+91-8076753736[email protected]
logo
logo
-->

Mechanical Properties Of Fluids

Question
CBSEENPH11018298
Wired Faculty App

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.

Solution

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


Some More Questions From Mechanical Properties of Fluids Chapter

Which phase of fluid is more compressible?

What is an ideal liquid?

Do liquids exert pressure?

Define pressure.

What is the direction of pressure?

What is the direction in which pressure exerts force on the walls of a container?

What is the SI unit of pressure?

You have two identical glass flasks. One is open mouthed and other is filled with helium and sealed. Which of the two will weigh more?

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation