See the attached file.
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, and 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.
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 This solution is FREE courtesy of BrainMass!
I have answered your question in the attached MS Word doc.
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 feet, after 2 hours the depth of water in the tank is 3 feet, and so on. After 9 hours the depth of water in the tank will be: (1.5 feet/hour)(9 hours) = 13.5 feet. Now assuming that the tank is big enough to hold all of this water we've got a "cylinder of water" inside of the water tank. The diameter of this "cylinder of water" is 180 feet and the height of this "cylinder of water" at 5 pm is 13.5 feet. With this information we can calculate the volume of water in this "cylinder of water" that is inside of the water tank from your formula:
Volume = (0.785)(Diameter2)(Height)
Since we were told that the diameter is 180 feet and we figured out that at 5 pm the height of the water inside of the water tank is 13.5 feet we may throw these numbers into the above equation to get that the volume of the water in the tank at 5 pm is: (0.785)(180 feet)2(13.5 feet) = 343359 feet3.
Now, if the problem had simply asked us to calculate the volume of water in the tank at 5 pm we'd be done, because feet3 is a volume measurement. But because the question asked how many millions of gallons of water were in the tank at 5 pm we're not done yet ... we must convert feet3 into gallons. As you pointed out above 1 cu. Ft. of water = 7.48 gallons of water, so:
(343359 cu. Ft. water)(7.48 gallons water/1 cu.ft water) = 2568325.32 gallons of water, which is 2.56832532 million gallons of water.
Since the problem asks you: "How many million gallons of water are in the tank at 5 PM if the diameter of the tank is 180 feet?", I don't see why you're trying to work the MGD (million gallons per day) into your answer ... you don't need it.
Setting all of this up as a dimensional analysis problem you'd have:
Vol. at 5 pm (in gallons)=(0.785)(180ft)2(1.5ft/hr)(9hr)(7.48gal/1cuft)=2,568,325.32 gals of water.© BrainMass Inc. brainmass.com December 24, 2021, 10:45 pm ad1c9bdddf>