Work in pumping water from a cylinder

[calc67x]

I've just started disk problems with work and I don't understand why these two problems are done differently.

Problem 1:
A vertical right circular cylindrical tank measures 18 ft high and 10 ft in diameter. It is full of oil weighing 57lb/ft^3. How much work does it take to pump the oil to the level at the top of the tank?

Answer: [0,18] 57 (25pi)(y) dy =725,236.664 ft-lb

Problem 2:
Find the work done by pumping out water from the top of a cylindrical tank 3 ft in radius and 10 ft tall. if the tank is initially full. Density of water=62.4 lb/ft^3

Answer:

[0,10] (62.4) (pi*3^2)(10-x) = 8.82 *10^4 ft-lb

My question is why does the first problem not have (18-y) instead of just y?
The second problem is almost exactly the same, and it has (10-x) for the height. Not sure why the book has only "y" in the first problem set up - I would assume it would be (18-y). Am I missing something here?

 

[Dr.Peterson]

I've just started disk problems with work and I don't understand why these two problems are done differently.

Problem 1:
A vertical right circular cylindrical tank measures 18 ft high and 10 ft in diameter. It is full of oil weighing 57lb/ft^3. How much work does it take to pump the oil to the level at the top of the tank?

Answer: [0,18] 57 (25pi)(y) dy =725,236.664 ft-lb

Problem 2:
Find the work done by pumping out water from the top of a cylindrical tank 3 ft in radius and 10 ft tall. if the tank is initially full. Density of water=62.4 lb/ft^3

Answer:

[0,10] (62.4) (pi*3^2)(10-x) = 8.82 *10^4 ft-lb

My question is why does the first problem not have (18-y) instead of just y?
The second problem is almost exactly the same, and it has (10-x) for the height. Not sure why the book has only "y" in the first problem set up - I would assume it would be (18-y). Am I missing something here?

An equation has no meaning until the variables are defined. You haven't stated the definitions of x and y.

I think you will find that in the first, y is defined as the distance from the top (which is therefore how far a given slice is moved), whereas x in the second is defined as the distance from the bottom (so that the distance a slice is moved is 10-x).

Always read the entire thing, including the variable definitions, which are an essential part of the work.

 

[calc67x]

An equation has no meaning until the variables are defined. You haven't stated the definitions of x and y.

I think you will find that in the first, y is defined as the distance from the top (which is therefore how far a given slice is moved), whereas x in the second is defined as the distance from the bottom (so that the distance a slice is moved is 10-x).

Always read the entire thing, including the variable definitions, which are an essential part of the work.

I think this may explain what's going on. The book was not kind enough in the first example to provide a picture and just gave a bare bones answer. Would the second question mean that the water goes 10 feet before it is pumped out and the first question mean that the water really does not have to move 10 feet as it is already at the top?

 

[Dr.Peterson]

I think this may explain what's going on. The book was not kind enough in the first example to provide a picture and just gave a bare bones answer. Would the second question mean that the water goes 10 feet before it is pumped out and the first question mean that the water really does not have to move 10 feet as it is already at the top?

No -- not all the water is at the top, is it?

Do you follow what I said about what x means in the second example? Water at the bottom (x=0) has to move 10 feet (10-0), while water at the top (x=10) has to move 0 feet (10-10). In the first, y is the distance any portion of water has to move.

If the book doesn't even tell you what the variable means (in words, if not in a picture), then it is not very well written. Does it? Are you implying that there is a picture for the second? And are these really from the same book?

 

[calc67x]

No -- not all the water is at the top, is it?

Do you follow what I said about what x means in the second example? Water at the bottom (x=0) has to move 10 feet (10-0), while water at the top (x=10) has to move 0 feet (10-10). In the first, y is the distance any portion of water has to move.

If the book doesn't even tell you what the variable means (in words, if not in a picture), then it is not very well written. Does it? Are you implying that there is a picture for the second? And are these really from the same book?

No, you're right they are not from the same book. There is a picture for the second question, the one that uses (10-x).
I think you've explained it pretty well, though, thanks for the help!

 

[Steven G]

No, you're right they are not from the same book. There is a picture for the second question, the one that uses (10-x).
I think you've explained it pretty well, though, thanks for the help!

Always draw the picture (if not given) and KNOW what the variables mean. It is so easy to do once you know what your variable means!