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Mechanical Properties of Fluids

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Physics Part II

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n identical drops (each of radius r) of liquid of surface tension T and density ρ coalesce to form single drop. The energy released in the process is converted into kinetic energy. Find the speed of drop.

Let R be the radius of big drop.

When the drops coalesces, the volume of liquid remains constant.

There are n identical drops of radius 'r'. 

Therefore, 

Decrease space in space surface space area space equals space straight A subscript 1 space minus space straight A subscript 2 space

increment straight A space equals space 4 straight pi space left parenthesis nr squared space minus space straight R squared right parenthesis space

space space space space space space space equals space 4 straight pi space left parenthesis thin space straight n space minus space straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis space

Energy space which space is space released space during space coalesce space is comma space

straight E space equals space increment straight A space cross times space straight T space equals space 4 straight pi space Tr squared space left parenthesis space straight n minus straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis space

The space enrgy space released space is space converted space into space Kinetic space energy. space

Therefore comma space

1 half mv squared space equals space 4 straight pi space Tr squared space left parenthesis space straight n minus straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis space

rightwards double arrow space 1 half straight rho space 4 over 3 straight pi space straight R cubed straight v squared space equals space space 4 straight pi space Tr squared space left parenthesis space straight n minus straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis space

rightwards double arrow space 1 half straight rho space 4 over 3 πnr cubed straight v squared space equals space space 4 straight pi space Tr squared space left parenthesis space straight n minus straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis space

rightwards double arrow space 1 over 6 space ρnrv squared space equals space straight T space left parenthesis straight n space minus space straight n to the power of begin inline style bevelled 2 over 3 end style end exponent right parenthesis

rightwards double arrow space straight v space equals space square root of fraction numerator 6 straight T space left parenthesis straight n space minus space straight n to the power of bevelled 2 over 3 end exponent right parenthesis over denominator ρnr end fraction end root




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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 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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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. 
977 Views

What is fluid?

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


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