Question

Hydraulic press is based upon :-
A. Archimedes principle
B. Bernoulli’s theorem
C. Pascal’s law
D. Reynold’s number

Answer 1

A hydraulic press id used to perform a large amount of work with a small force. It is mostly used to lift heavy objects. It works on the principle that a pressure applied on a confined liquid spreads out uniformly in all the directions.

Formula used:
$P=\dfrac{F}{A}$

Complete answer:
Let us first understand what a hydraulic press is. Hydraulic presses are used to do large amounts of work with a force of small magnitude. A hydraulic press consists of two pistons. One piston with a very small area and other with a larger area. A tube containing a liquid connects the two pistons.

A figure of a hydraulic press is shown below.

The most common use of a hydraulic press is lifting up cars while servicing. We will understand the working of the hydraulic press with this example.
The car is placed over the piston 1 (the one with the larger area). To lift a car we need a large force. However, a hydraulic press makes it very simple. With just a small force on piston 2 (the one with small area), the car on the other side will move up.

This process works on Pascal's law. According to Pascal’s law, the change in pressure in a confined liquid occurs uniformly everywhere inside the liquid irrespective of the size and shape of the container. Meaning, if we apply a pressure P on piston 2, this pressure will be transmitted uniformly in all the directions. Thus, the liquid will apply a pressure on piston 1, which is equal to pressure P. This means the liquid will apply a force on piston 2.
Now, let the area of piston 1 be ${{A}_{1}}$ and the force applied on it be ${{F}_{1}}$. Let the area of piston 2 be ${{A}_{2}}$ and the force applied on it be ${{F}_{2}}$.
The pressure on each piston is equal to the force applied upon its area.
This means that $P=\dfrac{{{F}_{1}}}{{{A}_{1}}}=\dfrac{{{F}_{2}}}{{{A}_{2}}}$.
$\Rightarrow {{F}_{1}}=\dfrac{{{F}_{2}}{{A}_{1}}}{{{A}_{2}}}$.
As discussed ${{A}_{1}}$ > ${{A}_{2}}$.
$\Rightarrow \dfrac{{{A}_{1}}}{{{A}_{2}}}$ > 1.
This means that ${{F}_{1}}$ will always be greater than ${{F}_{2}}$.
Hence, if the ratio of the areas of the respective piston is very large, we can lift the car with a small force.

So, the correct answer is “Option C”.

Note:
Let us discuss the other principles given in the options.
(i) Archimedes’ principle: It says that the buoyant force exerted by a liquid on an object that is fully or partially submerged in it is equal to the weight of the liquid displaced by the object.
(ii) Bernoulli’s theorem: It says that the mechanical energy of a flowing fluid is constant. Here, the mechanical energy of the fluid is the sum of the energy associated with the fluid pressure, the gravitational potential energy and kinetic energy of the fluid.
(iii) Reynold’s number: Reynold’s number is not a principle or a law. It is the ratio of inertial forces to viscous forces.