Question

Calculate the terminal velocity of a droplet (radius =R, density=\rho_d) when its settling in a stagnant fluid (density=\rho_f).

Answer 1

`V=(2)/(9\ \mu)R^2g(\rho_d-\rho_f)`

Step-by-step explanation:

Given that

Radius =R

`Density\ of\ droplet=\rho_d`

`Density\ of\ fluid=\rho_f`

When drop let will move downward then so

`F_(net)=F_(weight)-F_(b)-F_d`

Fb = Bouncy force

Fd = Drag force

We know that

`F_b=(4\pi )/(3)R^3\ * \rho_f* g`

`F_(weight)=(4\pi )/(3)R^3\ * \rho_d* g`

`F_(d)=6\pi \mu\ R\ V`

μ=Dynamic viscosity of fluid

V= Terminal velocity

So at the equilibrium condition

`F_(net)=F_(weight)-F_(b)-F_d`

`0=F_(weight)-F_(b)-F_d`

`F_(weight)=F_(b)+F_d`

`(4\pi )/(3)R^3\ * \rho_d* g=(4\pi )/(3)R^3\ * \rho_f* g+6\pi \mu\ R\ V`

So

`V=(2)/(9\ \mu)R^2g(\rho_d-\rho_f)`

This is the terminal velocity of droplet.