Question

Water from a pipe is coming at a rate of $100$ litres per minute. If the radius of the pipe is $5cm$, the Reynolds number for the flow is of the order of (density of water $=1000kg/m^3$, coefficient of viscosity of water $=1mPas$)

• A. ${10}^6$
• B. ${10}^3$
• C. ${10}^2$
• D. ${10}^4$

Answer 1

The correct option is D ${10}^4$

Given, flow rate,

$Q=100$ litres per minute

Radius of the pipe, $r=5cm$

Volume flow rate of water $Q=v\times \pi r^2$

$v=\frac{Q}{\pi r^2}$

$v=\frac{100\times {10}^{-3}}{60}\times \frac{1}{\pi \times 25\times {10}^{-4}}$

$v=\frac{2}{3\pi }m/s$

We know that $R_e=\frac{\rho vr}{\eta }$

Given, density of the water,

$\rho ={10}^{3}kg/m^3$

Coefficient of viscosity of water,

$\eta =1mPas={10}^{-3}Pas$

Reynolds number,

$R_e=\frac{\rho vr}{\eta }$

$R_e=\frac{{10}^3\times 2\times 5\times {10}^{-2}}{{10}^{-3}\times 3\pi }$

$\simeq {10}^4$

Hence, the order of Reynolds number for the flow is ${10}^4$