Question

water drop of radius 1.5 mm is falling from height 1 km having drag constant0.5 density of water drop 1000 kg per metre cube and density of air is 1.29 kg per metre cube find its terminal velocity

Answer 1

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Answer 2

Terminal velocity is 8.85 $kmhr^{-1}$

Explanation:

• Radius of Water Drop, R = 1.5 mm  

We know that,  

• 1 meter = 100 centimeter = 1000 mm

So, Radius becomes (in mm) = $\frac {1.5}{1000}$

= 0.0015 m

And Area of Drop, A = $\pi r^2$

= $3.14 \times (0.0015)^2$

= $7.06 \times 10^{-6} m^2$

Now, We know that Density = $\frac {Mass}{Volume}$

So, mass = Density $\times$ Volume

= $\rho \times \frac {4}{3} \pi R^3$

= $1000 \times \frac {4}{3} \times 3.14 \times (0.0015)^3$

= $1.413 \times 10^{-5}$ kg

$V_{Terminal} = \sqrt {\frac {2mg}{D \rho_a A}}$

= $\sqrt {\frac {2 \times 1.413 \times 10^{-5} \times 9.8}{0.5 \times 1.29 \times 7.06 \times 10^{-6}}}$

$V_{Terminal}$= 2.46 = 8.85 $kmhr^{-1}$