Q 11-09-144JEE MainJEE Main 2019 (8 Apr, Shift 1)Medium
Water from a pipe is coming at a rate of $100$ litres per minute. If the radius of the pipe is $5\ \text{cm}$, the Reynolds number for the flow is of the order of (density of water $= 1000\ \text{kg/m}^3$, coefficient of viscosity of water $= 1\ \text{mPa s}$)
Answer: (B) $10^4$
Flow rate $Q = \dfrac{100\times10^{-3}}{60} = 1.67\times10^{-3}\ \text{m}^3/\text{s}$; area $A = \pi(0.05)^2 = 7.85\times10^{-3}\ \text{m}^2$, so
$$v = \frac QA \approx 0.21\ \text{m/s}$$
Using the diameter $D = 0.1\ \text{m}$:
$$Re = \frac{\rho vD}{\eta} = \frac{1000\times0.21\times0.1}{10^{-3}} \approx 2\times10^4$$
which is of the order of $10^4$.
Solution by Sreeraj P, M.Sc Physics