Question

If it takes $5$ minutes to fill a $15L$ 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 visocsity of water =${10}^{-3}Pa.s$) close to.

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

Answer 1

The correct option is D $5500$

The velocity can be determined from $Q=Av$...(i) where $Q$ is volume flow rate, $A$ and $V$ are area and velocity of tube.

Given $V=15L=15\times {10}^{-3}{m}^3,A=\frac{\pi D^2}{4}=\frac{\pi {\frac{0.02}{\sqrt{\pi }}}^2}{4}={10}^{-4}{m}^2$

$V=Qt$

$Q=\frac{V}{t}=\frac{15\times {10}^{-3}}{60\times 5}=0.5\times {10}^{-4}{m}^3/s$

Using Q in equation (i)

$v=\frac{Q}{A}=\frac{0.5\times {10}^{-4}}{{10}^{-4}}=0.5m/s$

Reynolds number for flow in a tube is given as $R_n=\frac{vD}{\nu }$ where $\nu$ is kinematic viscosity of fluid.

$R_n=\frac{vD}{\frac{\mu }{\rho }}$ where $\mu$ is viscosity of fluid

$R_n=\frac{0.5\frac{0.02}{\sqrt{\pi }}\times {10}^3}{{10}^{-3}}$

$R_n=5649$ hence correct answer is option D