David W. Spitzer, P.E.

To verify the approximate operation of a flowmeter, it may be desirable to calculate the amount of fluid in a vessel before and after fluid flows into (or out of) the vessel. Comparing the calculations with the totalized flow can provide a check on the performance of the flowmeter.

Consider checking a flowmeter that is piped to fill a sump measuring six feet long by nine feet wide and 12 feet deep. The liquid level is three feet before water is pumped into the sump. When pumping is complete, the liquid level is nine feet high. Approximately what flow should be totalized on the flowmeter?

A. 1,212
B. 1,818
C. 2,424
D. 3,635

Commentary
It should be understood that the validity of this checking technique is dependent upon liquid being only added to the sump. Any liquid that leaves the sump during this procedure will result in error because a lower-than-actual volume will be calculated.
To ensure there is no flow out of the sump, the sump should be checked for leaks and the sump pump should not be allowed to operate during the test period.
Before the water is added, the sump contains 6x9x3, or 162 cubic feet of water. After the water is added, the sump contains 6x9x9, or 486 cubic feet of water. The difference of 486-162, or 324 cubic feet of water was added to the sump. Because each cubic foot contains 7.48 gallons, a volume of 324 cubic feet contains 324×7.48, or 2,424 gallons (Answer C).

If this type of calculation is needed, you might consider using metric measurements. Consider a similar size sump measured to be two meters long by three meters wide and four meters high, with sump levels of one meter and three meters before and after filling, respectively. Before the water is added, the sump contains 2x3x1, or six cubic meters of water. After the water is added, the sump contains 2x3x3, or 18 cubic meters of water. The difference of 18-6, or 12 cubic meters of water was added to the sump. Because each cubic meter contains 1,000 liters, a volume of 18 cubic meters contains 18×1,000, or 18,000 liters.

The point of using metric measurements is not a preference of one over the other, but rather the ease with which some of the calculations are preformed — in particular, the conversion from volume to gallons or liters. And how much does the water in each of these examples weigh? To convert gallons to pounds, multiply by 8.34. To convert liters to kilograms, multiply by one. The latter is less taxing on my mind.