The Black Magic of Water
by David Orient
Water Plant Operator fot the City of Grand Junction
I came across this math problem in the last edition of the Opflow publication. The level in a storage tank (c1earwell) rises 3.1 ft. in 45 hrs. If the tank has a diameter of 225 ft. and the plant is producing 32.4 mgd, what is the average discharge rate of the treated water discharge pumps in gallons per minute?
a. 3,408 gpm
b. 15,336 gpm
c. 19,100gpm
d. 22,518 gpm
I hate this problem. No, I love this problem. I tried working this annoying question out, but I did not come up with any of their answers.
I thought great, I can call up Opflow and chuckle at them for not publishing the right answer. Before that though I asked one of my fellow operators to give it a try. He worked it and came up with a different answer than mine, but not one of the listed ones either. I thought maybe there is no right answer to this problem. It might be like infinity, it just keeps going and going. This is a great example of why operator exams are hard. This is not a terribly hard question, but it is confusing. The certification exam makers have a knack for that. The key to this question is to read it right and understand what they are asking for. I wasn't reading it right. I was reading that the tank rose from 3.1ft. to 45ft. in 45 hrs. When you don't read a problem right you tend to get the wrong answer. I always thought math to be an exact science. Sometimes your brain gets in the way. So, do you want to know the right answer? Me too.
This plant is producing more water than it is sending to town, hence the level going up in the tank. They want to know the average rate going to town per minute.They told us the plant is producing 32.4 mgd so let's get that to a minute's worth.
32,400,000 gallons 1,440 minutes per day = 22,518 gpm
Some water is going in the tank so we need to subtract that amount. The formula is (0.785) X (diameter2) X (depth of water rise) X (gallons in a cubic foot) or (0.785) X (2252) X (3.1) X (7.48) = (0.785) X (50,625) X (3.1) X (7.48) = 921,506 gallons in 4.5 hours.
Remember we also need to get this answer to a minute's worth of water.
921,506 and 270 minutes = 3,413 gpm
22,518gpm, 3,413gpm, 19,105gpm
I would choose answer c. They are off by 5 gallons. Maybe I'll still call Opflow and tell them they didn't get the right answer.