Question: In the figure shown water is filled in a symmetrical container. Four Pistons of equal area are used ...

Question

In the figure shown water is filled in a symmetrical container. Four Pistons of equal area are used at the four openings to keep the water in equilibrium. Now an additional force is applied at each piston. The increasing pressure at the center of the container due to this addition is

A. $\dfrac{F}{A}$
B. $\dfrac{{2F}}{A}$
C. $\dfrac{{4F}}{A}$
D. $0$

Answer 1

Solution

In order to solve this type of questions we have to be clear with the concept of fluid mechanics. We also have to know Archimedes' principle and its applications. Also we have to be clear with the pascal's law and its applications. Observing the question we see that each side is applied force of F, thus our total force of $4F$ is applied.

Complete step by step answer:
Pascal law—For a fluid at rest in a closed container, the pressure applied at any point is transmitted equally to all the portions inside the container without any loss in energy. From the question we can see the net force applied on the symmetrical container is $4F$ .The total area upon which this force is acted upon is $4A$ .From the definition of pressure, we see that the pressure is $\dfrac{{4F}}{{4A}} = \dfrac{F}{A}$ .

Now from Pascal’s principle we see that a change in pressure applied to an enclosed fluid is transmitted in equal amount to all portions of the fluid and to the walls of the container; thus we can say that $\dfrac{F}{A}$ is transferred all the other three Pistons where $F_4,F_2,F_3$ are applied.

Now forces $F_4,F_2,F_3$ balance the applied pressure and keeps the water in equilibrium. Thus, from this we can see that there is no additional force due to the other forces. Hence, we can say the pressure exerted on the cylindrical container is $\dfrac{F}{A}$ .

Note: This type of questions can easily be solved if we know the Pascal Law. Some of the applications of Pascal's principle are used in the functioning of the hydraulic press, hydraulic lift and brakes, which are asked in questions. DON’T get confused over Force and Pressure, pressure is equally transmitted and not force.