Question

If it takes $5$ minutes to fill a $15litre$ bucket from a water tap of diameter $\frac{2}{\sqrt{\pi }}cm$ then the Reynoids number for the flow is (density of water $={10}^{3}kg/m^3$ and viscosity of water $+{10}^{-3}Pa-s$) close to

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

Answer 1

The correct option is C $5500$

density of water $={10}^{3}kg/m^3$

viscosity of water $={10}^{-3}Pa.s$

Reynolds number is given by $R=\rho vd/\eta$

The volume of the water flowing out per second is

$Q=v\times \pi d^2/4v$

$=4Q/d^2\pi$

$R=\rho vd/\eta$

$R=4\rho Q/\pi d\eta$

$\rho =$ Density of water $={10}^{-3}kg/m^3$

$Q=3L/min=3\times {10}^{-3}/60=5\times {10}^{-5}{m}^3/s$

$d=2/\surd \pi \times {10}^{-2}m=1.125\times {10}^{-2}m$

$\eta =$ Viscosity $={10}^{-3}Pa.s$ So,

$R=(4\times {10}^3\times 5\times {10}^{-5})/(3.14\times 1.125\times {10}^{-2}\times {10}^{-3})$

$R\cong 5500$