Pumping a Cylindrical Storage Tank (different variables)

[dudicuff]

Homework Statement

A cylindrical storage tank 8 feet in diameter and 20 feet long is lying horizontally on the ground. The tank is full of olive oil whose weight density is 57 lb/ft^3. How much work does it take to pump the olive oil to a level of 6 feet above the top of the tank?

Almost identical to one posted a while ago.

Homework Equations

V = 20 * 2x

$$\int$$ [from -4 to 4] 20 * 2 * 57 * (14 - y) * ($$\sqrt{}16 - y^2$$) dy

The Attempt at a Solution

Cranked it out and got 255360 pi -97280 ft - lbs
or 704957 ft - lbs


I think this is right, but an affirmative by a few more people would be a great help.

 

[Defennder]

Does "lying horizontally" mean that the cylindrical tank is lying on its curved surface?

 

[dudicuff]

No, actually it means it is lying on the side that is 20ft. I think I got the answer, though. I needed to do my distance from (10 - y) because the origin is in the middle.

 

[Defennder]

Ok this is confusing. Isn't the 20ft a measurement of the height of the tank? And if it is lying down on that side, wouldn't it be lying on the curved surface? Another (quite unlikely) possibility would be that it is somehow balanced on its curved edge.

 

[HallsofIvy]

Does "lying horizontally" mean that the cylindrical tank is lying on its curved surface?

No, actually it means it is lying on the side that is 20ft. I think I got the answer, though. I needed to do my distance from (10 - y) because the origin is in the middle.

The "side that is 20 ft" is the curved side! You meant "yes".

Ok this is confusing. Isn't the 20ft a measurement of the height of the tank? And if it is lying down on that side, wouldn't it be lying on the curved surface? Another (quite unlikely) possibility would be that it is somehow balanced on its curved edge.

Why is that "quite unlikely"? That's the way small fuel tanks are normally positioned.

 

[dudicuff]

Here's a picture to clarify:

_
l`````````l.l
6ft```````l.l`<- Spout for pump.
l`````````l.l
_
l````````` ___``_______________________________
l````````/...\ ----------------------------------\
l```````/....\----------------------------------\
l``````/....\---------------------------------\
8 ft```l......l---------------------------------l
l``````\...../---------------------------------/
l```````\.../---------------------------------/
l````````\...___.../_____________________________/
l
_```````````````l------------- 20 ft ---------------l

Lying horizontally on the side that is 20 ft.

 

[HallsofIvy]

A "layer" of water at a given height is a rectangle. The length of that rectangle is 20 ft. The width depends upon the height.

 

[viciousp]

I didn't do the problem but by the setup it seems correct.