Question

Two spherical raindrops of equal size are falling vertically through air with a velocity of 1 m//s. What would be the terminal speed if these two drops were to coalesce to form a large spherical drop?

Answer 1

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Answer 2

Final terminal velocity =  1.586 m/s

Given:

Two spherical raindrops of equal size are falling vertically through air with a velocity of 1 m/s.

To find:

What would be the terminal speed if these two drops were to coalesce to form a large spherical drop.

Formula used:

Terminal velocity ∝ r²

Where     r = Radius of the sphere.

Explanation:

Two equal size rain drops are falling these two drops were to coalesce to form a large spherical drop so that,

Volume of both small rain drop =  Volume of large spherical drop.

                                          $\frac{4}{3} \pi R^{3}=2\left(\frac{4}{3} \pi r^{3}\right)$

                                            $\therefore R=(2)^{1 / 3} \cdot r$

                                               $\frac{R}{r}$ = $(2)^{1 / 3}$

Final terminal velocity =   ( $\frac{R}{r}$)² × Initial terminal velocity

Final terminal velocity = ( $(2)^{1 / 3}$ )² × 1

Final terminal velocity =  1.586 m/s

To learn more...

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