Find Work: Empty 6ft Hemisphere Tank of Oil (50lb/ft^3)

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In summary, to find the work done in emptying a tank containing oil, the tank must be divided into horizontal slices and the energy needed to raise each slice to a height of 7 feet must be calculated and integrated over the height of the tank. The size of each slice will vary depending on the height, requiring further calculations.
  • #1
idle_09
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Find the work done in emptying a tank containing oil if the tank is hemisphere with a diameter of 6 feet. The tank is full and the density of the oil is 50lb/ft^3. The oil is raised to a point 4 ft about the top of the tank. Thank you for helping. I have no idea how to start.
 
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Hi idle_09! :smile:
idle_09 said:
Find the work done in emptying a tank containing oil if the tank is hemisphere with a diameter of 6 feet. The tank is full and the density of the oil is 50lb/ft^3. The oil is raised to a point 4 ft about the top of the tank. Thank you for helping. I have no idea how to start.

(i assume you mean "4 ft above …"?)

work done = change in energy (that's the work-energy theorem) …

so divide the tank into horizontal slices of thickness dz, calculate the mass of each slice, how much energy is needed to raise it to z = 7, and integrate over z. :wink:
 
  • #3
you'll have to find the size of a slice of the hemisphere as a function of z... just figured I'd throw that hint out there.
 

Related to Find Work: Empty 6ft Hemisphere Tank of Oil (50lb/ft^3)

1. What is the purpose of emptying the 6ft hemisphere tank of oil?

The purpose of emptying the 6ft hemisphere tank of oil is to remove the oil from the tank in order to clean or repair the tank, or to repurpose the tank for a different use.

2. How much does the oil in the tank weigh?

The oil in the tank weighs 50 pounds per cubic foot. This means that the total weight of the oil in the tank will depend on the volume of the tank.

3. What is the capacity of the 6ft hemisphere tank?

The capacity of the 6ft hemisphere tank can be calculated using the formula for the volume of a hemisphere: V = (2/3)πr^3, where r is the radius of the tank. The capacity will vary depending on the thickness of the tank walls, but on average, a 6ft hemisphere tank can hold approximately 56 cubic feet of oil.

4. What equipment is needed to empty the tank of oil?

In order to empty the tank of oil, you will need a pump, hoses, and a container to collect the oil. You may also need safety equipment, such as gloves and goggles, to protect yourself while handling the oil.

5. How long will it take to empty the tank of oil?

The time it takes to empty the tank of oil will depend on the capacity of the tank and the flow rate of the pump being used. On average, it can take anywhere from 30 minutes to several hours to empty a 6ft hemisphere tank of oil.

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