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Mechanical Properties of Fluids

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Physics Part II

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Class 10 Class 12
Obtain an expression for the pressure exerted by liquid column.

Consider a liquid of density ρ in a vessel as shown in figure.

To find: Pressure difference between two points A and B separated by vertical height h.

Consider an imaginary cuboid of area of cross-section a of liquid with upper and lower cap passing through A and B respectively in order to evaluate the pressure difference between points A and B. 

Volume of the imaginary cylinder is, V = ah 

Mass of liquid of imaginary cylinder, m = ρah

Let, P1 and P2 be the pressure on the upper and lower face of cylinder.

Forces acting on the imaginary cylinder are:

(i) Weight, mg = ρahg in vertically downward direction.

(ii) Downward thrust of F1 =P1a on upper cap.

(iii) Upward thrust of F2 = P2a on lower face.

As the imaginary cylinder in the liquid is in equilibrium, therefore the net force on the cylinder is zero. 

             i.e., F1 + mg = F2  P1a + ρahg = P2a    P2 - P1 = ρgh 

Thus, the pressure difference between two points separated vertically by height h in the presence of gravity is ρgh.

Note: In the absence of gravity this pressure difference becomes zero.



Why solids have definite shape while liquids do not have definite shape?

Solids: Intermolecular forces are very strong and thermal agitations are not sufficiently strong to separate the molecules from their mean position. Solids are rigid and hence they have definite shapes.
Liquids: In liquids intermolecular forces are not sufficiently strong to hold the molecules at definite sites, as a result they move freely within the bulk of liquid, therefore, do not possess definite shapes. Liquids take the same shape as that of the container. 

What is hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids. 

Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law. 

What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.


What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.