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

Mechanical Properties Of Fluids

Question
CBSEENPH11020053
Wired Faculty App

Derive the expression for viscous force acting on spherical body of radius r moving with velocity v through viscous liquid of coefficient of viscosity η.

Solution
Let space straight F space proportional to space straight r to the power of straight a space space space space space space space space space space space proportional to space straight v to the power of straight b space space space space space space space space space space proportional to space straight eta to the power of straight c space space space space space space straight F space proportional to space straight r to the power of straight a space straight v to the power of straight b space straight eta to the power of straight c space straight i. straight e. comma space straight F space equals space straight k space straight r to the power of straight a space straight v to the power of straight b straight eta to the power of straight c space space space space space space space space space space space... space left parenthesis 1 right parenthesis thin space straight k space is space the space constant space of space proportionality. space Now comma space putting space the space dimension space formula space of space each space quantity space in space equation space left parenthesis 1 right parenthesis comma space we space get space space space space space space space space space space space left square bracket straight M to the power of 1 straight L to the power of 1 space straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket straight M subscript straight o straight L to the power of 1 straight T subscript straight o right square bracket to the power of straight a space left square bracket straight M to the power of 0 straight L to the power of 1 straight T to the power of negative 1 end exponent right square bracket to the power of straight b space left square bracket straight M to the power of 1 straight L to the power of negative 1 end exponent straight T to the power of negative 1 end exponent right square bracket to the power of straight c space rightwards double arrow space space space left square bracket straight M to the power of 1 straight L to the power of 1 space straight T to the power of negative 2 end exponent right square bracket space equals space left square bracket straight M to the power of straight c space straight L to the power of straight a plus straight b minus straight c end exponent space straight T space to the power of negative straight b minus straight c end exponent right square bracket space Equating space the space powers space of space straight M comma space straight L space and space straight T space on space both space sides comma space we space have space straight c space equals space 1 straight a plus straight b minus straight c space equals space 1 minus straight b minus straight c space equals space minus 2 space On space solving comma space we space get straight a space equals space 1 comma space straight b space equals space 1 comma space straight c space equals space 1 space Putting space the space values space of space straight a comma space straight b space and space straight c space in space equation space left parenthesis 1 right parenthesis comma space we space get straight F space equals space straight k space straight r space straight v space straight eta

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?

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation