Q: What should be the average velocity of water in a tube of diameter 2 cm so that the flow is (i) laminar (ii) turbulent ? The viscosity of water is 0.001 Pa-s. (for water R<2000 stream line flow, R > 3000 turbulent flow)

Sol: Here, d = 2 cm = 0.02 m ;

η = 0 0.001 Pa – s ; ρ = 10^{3} kg / m^{3}

(i) For stream line flow; Reynolds no. R = 2000; v = ?

$\large v = \frac{R \eta}{\rho d} = \frac{2000 \times 0.001}{10^3 \times 0.02} $

v = 0.1 m/s

(ii) For turbulent flow, Reynolds number,

R = 3000; v = ?

$\large v = \frac{3000 \times 0.001}{10^3 \times 0.02}$

v = 0.15 m/s