Chapter 4

Fluids

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

You might have experienced gases gushing out when you try opening a bottle of coke. It is a result of the pressure exerted by fluids. Now let us first understand what fluids are.

Now let us find how the liquid column’s pressure is based on the depth of the liquid from the free surface.

Here let us consider the liquid with density in a large container. There is a cylinder with a surface XY(Area A) at a depth of h from the free surface AB, as shown in the figure.

Source: From the book Concise Physics Part 1(Class 9)

The next step is to find the thrust of the liquid in the cylinder VWXY of height h exerted on its bottom surface XY.

Thrust exerted on surface XY= Weight of the liquid in the liquid column VWXY

= Volume of the liquid column VWXY \times density \times acceleration due to gravity

= (Area of bottom surface XY \times height) \times \rho \times g

Thrust exerted on surface XY =(A \times h) \rho \times g

Now pressure applied on the liquid column =Thrust \above 1pt Surface\ Area

         = {(A \times h) \times \rho \times g} \above 1pt A

\Rightarrow Pressure applied on the liquid column=h \times \rho \times g

\Rightarrow Pressure applied on the liquid column= depth of the liquid from the free surface \times density of liquid \times acceleration due to gravity 

At a particular point on Earth, g is constant. So the pressure on the liquid will only depend on its depth h from the free surface and density of the liquid. The pressure of the liquid is independent of the containers’ shape and size. It is also independent of the area occupied by this container.

But it will depend on the atmospheric pressure applied to the liquid at a given point. Atmospheric pressure is the pressure applied within the atmosphere present on Earth.

Total pressure applied on any liquid at depth h = Atmospheric Pressure + Pressure exerted by the liquid column

Pascal’s law will explain the transmission of pressure in liquids. We have seen in the above section that the pressure exerted by a liquid of density at a depth of h from the free surface is given as,

The pressure exerted by the liquid = h \times \rho \times g

It implies that the difference in pressure between stationary points in the liquid should only depend on the vertical height difference between the free surface and these points. It would imply that if we decrease the pressure at some point in the liquid, the pressure must drop by at the same amount at all other points in the liquid.

Pascal’s law states that when the liquid is confined in a container, the pressure exerted by this liquid will equally transmit without reducing its magnitude across all directions.

Hydraulic machines are a perfect example of the transmission of pressure in liquids, as explained in Pascal’s law.

Buoyancy is a force exerted on an object partially or entirely immersed in a stationary fluid. It is a result of the pressure acting on the opposite sides of the object.

Archimedes Principle states that the buoyant force applied on the partially or wholly immersed object is equivalent to the fluid’s weight displaced by the object. This force will always act in the upward direction from the centre of mass of the complete fluid. Archimedes of Greece derived this principle, hence the name.

Mathematically it can be written as Buoyant force=Weight of the fluid displaced by the object.

Suppose when an object is immersed entirely in the fluid, and it displaces volume V of fluid.

Mass of the fluid displaced= Density X Volume

\Rightarrow Mass of the fluid displaced = \rho \times V

Weight of the fluid displaced = Mass of the fluid X Acceleration due to gravity

\Rightarrow Weight of the fluid displaced = \rho \times V \times g

We can write Archimedes principle as,

F_b = \rho \times g \times V

Where F_bis the buoyant force

The flotation principle states that when an object floats on the liquid, the buoyant force acting on the object is equal to its weight.

  • Hot-air balloon
    This type of balloon is filled with hot air. The buoyant force of the hot air present in such balloons is less than the atmospheric pressure. As a result, this balloon can travel upwards in the air. If we vary the amount of hot air in these balloons, then the buoyant force becomes more than the air surrounding it. As a result, it comes down to land.
  • Hydrometer
    A hydrometer contains lead shots because of which can vertically float on the liquid. If it goes lower in the liquid, it will indicate that the liquid’s density is lesser than the lead density.

It is important to remember that the pressure exerted by any liquid will depend only on the density of the liquid and acceleration due to gravity at that particular point. Also, the buoyant force exerted on a fluid is equal to the weight of the fluid displaced.

  1. How are you able to suck a juice using a straw?
    When we suck the juice using a straw, the straw’s air will reach our lungs, thereby decreasing the straw’s air pressure. The atmospheric pressure that will act on the juice will force it to travel upwards into the straw and ultimately to your mouth.
  2. How are we able to fill the ink in a fountain pen?
    When the rubber tube of the pen is pressed, air will escape in the form of bubbles in ink. It will result in reductions in the air pressure in the rubber tube of the fountain pen. Once we release the rubber tube, the ink will rise into the rubber tube as the nib’s atmospheric pressure is higher than the tube’s air pressure.
  3. What is atmospheric pressure?
    The thrust exerted on Earth’s unit surface area by the surrounding air column is called atmospheric pressure.
  4. Why do we make two holes in a sealed oil can?
    The air from outside enters through the first hole creating atmospheric pressure, thereby pushing the oil out from the second hole.
  5. What are the factors on which the pressure in the liquid does not depend?
    It does not depend on the liquid’s volume and the surface area or the container’s size containing the liquid.

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