Question

± Tactics Box 14.1 Hydrostatics 

Learning Goal:

To practice Tactics Box 14.1 Hydrostatics.

In problems about liquids in hydrostatic equilibrium, you often need to find the pressure at some point in the liquid. This Tactics Box outlines a set of rules for thinking about such hydrostatic problems.

TACTICS EOX 14+ Hydrostatics

1. Draw a picture. Show open surfaces, pistons, boundaries, and other features that affect the pressure. Include height and area measurements and fluid densities. identify the points at which you need to find the pressure. These objects make up the system, the environment is everything else.

2. Determine the pressure at the various surfaces.

- For a surtace open to the air, P₀= Patoon. usually t  atm.

- For a surface covered by a gas, P0 = Pgas.

- For a closed surface, p=F / A, where F is the force the surface, such as a piston, exerts on the fluid and A is the area of the surface.

3. Use horizontal lines. Pressure in a connected fluid is the same at any point along a horizontal line.

4. Alow for gauge pressure. Pressure gauges read Pk=P-1 atm.

5. Use the hydrostatic pressure equation p=p₀+pgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid.

Use these rules to work out the following problem: A U-shaped tube is connected to a box at one end and open to the air at the other end. The box is full of gas at pressure Pgas, and the tube is filled with mercury of density 1.36 k 10⁴ kg / m³. When the liquid in the tube reaches static equilibrium, the mercury column is h₁=12.5 cm high in the lest arm and h₂=5.50 cm high in the right arm, as shown in the figure.(Figure 1) What is the gas pressure Pgas inside the box?

- Part A

Find the pressures pA and pB at surfaces A and B in the tube, respectively. Use patmen to denote atmospheric pressure.

- Part C

Assume patem=1.00 atm. What is the gas pressure pgas ?

Express your answer in pascals to three significant figures.

Answer 1