SOLUTION: Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water. a) What is

Question 956018: Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a) What is the volume, in cubic inches, of water flowing out of the pipe every second?
b) What is the height, in inches, of the water in the tank after 5 minutes?
c) How many minutes will it take to fill 75% of the tank?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Water flows at 2 feet per second through a pipe with a diameter of 8 inches.
A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a) What is the volume, in cubic inches, of water flowing out of the pipe every second?
The volume of water is in the shape of a cylinder 24" long (2 ft), 4 in radius ( half the diameter)

V = 1206.37 cu/in/sec
:
b) What is the height, in inches, of the water in the tank after 5 minutes?
Radius of the tank is 7.5 ft, change to inches 7.5(12) = 90 inches
Find how much water flows in 5 min: 1206.37 * 5 * 60 = 361911 cu/inches
let h = the height of of the water after 5 min

h = 14.22 inches
:
c) How many minutes will it take to fill 75% of the tank?
Find the volume of 75% of the tank (6' = 72")
= 1374132.63 cu/in
Find how many seconds to obtain this amt of water
= 1139.064 seconds
Change this to minutes
= 18.98 ~ 19 minutes to fill 3/4 of the tank
:
------------------------------------------------------------------------
I am ashamed to say we could have done this last question much easier.
The amt of water varies directly with the height
3/4 of the height of the tank = .75(72) = 54 inches
A simple ratio equation, let t = time for fill it 3/4 full
=
Cross multiply
14.22t = 5 * 54
14.22t = 270
t = 270/14.22
t = 18.98 the same answer we got with all that tedius calculating.
:
What do you think of that?
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