Ncert Exercises & Solutions

Streamline flow is more likely for liquids with

(a)	high density.	(b)	high viscosity.
(c)	low density.	(d)	low viscosity.

Choose the correct option:

1.	(a), (b)	2.	(c), (d)
3.	(b), (c)	4.	(a), (d)

Hint:

R_{e} = \frac{ρ v D}{μ}

$R_e=\frac{\rho v D}{\mu}$

Explanation: To determine the conditions under which streamline flow is more likely for liquids, we need to analyze the concept of Reynolds number

(R_{e}) .

$(R_e).$ The Reynolds number is given by;

\Rightarrow ​ ​ R_{e} = \frac{ρ v D}{μ}

$\Rightarrow R_e=\frac{\rho v D}{\mu}$
where

ρ =

$\rho=$ density of the fluid,

v =

$v=$ velocity of the fluid,

D =

$D=$ diameter of a pipe,

μ =

$\mu =$ dynamic viscosity of the fluid.
We know that the greater the coefficient of viscosity of a liquid, more will be the velocity gradient. So, each line of flow can be easily differentiated. Also, the higher the coefficient of viscosity, the lower the Reynolds number

(R_{e}) .

$(R_e).$ Thus, the flow is more likely to be streamlined. Therefore, streamline flow is more likely for liquids with high viscosity and low density.
Hence, option (3) is the correct answer.

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