A First Course in Physics · Ch. III, §§ 57–65 · Chapter 3: Pressure in Liquids
7. Pressure under water
Goal: Your student can explain that liquid pressure grows with depth and pushes equally in all directions, use p = hd and F = Ahd, and explain the hydrostatic paradox and why water finds its level.
You'll need
- The book, open to these pages
- A tall plastic bottle (a 2-liter soda bottle) and a nail or skewer to poke holes (adult does the poking)
- A sink or the outdoors
- A clear bendy straw or a short piece of clear tubing
- A teapot or watering can
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
The upward push on a tube held under water; a pressure gauge made from a thistle tube and a drop of ink; force proportional to depth and the same in every direction; the force on a surface (F = Ahd); the hydrostatic paradox, with vessels of different shapes; pressure as force per square centimeter (p = hd); and why water stands at the same level in connected vessels. Nine problems follow.
The lesson, step by step
Hook question
SayWhy do your ears hurt at the bottom of a deep swimming pool but not at the top?
Read together
Read §§ 57–65. The book's summary of the gauge experiments:
We conclude, therefore, that at a given depth a liquid presses up and down and sidewise with exactly the same force.
Try it: the leaky bottle
An adult pokes three holes up the side of a plastic bottle, one above the other. Cover them with tape, fill the bottle with water, stand it in the sink and pull off the tape. The jet from the lowest hole shoots out farthest: more depth, more pressure.
Poke one more hole in the side near the bottom and one in the bottom itself: water comes out sideways and downward just as easily.
Explain the idea
Pressure means force on each square centimeter. In water (density 1), the pressure at a depth of h centimeters is h grams per square centimeter: p = hd. The total force on a surface is the area times the average depth times the density: F = Ahd.
The paradox (§ 62): the force on the bottom of a vessel depends only on the depth and the area of the bottom, not on how much water is in it. The slanting walls push up or down on the water and make up the difference (§ 63).
Try it: water finds its level
Fill a teapot or watering can and look at the spout: the water stands at the same height as in the pot. Fill a bendy straw partly with water and hold the two ends up like a U; tip it and watch both surfaces stay level.
What we know now
In SI units pressure is measured in pascals (1 Pa = 1 newton per square meter), named for Pascal. Ten meters of water adds about 100,000 Pa, roughly one atmosphere.
Say it back
Your student explains the hydrostatic paradox in their own words, pointing to Fig. 32.
Problems
Work problems 1–9 on book pages 44–45. Remember: pressure is grams per square centimeter; force is pressure times area.
Afterwards
Look for a water tower or a hilltop reservoir near you and ask why it is built so high.
Tip
A dam is thickest at the bottom for the same reason the bottom jet goes farthest.
Answers to the book's problems
1. 102,600 g (102.6 kg) per sq. cm. 2. 24,000,000 g = 24,000 kg (24 metric tons). 3. Each long side: 24,000 kg; each end: 16,000 kg (area times half the depth). 4. 20,000 g = 20 kg. 5. Less: the water in the cone weighs only a third as much as the force on its bottom, because the slanting sides push down on the water. 6. Bottom: 13,600 g; each side: 6800 g. 7. About 151 cm. 8. 17.5 kg. 9. The tap is 230 ft. = 6900 cm below the reservoir surface, so the pressure is 6.9 kg per sq. cm; with 1 in. = 2.5 cm that is about 95 lb. per sq. in.
Worked out for this site from the scan. If a number in your copy differs, trust the book.