Question

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.

Determine the pressure at the various surfaces.

For a surface open to the air, p0=patmos, usually 1 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.

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

Allow for gauge pressure. Pressure gauges read pg=p−1atm.

Use the hydrostatic pressure equation: p=p0+ρgh, 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 1.36×10⁴kg/m3 . When the liquid in the tube reaches static equilibrium, the mercury column is h1 = 16.0 cm high in the left arm and h2 = 5.00 cm high in the right arm, as shown in the figure.(Figure 1) What is the gas pressure pgas inside the box?

Part C

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

Express your answer in pascals to three significant figures.

Answer 1

Here

P_a=P_gas

P_b=P_atmos

since

P_a=P_gas=P_atm-pg(h₁-h₂)

Gas pressure inside the box

P_gas=101325-(1.36*10⁴)(9.81)(0.16-0.05)

P_gas=8.66*10⁴ pa