Explain the logic behind using millimeters to measure pressure. In order to measure the pressure of a gas using a manometer, you open one end of the sealed tube to allow the gas to flow into it. You gauge the pressures of different gases against one another by how many millimeters the mercury rises. Therefore, scientists calibrate manometers in millimeters of mercury -- or, sometimes, "Torrs."
Relate pressure to force using Newton's Second Law, F = mg, where "m" is mass and "g" is the acceleration of gravity. Explain that one Pascal (the international scientific unit for pressure) is equal to one Newton (the international scientific unit for force) per meter squared (the international scientific unit for area), so you can think of pressure as the force spread over an area. In mathematical terms: P = F/A and F = mg, so P = mg/A, where "m" is the mass of mercury that rises over "A," the cross-sectional area of the tube.
Represent the mass of mercury as a product of its density and volume. Rearrange the common physics equation d = m/v, where "d" is density, "m" is mass and "v" is volume by multiplying both sides by "v" as follows: d x v = (m/v) x v, or dv = m or, for simplicity's sake, m = dv. Substitute "dv" for mass in the equation P = mg/A to get P = dvg/A.
Simplify the equation to show that the height of mercury in the column is directly proportionate to the pressure, which is why a rise in mercury corresponds to a rise in pressure. Remind your students or peers that the volume of a cylinder is equal to its cross-section area times its height and rewrite the equation to reflect this as follows: P = dmg/A = d(h x A)g/A. Note that the "A" on top cancels the "A" on bottom, leaving you with the equation P = dhg -- pressure is equal to density times height times the acceleration of gravity. Remind your students that since both the density of mercury and the acceleration of gravity are static values, the height of mercury in the column will always directly relate to the pressure.