JEE Main 2021 — Mechanical Properties of Fluids Question with Solution

The nature of flow is determined by Reynolds
Number. 

$R_e=\frac{\rho vD}{\eta }$

$\left[\begin{array}{l}\rho \to \mathrm{density} \mathrm{of} \mathrm{fluid} ; \eta \to \mathrm{coefficient} \mathrm{of} \mathrm{velocity}\\ v\to \mathrm{velocity} \mathrm{of} \mathrm{flow} \\ D\to \mathrm{Diameterofpipe} \end{array}\right]$

From NCERT 

If $R_e<1000 \to$ flow is steady

$1000<R_p<2000\to$ flow becomes unsteady

$R_{\mathit{e}}>2000\to$ flow is turbulent 

$R_{\mathrm{einitial} }={10}^3\times \frac{0.18\times {10}^{-3}}{\pi \times {\left(0.5\times {10}^{-2}\right)}^2\times 60}\times \frac{1\times {10}^{-2}}{{10}^{-3}}$

$=382.16$

$R_{e \mathrm{final}}={10}^3\times \frac{0.48\times {10}^{-3}}{\pi \times {\left(0.5\times {10}^{-2}\right)}^2\times 60}\times \frac{1\times {10}^{-2}}{{10}^{-3}}$

$=1019.09$