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.
draw a picture.
1. show open surfaces, pistons, boundaries, and other features that affect 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 p0 at surfaces.• surface open to the air: p0=patmos, usually 1 atm. • surface in contact with a gas: p0=pgas. • closed surface: p0=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. the pressure in a connected fluid (of one kind) is the same at any point along a horizontal line.
4. allow for gauge pressure. pressure gauges read pg=p? 1atm.
5. use the hydrostatic pressure equation: p=p0+? gh, where ? 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 1.36×104 kg/m3 . when the liquid in the tube reaches static equilibrium, the mercury column is h1 = 11.0 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?