Work and Fluid Force, lifting water out of a triangular prism tank

In summary: Wand thats the same thing as finding the work done to get the infinitesimal volume to the required height
  • #1
schlynn
88
0

Homework Statement


A vertical cross section of a tank is shown. Assume the tank is 16 feet long and full of water. ([tex]\delta=62.4[/tex], and that the water is to be pumped to a height of 8 feet above the top of the tank. Find the work done in emptying the tank. The tank is a triangular prisim with base=5ft and height=8ft.

Homework Equations


Not sure that there are any.

The Attempt at a Solution


First, I am supposed to find the force of the water. It says to find the width as a function of the height, and the book is unclear how to do this very well. From what I can gather it's the height divided by half the base equals the distance to pump the water divided by W, W being the width. So I solved and got W=[tex]\frac{5}{2}-\frac{5}{16}y[/tex]. And then since work is force times height, you just multiply that by the distance it has to be lifted, that's 16-y. And that's your integrad, but you have a 16[tex]\delta[/tex] factor too, but you just bring that outside of your integral. After I simply the integrand and anti differentiate I got [tex]40y-\frac{15}{4}y^{2}+\frac{5}{48}y^{3}[/tex] evaluated from 0 to 8, again, with the factor of 16[tex]\delta[/tex]. Fundamental theorm it and I got 132787 rounded to the nearest whole number. The answer is wrong, and I'm fairly certain I know how to do all of this except finding the width as a function of the height. The book says it has to do with similar triangles. But I don't get what they are saying. Can someone shed some light on this for me?
 
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  • #2
how about using conservation of energy and consider the centre of mass's
 
  • #3
Because this is a calculus 2 class, not a physics class, I don't know how to do it that way. I know how to find the centroid of an area that has uniform density, but that's not how we are supposed to do it.
 
  • #4
ok well i would find w(h)

then infinetsimal vol element
dV = w(h).L.dh

think of the work dW required to get this infinitesimal element to teh reuired hieght and then integrate over h

its all the same thing though
 
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  • #5
That's what I'm having trouble with. I can't find the infitesimal volume, I can't get the width as a function of the height. Could you walk me through it?
 
  • #6
changed notation in last post

ok so you know
w(0) = 5
w(8) = 0

and as its a triangle, its width will vary linearly in between...

so basically you have two points (0,5) and (8,0) find the equation of the line that connects them, and that will be w(h)
 

1. How does lifting water out of a triangular prism tank relate to work and fluid force?

When lifting water out of a triangular prism tank, work is being done against the force of gravity. This requires energy to be exerted in order to overcome the weight of the water and the force of gravity, which is known as fluid force.

2. What factors affect the amount of work required to lift water out of a triangular prism tank?

The amount of work required to lift water out of a triangular prism tank is affected by the weight of the water, the height of the tank, and the force of gravity. The greater the weight and height of the water, the more work will be required.

3. How is the work done when lifting water out of a triangular prism tank calculated?

The work done when lifting water out of a triangular prism tank is calculated using the formula W = Fd, where W is work, F is force, and d is distance. In this case, the force is the weight of the water and the distance is the height of the tank.

4. Can the shape of the tank affect the amount of work required to lift water out of it?

Yes, the shape of the tank can affect the amount of work required to lift water out of it. A triangular prism tank has a smaller surface area compared to a rectangular tank, meaning there is less resistance against the water being lifted. This can result in less work being required.

5. Is there a more efficient way to lift water out of a triangular prism tank?

Yes, a more efficient way to lift water out of a triangular prism tank is by using a pump or other mechanical device. This reduces the amount of work required by using external energy to lift the water instead of relying solely on human effort.

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