Water from a pipe is coming at a rate of $100\, litres$ per minute. If the radius of the pipe is $5\, cm$, the Reynolds number for the flow is of the order of : (density of water $= 1000\, kg/m^3$, coefficient of viscosity of water $= 1\, mPa\, s$)
JEE MAIN 2019, Diffcult
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Reynolds number$ = \frac{{\rho vd}}{\eta }$
Volume flow rate$ = v \times \pi {r^2}$
$v = \frac{{100 \times {{10}^{ - 3}}}}{{60}} \times \frac{1}{{\pi \times 25 \times {{10}^{ - 4}}}}$
$v = \frac{2}{{3\pi }}m/s$
Reynolds number $ = \frac{{{{10}^3} \times 2 \times 10 \times {{10}^{ - 2}}}}{{{{10}^{ - 3}} \times 3\pi }} = 2 \times {10^4}$
$Order\,{10^4}$
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