Work required to fill a conical tank

In summary, the conversation discusses finding the work required to pump all the water out of a right circular conical tank that is filled with water to a height of 2 feet. The tank has a height of 3 feet and a radius of 1 foot at the top. Similar triangles are used to set up the problem and the weight of water is given as 62.5 lb/ft^3. The incremental work is calculated by multiplying the weight of a typical volume element by the distance it has to be raised. The limits of integration are determined by the range of \Delta y.
  • #1
nameVoid
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A right circular conical tank of height 3 feet and radius 1 foot at the top is filled with water to a height of 2 feet. Find the work required to pump all the water up and over the top of the tank.

similar triangles : x=y/3

water 62.5 lb/ft^3

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?? am i setting this up right
 
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  • #2


Please show us how you set it up so that we can check your work. What is the weight of a typical volume element? The incremental work, [itex]\Delta W[/itex], is the weight of a typical volume element times the distance it has to be raised. Finally, the limits of integration will be the interval over which [itex]\Delta y[/itex] ranges.
 

What is the formula for calculating the work required to fill a conical tank?

The formula for calculating the work required to fill a conical tank is W = (πr²hρg)/3, where W is the work required, r is the radius of the tank, h is the height of the tank, ρ is the density of the liquid being filled, and g is the acceleration due to gravity.

How do I determine the radius and height of a conical tank for the calculation?

To determine the radius and height of a conical tank, you will need to measure the diameter and height of the tank. Then, divide the diameter by 2 to get the radius. The height will be the vertical distance from the base of the tank to the top.

What units should be used in the calculation for work required to fill a conical tank?

The units used for the calculation of work required to fill a conical tank will depend on the units used for the other variables in the formula. However, it is important to ensure that all units are consistent, such as using meters for length and kilograms per cubic meter for density.

Can the formula for work required to fill a conical tank be used for any liquid?

Yes, the formula for work required to fill a conical tank can be used for any liquid, as long as the density of the liquid is known. The formula takes into account the density of the liquid in the calculation, making it applicable for any type of liquid.

Is there a way to reduce the work required to fill a conical tank?

Yes, there are a few ways to reduce the work required to fill a conical tank. One way is to decrease the height of the tank, as this will decrease the amount of liquid that needs to be lifted. Another way is to increase the radius of the tank, as this will spread out the weight of the liquid over a larger area, reducing the overall force needed to lift it. Additionally, using a liquid with a lower density can also decrease the work required.

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