n identical drops of liquid of surface tension T each of radius r coalesce to form single drop. Find the energy released in the process. from Physics Mechanical Properties of Fluids Class 11 Manipur Board
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n identical drops of liquid of surface tension T each of radius r coalesce to form single drop. Find the energy released in the process.

Let R be the radius of the big drop.

Since on coalesce of droplets, the volume of liquid remains constant, therefore

Decrease space in space surface space area space during space coalesce space is comma space

increment straight A space equals space straight A subscript 1 space minus space straight A subscript 2 space

space space space space space space space space equals space 4 straight pi space left parenthesis nr squared space minus space straight R squared right parenthesis space equals space 4 πr squared left parenthesis straight n space minus space straight n to the power of 2 divided by 3 end exponent right parenthesis space

Energy space released space during space coalesce space is comma space

straight E space equals space increment straight A space cross times straight T space equals space 4 πTr squared space left parenthesis straight n space minus space straight n to the power of 2 divided by 3 end exponent right parenthesis space

rightwards double arrow 1 half straight rho 4 over 3 straight pi space straight R cubed straight v squared space equals space 4 πTr squared left parenthesis straight n space minus space straight n to the power of 2 divided by 3 end exponent right parenthesis

rightwards double arrow space 1 half straight rho 4 over 3 straight pi space nr cubed space straight v squared space equals space 4 πT space straight r squared space left parenthesis straight n minus straight n to the power of 2 divided by 3 end exponent right parenthesis space

rightwards double arrow space 1 over 6 space straight rho space nrv squared space equals space straight T space left parenthesis straight n minus straight n to the power of 2 divided by 3 end exponent right parenthesis space

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


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