Force to area ratio in hydraulic press

If both vertically positioned cylinders of communicating vessels are closed with pistons, then with the help of external forces applied to the pistons, a large pressure can be created in the liquid, many times exceeding the hydrostatic pressure at any point in the system. If the pistons have different areas, then different forces act on them from the liquid side. The same modulus, but oppositely directed external forces must be applied to the pistons to keep the system in balance.

Conditions:

1. This ratio is performed only in an ideal hydraulic press, i.e. one in which there is no friction.

Links:

1. Physics LibreTexts, formula 53.1.2.

input_force

force acting on the first piston.

Symbol:

F_1

Latex:

\(F_{1}\)

Dimension:

force

input_area

area of the first piston.

Symbol:

A_1

Latex:

\(A_{1}\)

Dimension:

area

output_force

force acting on the second piston.

Symbol:

F_2

Latex:

\(F_{2}\)

Dimension:

force

output_area

area of the second piston.

Symbol:

A_2

Latex:

\(A_{2}\)

Dimension:

area

law

F_1 / A_1 = F_2 / A_2

Latex:

\[\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}\]