Calculating Work for Pumping Liquid in a Vertical Cylindrical Tank

[whatlifeforme]

Homework Statement

A vertical right circular cylindrical tank measures 32 feet high and 8 feet in diameter. It is full of liquid weighing 62.4 lb / ft^3 How much work does it take to pump the liquid to the level of the top of the tank?

Homework Equations

h=32
d=8 (radius = 4)
liquid weight = 62.4 lb / ft^3

The Attempt at a Solution

1. integral (0 to 32) (62.4x) dx
2. (156/5)x^2 | (0 to 32)
3. answer: 31,948.8

actual correct answer: 1,605,922 ft-lb

 

[Mark44]

Homework Statement

A vertical right circular cylindrical tank measures 32 feet high and 8 feet in diameter. It is full of liquid weighing 62.4 lb / ft^3 How much work does it take to pump the liquid to the level of the top of the tank?

Homework Equations

h=32
d=8 (radius = 4)
liquid weight = 62.4 lb / ft^3

The Attempt at a Solution

1. integral (0 to 32) (62.4x) dx

This (above) is way off.

Have you drawn a sketch of a typical "layer" of water? Each of the layers has the same volume, and hence the same weight, but a layer at the bottom of the tank has to be lifted all the way to the top, while the layer at the top doesn't have to be lifted at all.

I don't see any accounting for this in your work.

2. (156/5)x^2 | (0 to 32)
3. answer: 31,948.8

actual correct answer: 1,605,922 ft-lb

 

[tiny-tim]

hi whatlifeforme!

ok-ish, but you haven't used the area of the cylinder!