Work done by gravity on fluid in u-tube.

[Addem]

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

p_0 + \rho g h = C

Gravitational potential energy

U=mgh

Work-energy theorem

W = \Delta U

The Attempt at a Solution

So I know the fluids will come to rest at a height, in each cylinder, of \frac{1.560-.854}{2}m. 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 \frac{1.560-.854}{2}m\times 4cm^2 \times \left(\frac{m/100}{cm}\right)^2. 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 \frac{1.560-.854}{2}m 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.

 

[Addem]

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.