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

Answer:

$V=\dfrac{2}{9\ \mu}R^2g(\rho_d-\rho_f)$

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

$F_b=\dfrac{4\pi }{3}R^3\ \times \rho_f\times g$

$F_{weight}=\dfrac{4\pi }{3}R^3\ \times \rho_d\times g$

$F_{d}=6\pi \mu\ R\ V$

μ=Dynamic viscosity of fluid

V= Terminal velocity

So at the equilibrium condition

$F_{net}=F_{weight}-F_{b}-F_d$

$0=F_{weight}-F_{b}-F_d$

$F_{weight}=F_{b}+F_d$

$\dfrac{4\pi }{3}R^3\ \times \rho_d\times g=\dfrac{4\pi }{3}R^3\ \times \rho_f\times g+6\pi \mu\ R\ V$

So

$V=\dfrac{2}{9\ \mu}R^2g(\rho_d-\rho_f)$

This is the terminal velocity of droplet.