Hydraulic Battle
Two different-sized syringes full of water are connected together. Push on one, and feel the force—multiplied—in the other.
- Basin, bucket, or big bowl of water
- 10-mL plastic syringe
- 1-mL plastic syringe
- 1 foot (30 cm) of clear plastic tubing that fits over the syringe tips
- Optional: a second 10-mL plastic syringe
- Submerge the tubing and let it fill completely with water. Make sure there are no air bubbles at all inside the tubing.
- Push the plunger all the way into the 1-mL syringe so there’s no air in it. Hold the syringe underwater to prevent any air bubbles from getting in and insert its tip into one end of the submerged, water-filled tubing.
- Submerge the 10-mL syringe and pull out the plunger to fill it with water. Holding everything underwater, insert the syringe tip into the other end of the tubing. Then take the entire assembly out of the water.
Now it’s time to duel. Hold one syringe in each hand and put your thumbs on the plungers. Take turns pushing in one plunger, then the other. Can you feel how the motion of one forces the other? Which plunger is easier to push? Which plunger travels the farthest with each push?
You probably noticed that the smaller syringe plunger was much easier to push than the larger one, yet traveled a much greater distance in the process.
This phenomenon arises as a direct result of Pascal’s principle, a cornerstone of hydraulics, the use of fluids to transmit forces. Pascal’s principle says that a change in pressure in any part of an enclosed fluid is transmitted undiminished to all parts of the fluid. Pushing on the plunger applies pressure on the water inside, and the transmitted pressure causes the plunger in the other syringe to move.
Though the pressure on the water is equal everywhere, the force on the two plungers is not. The force on a surface is equal to the pressure times the area of the surface.
\[ \text{force} = \text{pressure} \times \text{area} \]
Since the base of the smaller syringe plunger has a significantly smaller surface area, it takes much less force to get it to move.
The good news with the small syringe is that you’ve obtained a force advantage; the bad news is that you’re paying for it with a distance penalty and have to push the plunger further. Mechanical work is the product of force times the distance the force moves through.
\[ \text{work} = \text{force} \times \text{distance} \]
The work done by one plunger must equal the work put into the other—so what you gain in increased force you lose in decreased distance.
Hydraulic systems like the one you just made are common in countless applications: lifts and jacks for servicing cars, brake systems, airplane wing flaps and landing gear, mechanical arms on garbage trucks, and so on.
Modify your hydraulic system by replacing the 1-mL syringe with a second 10-mL syringe, so there are 10-mL syringes on both ends of the water-filled tube. You’ll notice that the force required to push the plungers—and the distance they travel—is now the same.
You can also try repeating these experiments using air instead of water. Air-filled systems are called pneumatic systems. Unlike water, air is compressible, so some energy goes into compressing the air, with the result that the cylinders don’t move quite as much as when filled with fluid.
Be on the watch for water fights: Water-filled syringes readily transform into squirt guns.
