A First Course in Physics · Ch. III, §§ 66–72 · Chapter 3: Pressure in Liquids
8. Pascal's law and the hydraulic press
Goal: Your student can state Pascal's law, explain how a hydraulic press multiplies force, and show that force × distance is the same at both ends.
You'll need
- The book, open to these pages
- Two plastic syringes of different sizes and a short piece of tubing (from a pharmacy or hobby kit), or two squeeze bottles
- Water and a towel
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Pascal's reasoning that pressure applied to a confined liquid is passed on undiminished; multiplying force with a small and large piston; the hydraulic press; no gain in force × distance; hydraulic elevators; city water supply; artesian wells. Five problems follow.
The lesson, step by step
Hook question
SayHow can a car mechanic lift a whole car by pumping a little handle?
Read together
Read §§ 66–72. Pascal's own words, as the book quotes them:
A vessel full of water is a new principle in mechanics, and a new machine for the multiplication of force to any required extent, since one man will by this means be able to move any given weight.
Explain the idea
Pressure pushed into a closed liquid reaches every part of it. If the small piston has 1 sq. cm and the big one 1000 sq. cm, then 1 kg on the small one pushes up 1000 kg on the big one.
But nothing is free (§ 69): the small piston must move 1000 cm to raise the big one 1 cm. Force × distance is the same at both ends. Your student will meet this rule again with levers and pulleys.
Try it: syringe hydraulics
Fill two syringes and the tube with water, with no air bubbles. Push the small syringe: the big plunger moves out only a little but pushes hard. Push the big one: the small plunger shoots out. Have your student feel the difference in force with a thumb on each plunger. Measure how far each plunger moves.
Look at the pictures
Study Fig. 38 (the press) and Fig. 42 (city water supply). Ask your student to trace the water's path and to explain why the fountain cannot rise higher than the water in the reservoir.
Say it back
Your student explains how a hydraulic press works and why it does not create energy for free.
Problems
Work problems 1–5 on book pages 50–51. Problem 1 uses the weight of a cubic foot of water, 62.3 lb.
Afterwards
Spot hydraulics this week: a car jack, a barber's chair, the arm of a digger, a car's brakes.
Tip
Syringes without needles are sold for giving medicine to children or pets, and they are perfect for this.
Answers to the book's problems
1. About 185 ft. (80 lb. per sq. in. = 11,520 lb. per sq. ft.; ÷ 62.3). 2. 12,460 lb. (623 lb. per sq. ft. × 20). 3. About 6283 lb. (piston area 78.5 sq. in. × 80); with 30 per cent lost, about 4400 lb. 4. About 865 lb. (400 sq. in. = 2.78 sq. ft., under 5 ft. of water). 5. The areas must be as 1000 : 1, so the diameter is √1000 ≈ 31.6 in.
Worked out for this site from the scan. If a number in your copy differs, trust the book.