Question

The area of piston in a hydraulic machine is $6\,c{m^2}$ and $576\,c{m^2}$. What force on the smaller piston will support a load of $1152\,N$ on the larger piston? State the assumption made in the above calculation.

Answer 1

Before solving the problem let us first get some idea about Pascal law. Pascal's law (also known as Pascal's principle or the principle of fluid-pressure transmission) is a fluid mechanics principle proposed by Blaise Pascal that states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid, resulting in the same change everywhere. Blaise Pascal, a French mathematician, established the law in $1653$ and published it in $1663$.

Complete answer:
A piston can be found in reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders, and pneumatic cylinders, among other things. The purpose of a piston rod and/or connecting rod in an engine is to transfer force from expanding gas in the cylinder to the crankshaft.
Given
Area of smaller piston, ${a_1} = 6\,c{m^2}$
Area of larger piston, ${a_2} = 576\,c{m^2}$
Load on the larger piston, ${F_2} = 1152\,N$
Using Pascal’s law
(In a confined incompressible fluid, any change in pressure at any point is propagated throughout the fluid volume at each location.)
${P_1} = {P_2}$
$\dfrac{{{F_1}}}{{{A_1}}} = \dfrac{{{F_2}}}{{{A_2}}}$
$\dfrac{{{F_1}}}{6} = \dfrac{{1152}}{{576}}$
${F_1} = 12\,N$

Note:
Pascal's barrel refers to a hydrostatics experiment that Blaise Pascal is said to have conducted in $1646.$Pascal is said to have conducted the experiment by inserting a long vertical tube into a water-filled barrel. The rise in hydrostatic pressure caused the barrel to rupture when water was put into the vertical tube.