Question

In: Physics

2 cylinders are connected by a horizontal tube at the bottom of each cylinder. Cylinder A...

2 cylinders are connected by a horizontal tube at the bottom of each cylinder. Cylinder A has an internal diameter of 0.50
m, while Cylinder B has a diameter of 1.50 m. Both are the same height (2.0 m) are filled halfway with oil (density of
700. kg/m3). Both are topped by a thin metal seal that is free move up and down and can be considered massless.
a. What is absolute pressure at 0.20 m from the bottom in Cylinder A?
b. What is the gauge pressure at that level in Cylinder B?

c. A 2.0 kg mass is placed on top of Cylinder A. What mass must be placed on Cylinder B to balance?

Expert Solution

Part A

The pressure at that depth will be given by

where is the depth from the surface of the liquid.

The liquid is filled upto .

Thus,

Therefore,

Part B

From the formula for pressure at a depth, it does not depend on the surface area of the vessel.

Therefore, in this cases also.

Part C

Since fluids are incompressible, the pressure change at one point is transmitted to all points in the fluid. This is called Pascal's Law. It can be stated here as

The force is due to the mass placed and is equal to

Now we can find the other mass required.

Solving for , we get

We can also solve this by realizing that since pressure varies inversely with area, it varies inversely to the square of the diameter.

genius_generous answered 8 months ago

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