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Valentin [98]
3 years ago
8

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

Chemistry
1 answer:
julia-pushkina [17]3 years ago
7 0

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.

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