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) close to :

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

Answer 1

Answer: (A)

Reynolds Number, $R_{N}=\frac{C v d}{\mu}$
Where $d$ is the diameter and $\mu$ is the coefficient of viscosity. Rate of flow $=A v\left( m ^{3} / s \right)$
Where $A$ is the area of cross section and $V$ is the velocity of flow.
$\frac{V}{\Delta t}=\frac{\pi d^{2}}{4} v$
$\Rightarrow v=\frac{4 V}{\pi d^{2} \Delta t}$
Hence