The hydraulic press
A hydraulic press is two pistons of different sizes joined by the same liquid. Let us see by calculation how a small force applied to one comes out much larger at the other.
Figure to be added
The problem
The area of piston A is 10 cm2 and the area of piston B is 200 cm2. If a force of 20 N is applied to piston A, what force acts on piston B?
Step 1 — the pressure at A
10 cm2 = 10−3 m2
P = F ÷ A = 20 N ÷ 10−3 m2 = 20 000 N m−2
= 2 N cm−2
Step 2 — the force at B
This pressure is transmitted through the liquid to piston B. That is, a force of 2 N acts upwards on every 1 cm2 of B.
area of B = 200 cm2
force = 2 N cm−2 × 200 cm2 = 400 N
How 20 N became 400 N
What was transmitted was not the force but the pressure. The pressure at the two pistons is the same, but the area of B is 20 times that of A, so the force it receives is 20 times as large.
What the calculation leaves out
In presses like this the forces on the pistons are far larger than the force due to the weight of the liquid column inside them, so the pressure from that column is not taken into account in the calculations.