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NEET Sample Paper NEET Sample Test Paper-86

  • question_answer
    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 close to (density of water \[={{10}^{3}}kg/{{m}^{3}}\] and viscosity of water \[={{10}^{-3}}Pa.s\]):

    A) 1100    

    B)        11,000

    C) 550                              

    D) 5500

    Correct Answer: D

    Solution :

    [d] Given: Diameter of water tap \[=\frac{2}{\sqrt{\pi }}\,cm\]           \[\therefore \]  Radius, \[r=\frac{1}{\sqrt{\pi }}\times {{10}^{-2}}\,m\] \[\frac{dm}{dt}=\rho AV\] \[\frac{15}{5\times 60}={{10}^{3}}\times \pi {{\left( \frac{1}{\sqrt{\pi }} \right)}^{2}}\times {{10}^{-4}}V\] \[\Rightarrow \,\,\,V=0.05\,m\text{/}s\] Reynold's number, \[{{R}_{e}}=\frac{\rho \,V\,r}{n}\] \[=\frac{10\times 0.5\times \frac{2}{\sqrt{\pi }}{{10}^{-2}}}{{{10}^{-3}}}\cong 5500\]


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