technical perspective. The point of performing the calculation in both the English and metric systems is that the English system is more prone to error. The metric system is more elegant — even though both will yield the same answer for the same size tanks. The metric system is less prone to calculation error because many of its conversion factors are one or multiples of 10. (If you have already attended one of my seminars, you know that I am good at multiplying and dividing by one.)

This exercise may not seem important, but small errors can make a big difference in results. I seem to recall that a space probe crashed into a planet (instead of orbiting) due to a misunderstanding regarding the measurement units used during design.

Additional Complicating Factors

The above calculations in the English system can be made even more complicated by using the weight of water per gallon and the number of gallons per cubic foot. In addition, the liquid could be different from water and have a density that is different from that of water so the tank contents could be heavier or lighter than calculated in either system.

David W. Spitzer, is a regular contributor to Flow Control. He has more than 30 years of experience in specifying, building, installing, startup and troubleshooting process control instrumentation. He has developed and taught seminars for over 20 years and is a member of ISA and belongs to the ASME MFC and ISO TC30 committees. Mr. Spitzer has written a number of books concerning the application and use of fluid handling technology, including the popular “Consumer Guide” series, which compares flowmeters by supplier. Mr. Spitzer is currently a principal in Spitzer and Boyes LLC, offering engineering, product development, marketing and distribution consulting for manufacturing and automation companies. He can be reached at 845 623-1830.

David W. Spitzer