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Mechanical Properties Of Fluids

Question
CBSEENPH11018353
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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.)

Solution

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 

Some More Questions From Mechanical Properties of Fluids Chapter

What is hydrostatics?

What is hydrodynamics?

Can fluids withstand tangential stress?

Can fluids withstand normal stress?

Why the fluids do not have any modulus of rigidity?

Which phase of fluid is more compressible?

What is an ideal liquid?

Do liquids exert pressure?

Define pressure.

What is the direction of pressure?

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