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Basic Water Distribution Math for Water Distribution Operator Certificate

I'm taking a Water Supply Technology math class to get a Water Distribution Operator Certificate.
We are covering Volume of Rectangular and Cylindrical Tanks, Pipelines, abd Rectangular Channels.
We have not covered things like flow rate as it relates to time as in detention time. We are not there yet. We are using dimensional analysis.

Problem 24:
A tank is filled at the rate of 1-foot 6-inches per hour. The tank is empty at 8 AM. How many million gallons of water are in the tank at 5 PM if the diameter of the tank is 180 feet?

We have been using a Volume of a cylinder formula:
V = .785 x Diameter (squared) x H x 7.48 gals. I know Height aka Depth
1 cu. ft. = 7.48 gallons water
I understand .785 x Diameter (squared) x H gives the Volume only.
I know by multiplying the resulting Volume (cubic Ft) answer x 7.48 gals gives gallons of water in that tank. Please see the attachment of water math conversions and a box method (2 pg. doc).

Known: Rate is 1-ft 6-inches per hr = 1.5 feet Unknown: Problem asks for how many MGD
8AM to 5PM = 9 hours in tank
Diameter = 180 feet

I have been trying to do dimensional analysis to go from 1.50 ft./hr x 1 hr/60 min x 540 min/9 hrs x
1 ft/12 in x 1728 cu. in./1 cu. ft.

I am trying to use 1 cu. ft = 7.48 gals. I understand I want gallons to be in the numerator and I need "day" to be in the denominator. Am I going too long with this conversion? There is an equivalency of 1 MGD = 694.4 gpm. Do I use this?
Do I use 1 gpm = 1440 gpd? How? Do I use 60 mins = hour? How do I set up the dimensional analysis for this problem?


Solution Preview

I have answered your question in the attached MS Word doc. I hope this helps. Good luck.

Okay, since you know that the water tank (which we'll assume is cylindrical, even though it doesn't state that anywhere in the problem) is being filled at the rate of 1.5 feet per hour and that the tank is empty at 8 am (when we presumably "open the faucet" and start to fill the tank at the rate of 1.5 feet per hour), at 5 pm we have been filling the tank for 9 hours. The "1.5 feet per hour" is a measure of how the depth is changing over time ... after 1 hour the depth of the water in the tank is 1.5 ...

Solution Summary

The basic water distribution math for water distribution operator certificate is examined.