Question

What is the value of the Reynolds number?

• A. $0.01$
• B. $0.03$
• C. $0.15$
• D. $0.26$

Answer 1

The correct option is A $0.01$

The terminal velocity $V_T$ of the body of radius $r$, density $\rho$ falling through a medium of density ${\rho }_o$ is given by
$V_T=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.
$\Rightarrow 0.7\times {10}^{-2}=\frac{2\times (0.5\times {10}^{-3}{)}^2\times (11.20\times {10}^3-1.26\times {10}^3)\times 9.8}{9\times \eta }\Rightarrow \eta =0.77N/m^2$

And Reynold's number is given by
$Re=\frac{\rho vD}{\eta }\Rightarrow Re=\frac{(1.26\times {10}^3)\times (0.7\times {10}^{-2})\times {10}^{-3}}{0.77}=0.01145\approx 0.01$