work with cylindrical tank

• May 10th 2009, 07:10 PM
linlinrocks
work with cylindrical tank
A right cylindrical tank is filled with sea water. The tank has a radius of 6 feet and a height of 12 feet. If the water level is now 3 feet below the top of the tank, how much work will be required to pump the sea water to the top of the tank? (The weight-density of seawater is 64 lb/ft^3)

I have

r=6 ft, and h=12ft
so far my equation is like this
W= pi (6)^2 (64)y
• May 11th 2009, 09:40 AM
Calculus26
See attachment

For a general discussion of tank problems you might want to check out

Work
• May 11th 2009, 11:38 AM
skeeter
Quote:

Originally Posted by linlinrocks
A right cylindrical tank is filled with sea water. The tank has a radius of 6 feet and a height of 12 feet. If the water level is now 3 feet below the top of the tank, how much work will be required to pump the sea water to the top of the tank? (The weight-density of seawater is 64 lb/ft^3)

I have

r=6 ft, and h=12ft
so far my equation is like this
W= pi (6)^2 (64)y

work = $\displaystyle \int WALT$

W = weight density
A = cross-sectional area of a representative horizontal "slice" of liquid (in terms of y if variable)
L = amount of lift in terms of y for a representative horizontal "slice" of liquid
T = "slice" thickness ... dy

work = $\displaystyle \int_0^9 64 \cdot 36\pi \cdot (12-y) \, dy$