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Mechanical Properties of Fluids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Fluids2 Marks
Question
What should be the maximum average velocity of water in a tube of diameter $2cm$ so that flow is laminar? The viscosity of water is $0.001Nm^{-2}s$.
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Answer

D = 2cm = 0.02m$\rho=10^3\text{kg m}^{-3}$
$\eta=0.001\text{ Nm}^{-2}\text{s}=10^{-3}\text{ Nm}^{-2}\text{s}$
Flow of water will be laminar if, $N_R = 1000$ where $N_R$ is Reynold number Let $\upsilon=$ maximum average velocity
​​​​​​​$\therefore$ Using the relation,
$\text{N}_\text{R}=\frac{\rho\upsilon\text{D}}{\eta}$ or $\upsilon=\frac{\text{N}_\text{R}\eta}{\rho\text{D}}$
$=\frac{1000\times0.001}{1000\times0.02}=0.05\text{ms}^{-1}$

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