If it takes $5\,minutes$ to fill a $15\,litre$ bucket from a water tap of diameter $\frac{2}{{\sqrt \pi }}cm$ then the Reynolds number for the flow is (density of water $= 10^3\,kg/m^3$ ) and viscosity of water $= 10^{-3}\,Pa.s$ ) close to
JEE MAIN 2015, Diffcult
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Given: Diameter of water tap $ = \frac{2}{{\sqrt \pi }}\,cm$
$\therefore \,\,Radius,\,r = \frac{1}{{\sqrt \pi }} \times {10^{ - 2}}\,m$
$\frac{{dm}}{{dt}} = \rho AV$
$\frac{{15}}{{5 \times 60}} = {10^3} \times \pi {\left( {\frac{1}{{\sqrt \pi }}} \right)^2} \times {10^{ - 4}}V$
$ \Rightarrow V = 0.05\,m/s$
Reynold's number, ${R_e} = \frac{{\rho Vr}}{n}$
$ = \frac{{{{10}^3} \times 0.5 \times \frac{2}{{\sqrt \pi }}{{10}^{ - 2}}}}{{{{10}^{ - 3}}}} \cong 5500$
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