Derive an expression for the terminal velocit of a sphere falling through a viscous liquid.

Explanation

`F_(G)=mg=(4)/(3)pir^(3)rho g` (downward force)

Up thrust , `U=(4)/(3)pir^(3) sigma g` (upward force)
viscous force `F=6pi eta rv_(1)`
At terminal velocity `v_(L)`.
downward force `=` upward force
`F_(G)-U=Fimplies(4)/(3)pir^(3)rho g-(4)/(3)pir^(3)sigma g=6pietarv_(1)`
`v_(1)=(2)/(9)xx(r^(2)(rho-sigma))/(eta)gimpliesv_(1)oor^(2)`