Question

The flow rate of water from a tap of diameter $ 1.25\, cm $ is $ 3\, L $ per min. The coefficient of viscosity of water is $ 10^{-3} $ Pa s. The nature of the flow is

• A. Unsteady
• B. Turbulent
• C. Laminar
• D. None of these

Answer 1

Answer: (B)

Here, diameter of the tap,
$ D = 1.25 \,cm = 1.25 \times 10^{-2} \, m $
Density of water, $ \rho=10^{3}\, kg\,m^{-3} $
Coefficient of viscosity, $ \eta=10^{-3}\,Pa s $
Volume of water flowing out per second is
$ Q=3\,L per \,min =\frac{3\times10^{-3}\,m^{3}}{60\, S}=5\times10^{-5}\,m^{3}\,s^{-1} $
Reynolds number is given by
$ R_{e}=\frac{4\rho Q}{\pi D\eta}=\frac{4\times10^{3}\,kg\,m^{-3}\times5\times10^{-5}\,m^{3}\,s^{-1}}{3.14\times1.25\times10^{-2}\,m\times10^{-3}\,pa\,s} $
$ =5095 >\,2000 $
Thus, the flow will be turbulent