Example for the above Derivation
Let us consider a ram of 300 mm diameter to be moved, the diameter of plunger is 20mm, and the force applied on the plunger is 100N.
Then the Force available at the ram = (Force applied on the plunger × Area of the ram) / Area of the plunger
Area of the ram = ( 3.14×0.32 ) / 4
Area of the ram=0.07068 mm2
Area of the plunger or piston = ( 3.14 ×.022 ) / 4
Area of the plunger or piston =0.00031 mm2
Force available at the ram = (100 × 0.07068 ) / 0.00031
Force available at the ram =22509.55 N
From the above example, it is clear that the force applied manually on the system is only 100N and this is converted to 22510N approximately which can be able to operate the heavy system that cannot be operated manually.