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