Coefficient of viscosity `(eta)`: The viscous force acting tangentially on unit area of the liquid when there is a unit velocity gradient in the direction perpendicular to the flow is defined as " Coefficient of viscosity".
Coefficient of viscossity `eta=(-F)/A(dx)/(dv)`
Unit `Nm^-2 -s` (or) pascal - second.
According to Stoke's law the viscous force acting on a freely falling, smooth spherical body of radius 'a' is proportional to the coefficient of viscosity `eta` radius 'a' and velocity 'v' of the body.
`therefore F prop eta a v ` or `F= 6 pi eta a v` where `6 pi` is the proportionally constant.
A rain drop of radius `'omega'`, density `rho` falling under gravity through air of density `sigma`experiences a force of buoyancy equal to the weight of displaced air which is
`(4/3pia^3)sigmag`
THe weight of the rain drop acting down wards =`(4/3pia^3)rhog` `therefore` Resultant force acting downwards `4/3pia^3rhog-4/3pia^3sigmag`
When this force is equal to the viscous drag acting upwards, then the rain drop acquires a constant velocity called terminal velocity , `v_1`
At terminal velocity viscous drag= `6 pi eta a v`.
`therefore6pietaav_t=4/3pia^3(rho-sigma)g`
`thereforev_t=2/9a^2(((rho-sigma)g)/eta)=` terminal velocity.
Defination: terminal velocity of a body falling through a liquid is defined as that constant velocity which the body acquires when it falls in a fluid.
