Revolving a tank around the y axis: Work needed to pump water

In summary, a tank is formed by revolving y=3x^2, x=[0,2] around the y-axis is filled to the 4 feet point with water (w=62.4 lb/ft^3). Find the work necessary to pump the water out of the tank over the top.
  • #1
think4432
62
0
1. A tank is formed by revolving y = 3x^2, x = [0,2] around the y-axis is filled to the 4 feet point with water (w = 62.4 lb/ft^3). Find the work necessary to pump the water out of the tank over the top.

I got the integral being from a = 0 and b = 4 and integrating [(12y-y^2)/3]dy with w and pi as constants outside of the integral.

And after the integration I got:

224/9 pi (62.4)

And when I multiplied the 62.4 out it came out to be 1553.066 pi

Would this be correct? Just seems bit of a weird number?

[I asked this question earlier...and received help on it on an earlier thread, but I just wanted to see if the numbers I got are correct]
 
Physics news on Phys.org
  • #2
At each y, the figure rotated around the y-axis is a disk or radius [itex]x= (y/3)^{1/2}[/itex] and so has area [itex]\pi x^2= (\pi/3)y[/itex] and a very thin disk of thickness dy would have volume [itex](\pi/3)y dy[/itex].

The weight of that disk is [itex](\pi w/3)y dy[/itex] and must be lifted the remaining 12- y feet so the work done in lifting just that disk is (force times distance) [itex](\pi w/3) y(12- y)dy[/itex].

Integrate that from y= 0 to y= 4- that appears to be exactly what you have done!:wink:
 
  • #3
HallsofIvy said:
At each y, the figure rotated around the y-axis is a disk or radius [itex]x= (y/3)^{1/2}[/itex] and so has area [itex]\pi x^2= (\pi/3)y[/itex] and a very thin disk of thickness dy would have volume [itex](\pi/3)y dy[/itex].

The weight of that disk is [itex](\pi w/3)y dy[/itex] and must be lifted the remaining 12- y feet so the work done in lifting just that disk is (force times distance) [itex](\pi w/3) y(12- y)dy[/itex].

Integrate that from y= 0 to y= 4- that appears to be exactly what you have done!:wink:

Wow. Ok.

Thanks! The number just seems really weird! Haha.

Thats all!

Thanks though! :]
 

1. How is the work needed to pump water in a revolving tank around the y axis calculated?

The work needed to pump water in a revolving tank around the y axis is calculated by multiplying the force needed to pump the water by the distance the water is pumped. This can be expressed as W = F x d, where W is work, F is force, and d is distance.

2. What factors affect the amount of work needed to pump water in a revolving tank?

The amount of work needed to pump water in a revolving tank is affected by the weight of the water, the height of the tank, the speed at which the tank is revolving, and the viscosity of the water. These factors impact the force needed to pump the water and the distance it is pumped.

3. How does the shape of the tank impact the work needed to pump water in a revolving tank?

The shape of the tank does not have a significant impact on the work needed to pump water in a revolving tank. As long as the tank is revolving around the y axis, the same amount of work will be needed regardless of its shape.

4. Is the work needed to pump water in a revolving tank different if the tank is stationary?

Yes, the work needed to pump water in a stationary tank is different from a revolving tank. This is because in a stationary tank, the force needed to pump the water is only dependent on the weight of the water, while in a revolving tank, it is also dependent on the speed of the tank's rotation.

5. Can the work needed to pump water in a revolving tank be reduced?

Yes, the work needed to pump water in a revolving tank can be reduced by increasing the speed of the tank's rotation. This reduces the distance the water needs to be pumped, therefore reducing the overall work needed. However, increasing the speed too much can also increase the force needed to pump the water, balancing out the reduction in work.

Similar threads

Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
10
Views
948
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
917
  • Calculus and Beyond Homework Help
Replies
6
Views
3K
  • Calculus and Beyond Homework Help
Replies
1
Views
889
  • Calculus and Beyond Homework Help
3
Replies
77
Views
13K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Back
Top