Putting it together
The whole chapter is built from one idea: a force spread over an area. Everything after that was a matter of applying it to liquids, to gases, and to objects placed in them.
| Section | The central idea | Formula or law |
|---|---|---|
| 15.1 Pressure | force spread over an area | P = F ÷ A; 1 N m−2 = 1 Pa |
| 15.2 Liquid pressure | pressure depends on depth alone | P = h ρ g |
| 15.3 Transmission | a liquid carries pressure undiminished | pressure at small piston = pressure at large piston |
| 15.4 Gas pressure | a column of air has weight too | 76 cm Hg at sea level |
| 15.5 Floating | a fluid pushes upwards | upthrust = weight of fluid displaced |
Mixed exercise (1)
The problem
The same cubical box is placed on a table first on its largest face and then on its smallest. What can be said about the force and the pressure on the table in the two cases?
The solution
The force is the same in both cases — it is the weight of the box, which does not depend on which face it stands on.
The pressure is greater on the smallest face — the same force is spread over a smaller area.
Mixed exercise (2)
The problem
A ship made of metal floats on water, while a solid block of the same metal sinks. Why?
The solution
A ship encloses a large empty space, so as it settles it displaces a large volume of water. There is therefore a level at which the upthrust equals the ship's weight — and there it floats.
A solid block displaces only a volume of water equal to its own. The upthrust from that is less than the block's weight, so it sinks.
Mixed exercise (3)
The problem
What happens to the height of the mercury column when a mercury barometer is carried from sea level to the summit of Everest, and why?
The solution
The height falls from 76 cm to about 25 cm.
As you climb, the height of the column of air above the point falls, so atmospheric pressure falls. That smaller pressure can support only a shorter mercury column.
Glossary
| පීඩනය | Pressure |
| ද්රාව පීඩන ජැක්කුව | Hydraulic jack |
| ඔසවනය | Hoist |
| වායුගෝලය | Atmosphere |
| රසදිය වායුපීඩනමානය | Mercury barometer |
| නිර්ද්රව වායුපීඩනමානය | Aneroid barometer |
| උඩුකුරු තෙරපුම | Upthrust |
| ද්රව මානය | Hydrometer |
Chapter summary
- Pressures arise from liquids and gases just as they do from solids.
- The pressure due to a liquid acts in every direction.
- The deeper you go in a liquid (the taller the liquid column), the greater the pressure.
- The formula P = h ρ g is used to calculate the pressure due to a liquid, where h is the height of the liquid column, ρ is the density of the liquid and g is the acceleration due to gravity.
- The air-filled space around the earth's surface is the atmosphere, and the pressure arising from that air is atmospheric pressure.
- The standard value of atmospheric pressure at sea level is 76 cm Hg. The mercury barometer and the aneroid barometer are used to measure it.
- When an object is immersed partly or wholly in a liquid, the liquid applies to it an upthrust equal to the weight of the liquid displaced.
- When an object floats in a fluid, the weight of the fluid it displaces is equal to the weight of the object.