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Mechanical Properties of Fluids

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Physics Part II

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
Derive an expression for excess of pressure inside a liquid drop.

Consider a liquid drop of radius R and surface tension T.

Due to surface tension the molecules on the surface film experience the net force in inward direction normal to the surface.

Therefore there is more pressure inside than outside.

Let pi be the pressure inside the liquid drop and po be the pressure outside the drop.

Therefore excess of pressure inside the liquid drop is,

                        p = p1– p0

Due to excess of pressure inside the liquid drop the free surface of the drop will experience the net force in outward direction due to which the drop will expand.

Let the free surface displace by dR under isothermal conditions.

Therefore excess of pressure does the work in displacing the surface and that work will be stored in the form of potential energy.

The work done by excess of pressure in displacing the surface is, 

dW  = Force x displacement

       = (Excess of pressure x surface area) x displacement of surface
       
       equals straight p cross times 4 πR squared xdR space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis

Increase in the  potential energy is,

dU = surface tension x increase in area of the free surface

  
equals straight T open square brackets 4 straight pi open parentheses straight R plus dR close parentheses squared minus 4 πR squared close square brackets

equals straight T open square brackets 4 straight pi open curly brackets 2 RdR close curly brackets close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis

straight p cross times 4 πR squared cross times dR equals straight T left square bracket 4 straight pi open curly brackets 2 RdR close curly brackets right square bracket

rightwards double arrow space space space space space space space space space space space space space space space space space space space straight p equals fraction numerator 2 straight T over denominator straight R end fraction  

The above expression gives us the pressure inside a liquid drop. 
     

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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. 
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What is hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids. 
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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.
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Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law. 
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What is fluid?

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


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