Question

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) approximately

• A. 5500
• B. 11,000
• C. 550
• D. 1100

Answer 1

The correct option is A. 5500

From continuity equation

$Q=Av$
$\frac{15\times {10}^{-3}}{5\times 60}=\frac{\pi }{4}{\left(\frac{2}{\sqrt{\pi }}\right)}^2\times {10}^{-4}\times v$
$\Rightarrow v=0.5m/s$
$R=\frac{pvd}{\mu }=\frac{{10}^3\times 0.5}{{10}^{-3}}\times \frac{2}{\sqrt{\pi }}\times {10}^{-2}$
$R=\frac{1}{\sqrt{\pi }}\times {10}^4=0.55\times {10}^4=5500$.