Pressure in Solids and Liquids
Senior 2 · Physics
Pressure in Solids and Liquids
Lesson 4 of 5
22 min
Let's begin
We live at the bottom of an ocean of air. The atmosphere presses on everything, about 101 000 N on every square metre at sea level, yet we hardly notice. Weather forecasters, pilots and gas engineers all need to measure pressure. The two classic instruments, the mercury barometer and the U-tube manometer, both use the rule P = hρg that you already know.
A barometer measures atmospheric pressure. To make a simple mercury barometer:
The air pressing on the mercury in the dish holds the column up. With a vacuum above the column, nothing presses down on its top, so:
atmospheric pressure = hρg (h = vertical height of the mercury column)
At sea level a mercury barometer reads 760 mm. Find the atmospheric pressure (ρHg = 13 600 kg/m³, g = 9.8 m/s²).
P = 0.760 × 13 600 × 9.8 = 101 293 Pa ≈ 1.01 × 10⁵ Pa.
In Kigali, which is about 1 500 m above sea level, there is less air above you. The atmospheric pressure is only about 84 kPa, and a mercury barometer stands at roughly 630 mm.
A manometer measures the pressure of a gas, for example in a gas cylinder or a biogas digester. It is a U-shaped tube containing a liquid, usually water or mercury. One arm is connected to the gas, and the other is open to the air.
A water manometer connected to a biogas digester shows a level difference of 15.0 cm. The atmospheric pressure is 101 300 Pa and g = 9.8 m/s². Find the gauge pressure and the absolute pressure of the gas.
Tip
Barometer = air. Manometer = gas in a container
For a manometer, the gas pushes the liquid AWAY from itself. If the liquid is lower on the gas side, the gas pressure is above atmospheric.
Why is there a vacuum, not air, at the top of a mercury barometer tube?
Solution: The tube was completely full of mercury before it was inverted. When the column falls, nothing can enter the sealed top, so it is left empty. Any air there would push down and make the reading too low.
A barometer in Kigali reads 630 mm of mercury. Find the atmospheric pressure (ρ = 13 600 kg/m³, g = 9.8 m/s²).
Solution: P = 0.630 × 13 600 × 9.8 = 83 966 Pa ≈ 8.4 × 10⁴ Pa.
A barometer tube is tilted. What happens to the vertical height of the mercury column?
Solution: It stays the same. The mercury moves further along the tube, but its vertical height is still set by the atmospheric pressure.
A water manometer on a gas supply shows the water 20.0 cm higher on the open side. Find the gauge pressure (g = 10 m/s²).
Solution: 0.200 × 1000 × 10 = 2000 Pa above atmospheric.
Summary
Sources and credits
The Rwandan examples, worked examples and practice items are written by Ganzaa.
