Calculating Work for Buried Gas Tank

In summary, the conversation discusses finding the amount of work needed to pump all the gasoline in a buried cylindrical tank to a nozzle 3 ft above the ground. It involves setting up a cylinder with a specified radius and using the weight of each strip, the distance it needs to travel, and the volume of the strips to calculate the total amount of work. The width of the strips is found to be 2√(16-y^2) and the integral is integrated from y=-4 to 4.
  • #1
Sheneron
360
0

Homework Statement


A cylindrical gasoline tank with radius 4ft and length 15 ft is buried under a service station. The top of the tank is 10ft underground. Find the amount of work needed to pump all the gasoline in the tank to a nozzle 3 ft above the ground. Gasoline weighs 42lb/ft^3.

The Attempt at a Solution



So the way I have started is by setting a cylinder with the specified radius centered at (0,0). With that I know the top is at (0,4), bottom is at (0,-4) and the place it needs to reach is y = 17 (13ft above the top of the cylinder).

I divide the cylinder into strips of thickness delta y. So I know I need to find the weight of each of those strips and multiply it by the distance it must travel (17-y).

I have the density so I really now just need the volume of those strips. Volume = length * width * thickness. I have the thickness (delta y), the length (15), but I need the width.

I can't figure out how to find the width of the strips. I know that at y = 0 the width is 8 and at y=4 and y = -4 the width is 0.

Something like
[tex] width = 2\sqrt{16-y^2}[/tex]
would tell me the width with respect to y, but that would only be true from y=-4 to y=4, and it needs to stop after that.

Any advice would be appreciated thanks.
 
Physics news on Phys.org
  • #2
Wait tell me if this would work:

[tex]width = 2\sqrt{16-y^2}[/tex]
[tex]thickness = \Delta(y)[/tex]
[tex]length = 15[/tex]

[tex]weight = 2\sqrt{16-y^2} * \Delta(y) * 15 * 42[/tex]

and the height = 17 - y
so the integral would be:

[tex]\int_{-4}^{4} 1260\sqrt{16-y^2}(y-17) dy[/tex]
 
  • #3
One important thing you did not specify: is the axis of the cylinder vertical or horizontal? You seem to be assuming it is horizontal. If so then, yes, [itex]width= \sqrt{16- y^2}[/itex]. You will only be integrating from y= -4 to 4 so the fact that it "has to stop at 4" is irrelevant. Looks to me like your final integral is correct.
 

1. How do you calculate the volume of a buried gas tank?

To calculate the volume of a buried gas tank, you will need the dimensions of the tank, typically its length, width, and height. You can then use the formula for the volume of a rectangular prism, which is length x width x height. If the tank is cylindrical, you can use the formula for the volume of a cylinder, which is π x radius^2 x height.

2. What is the importance of calculating the volume of a buried gas tank?

Calculating the volume of a buried gas tank is important for various reasons. It helps determine the amount of gas the tank can hold, which is crucial for planning and safety purposes. It also allows for accurate measurements of gas levels and potential leaks, as well as proper maintenance and replacement of the tank if needed.

3. How do you convert the volume of a buried gas tank to gallons?

To convert the volume of a buried gas tank to gallons, you will need to know the conversion factor for the unit of measurement used for the volume. For example, if the volume is given in cubic meters, you can use the conversion factor of 1 cubic meter = 264.172 gallons. Multiply the volume in cubic meters by the conversion factor to get the volume in gallons.

4. Can you calculate the volume of a buried gas tank without knowing its dimensions?

No, it is not possible to accurately calculate the volume of a buried gas tank without knowing its dimensions. The dimensions are necessary in order to use the appropriate formula for calculating volume. If the dimensions are unknown, it is important to measure or obtain them in order to calculate the volume accurately.

5. Are there any safety precautions to consider when calculating the volume of a buried gas tank?

Yes, there are several safety precautions to consider when calculating the volume of a buried gas tank. The tank should be properly marked and located before any measurements are taken. It is also important to follow safety protocols and regulations for handling and working with gas tanks. If there are any signs of damage or leaks, it is important to contact a professional for assistance.

Similar threads

  • Calculus and Beyond Homework Help
Replies
10
Views
948
  • Calculus and Beyond Homework Help
Replies
1
Views
6K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
Replies
1
Views
2K
  • Mechanical Engineering
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Mechanical Engineering
Replies
3
Views
895
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
4K
  • Calculus and Beyond Homework Help
Replies
1
Views
5K
Back
Top