Work done by gravity on fluid in u-tube.

In summary, the problem involves two cylinders with different heights of fluid that are joined together. The task is to find the work done by gravity on the fluid as it equalizes in height. Using Bernoulli's equation, gravitational potential energy, and the work-energy theorem, the work can be calculated by finding the change in potential energy of the mass of fluid and multiplying it by the height change. The correct answer can be obtained by multiplying the calculated value by the gravitational constant.
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Homework Statement



Two cylinders of base area 4cm2 hold fluid of density 1.30(103). In one the fluid has height .854 and the other has height 1.560. They are then joined and the fluids equalize in height--find the work done by gravity on the fluid.

Homework Equations



A version of Bernoulli's equation

[tex]p_0 + \rho g h = C[/tex]

Gravitational potential energy

[tex]U=mgh[/tex]

Work-energy theorem

[tex]W = \Delta U[/tex]

The Attempt at a Solution



So I know the fluids will come to rest at a height, in each cylinder, of [tex]\frac{1.560-.854}{2}m[/tex]. And effectively that means taking the top chuck of fluid from the taller cylinder and placing it on top of the fluid in the shorter one. I can find the volume of this chunk of water, it's just [tex]\frac{1.560-.854}{2}m\times 4cm^2 \times \left(\frac{m/100}{cm}\right)^2[/tex]. From that, together with density, I know how to find the mass.

I would think that, at this point, I just find the change in potential of the mass of fluid. The mass and gravitational constant are known. I would then just multiply by the height change, which is again [tex]\frac{1.560-.854}{2}m[/tex] and I should get the answer, no?

So I enter the following into my calculator: ((1.56-.854)/2)^2 * 4/(10^4) *1.3*10^3 and it gives me about 0.0648 when the answer in the back of the book is 0.6something.
 
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  • #2
Crap I just realized in my calculation I didn't include the gravitational constant. If I just take the answer I have an multiply by 9.8 it comes out correct.
 

1. What is work done by gravity on fluid in a u-tube?

Work done by gravity on fluid in a u-tube refers to the energy transferred to the fluid as it moves from one side of the u-tube to the other due to the force of gravity. This work is often used to measure the pressure difference between two points in the u-tube.

2. How is work done by gravity calculated in a u-tube?

The work done by gravity on fluid in a u-tube can be calculated by multiplying the change in height of the fluid by its mass and the acceleration due to gravity (W = mgh). This gives the amount of energy transferred to the fluid as it moves.

3. What factors affect the work done by gravity on fluid in a u-tube?

The work done by gravity on fluid in a u-tube is affected by the density of the fluid, the height difference between the two points in the u-tube, and the gravitational acceleration. Any changes in these factors will result in a change in the amount of work done by gravity on the fluid.

4. How is work done by gravity related to pressure in a u-tube?

The work done by gravity on fluid in a u-tube is directly related to the pressure difference between the two points in the u-tube. This is because the work done is equal to the pressure difference multiplied by the change in volume of the fluid (W = PΔV). As the pressure difference increases, the work done by gravity also increases.

5. Can work done by gravity on fluid in a u-tube be negative?

Yes, the work done by gravity on fluid in a u-tube can be negative. This occurs when the fluid moves from a higher point to a lower point in the u-tube, resulting in a decrease in gravitational potential energy. In this case, the work done by gravity is considered negative as the fluid is losing energy rather than gaining it.

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