Fluid Pressure in a U-Tube

Fluid Pressure in a U-Tube

A U-tube is filled with water, and the two arms are capped.(Figure 1) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube.

PART A

A one-inch depth of sand is poured onto the cap on each arm. (Figure 2) After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap?

ANSWER = the same height

PART B

The sand is removed and a 1.0-kg-mass block is placed on each cap. (Figure 3) After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap?

ANSWER = higher

PART C

If a 1.0-kg-mass block is on the left cap, how much total mass must be placed on the right cap so that the caps equilibrate at equal height?

ANSWER = 4.0

PART D

The locations of the two caps at equilibrium are now as given in this figure. (Figure 4) The dashed line represents the level of the water in the left arm.

What is the mass of the water located in the right arm between the dashed line and the right cap?

ANSWER = 3.0