Question

Water flows at a speed 5 cm/s through a pipe of radius 2cm .the viscosity of water is 0.001 pl.The reynolds number and the nature of flows are respectively ...........????????????????????????/

Answer 1

Answer on Question #36963, Physics, mechanics.

Water flows at a speed $5\mathrm{cm/s}$ through a pipe of radius 2cm. The viscosity of water is 0.001 Pl. The Reynolds number and the nature of flows are respectively...?

Solution

For flow in a pipe, the Reynolds number is defined as

$$Re = \frac {\rho v D _ {H}}{\mu},$$

where $\rho = 1000\frac{kg}{m^3}$ - density of water, $\mu = 0.001\mathrm{Pa}\cdot \mathrm{s}$ - dynamic viscosity of the water, $v = 5\frac{\mathrm{cm}}{\mathrm{s}} = 0.05\frac{\mathrm{m}}{\mathrm{s}}$ - a speed of flow, $D_H$ - the hydraulic diameter of the pipe (for a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter $D_H = D = 2R$).

The Reynolds number is

$$Re = \frac {1000 \frac {kg}{m ^ {3}} \cdot 0.05 \frac {m}{s} \cdot 2 \cdot 0.02 \, m}{0.001 \, \mathrm{Pa} \cdot \mathrm{s}} = 2000.$$

The Reynolds number $Re = 2000$. Its transition region or critical region – flow can either be laminar or turbulent – difficult to pin down exactly.

Answer: 2000; flow can either be laminar or turbulent.