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JEE Main 2015 · 10 Apr · Shift 1, Physics question 8

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter 2π\dfrac2{\sqrt\pi} cm then the Reynolds number for the flow is (density of water = 10310^3 kg/m3^3 and viscosity of water = 10−310^{-3} Pa.s) close to :

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Answer and worked solution

Official answer: A

Q=15×10−3300=5×10−5Q=\frac{15\times10^{-3}}{300}=5\times10^{-5} m³/s. The area is πD24=(2×10−2)24=10−4\pi\frac{D^2}4=\frac{(2\times10^{-2})^2}4=10^{-4} m² (with D=2πD=\frac2{\sqrt\pi} cm), so v=0.5v=0.5 m/s.
Re=ρvDη=103×0.5×2×10−2π10−3≈5640≈5500.Re=\frac{\rho vD}\eta=\frac{10^3\times0.5\times\frac{2\times10^{-2}}{\sqrt\pi}}{10^{-3}}\approx5640\approx5500.

Topics:Viscosity and Stokes' lawContinuity equation
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