Types of Flow, Reynolds Number & Continuity question from JEE Main 2021 (16 Mar, Shift 2)

Answer: (a)

1. $R_e = \dfrac{\rho v D}{\eta}$ with $v = \dfrac{Q}{\pi r^2}$ gives $R_e = \dfrac{2\rho Q}{\pi \eta r}$.
2. $Q_1 = 0.18\text{ L/min} = 3\times10^{-6}\text{ m}^3/\text{s}$: $R_e = \dfrac{2\times10^3\times3\times10^{-6}}{\pi\times10^{-3}\times0.005} \approx 382$
3. $Q_2 = 0.48\text{ L/min} = 8\times10^{-6}\text{ m}^3/\text{s}$: $R_e \approx 1019$
4. $R_e$ goes from below $1000$ (steady) to above $1000$ (unsteady).
5. So the answer is (a) steady flow to unsteady flow.