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Mechanical Properties of Fluids

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Physics Part II

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Physics

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Class 10 Class 12
A drop of mercury of radius 3mm splits into 27 identical droplets. Find the increase in surface energy. (Surface tension of mercury is 0.465 N/m.)

Let r be the radius of small droplet.

The volume of mercury will remain constant on splitting the drop into droplets.

Therefore,

straight R space equals space straight n to the power of begin inline style bevelled 1 third end style end exponent straight r space

Here comma space

straight R space equals space 3 space mm space and space straight n space equals space 27

therefore space straight r space equals space 1 space mm space

Surface space are space of space big space drop space is comma space

straight A subscript 1 space equals space 4 πR squared space equals space 4 straight pi space left parenthesis 3 cross times 10 to the power of negative 3 end exponent right parenthesis squared space

space space space space space space equals space 1.13 space cross times 10 to the power of negative 4 end exponent space straight m squared space

Surface space area space of space 27 space droplets comma space

straight A subscript 2 space equals space 27 space cross times space 4 πr squared space

space space space space space space equals space 27 space cross times space 4 straight pi space left parenthesis 10 to the power of negative 3 end exponent right parenthesis squared space

space space space space space space equals space 3.39 space cross times space 10 to the power of negative 4 end exponent space straight m squared space space

Increase space in space surface space area comma space

increment straight A space equals space straight A subscript 2 space minus space straight A subscript 1 space equals space 2.26 space cross times 10 to the power of negative 4 end exponent space straight m squared space

Increase space in space potential space energy space of space surface space film comma space

increment straight E space equals space increment straight A cross times straight T space

space space space space space space space space space equals space 2.26 space cross times space 10 to the power of negative 4 end exponent space cross times space 0.465 space

space space space space space space space space space equals 10.51 space cross times space 10 to the power of negative 5 end exponent space straight J space
space space space space space space space space space 
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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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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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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 fluid?

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


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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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