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Mechanical Properties of Fluids

Terminal velocity

Eight drops of equal size are falling through air with steady

Question

Medium

Solving time: 3 mins

Eight drops of equal size are falling through air with steady velocity of 10 cm/sec. If the drops coalesce, what could be its terminal velocity?

A

40 cm/sec

B

20 cm/sec

C

30 cm/sec

D

50 cm/sec

Views: 6,173 students

Updated on: Jun 9, 2022

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Eight drops of equal size are falling through air with steady velocity of 10 cm/sec. If the drops coalesce, what could be its terminal velocity?

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Text solutionVerified

Terminal velocity,

v_{T} = \frac{2}{9} \frac{r ^{2} ( ρ - σ ) g}{η}

∴ v_{T} \infty r^{2}

∴ \frac{v _{T}}{v _{T}^{'}} = \frac{r ^{2}}{R ^{2}}

...... (i)
Now, Volume of the big drop = 8

\times

volume of each small drop

\frac{4}{3} π R^{3} = 8 \times \frac{4}{3} π r^{3}

\Rightarrow R = 2 r

∴ \frac{10}{v _{T}^{'}} = \frac{r ^{2}}{( 2 r ) ^{2}} = \frac{r ^{2}}{4 r ^{2}}

[using equation (i)]

\Rightarrow v_{T}^{'} = 40 c m / s

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Question Text	Eight drops of equal size are falling through air with steady velocity of 10 cm/sec. If the drops coalesce, what could be its terminal velocity?
Updated On	Jun 9, 2022
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	248
Avg. Video Duration	8 min