Question

An oil of viscosity 0.5 N s/m² and relative density 0.6 is flowing through a circular pipe of diameter 60 cm and of length 500 m. The average velocity of the oil is 2 m/s. Determine the Reynolds number.

1. 1440
2. 1350
3. 1260
4. 1800

Answer 1

Correct Answer - Option 1 : 1440

CONCEPT:

Reynold's number: It is a pure number that determines the nature of the flow of liquid through a pipe. It is defined as the ratio of the inertial force per unit area to the viscous force per unit area for a flowing fluid. Reynold's number is written as NR.

\({N_R} = \frac{{{\rm{Inertial\;force\;per\;unit\;area\;}}}}{{{\rm{Viscous\;force\;per\;unit\;area}}}}\)

Mathematically Reynolds number is given by:

\(R = \frac{ρ v D}{μ}\)

Where R = Reynolds number, ρ = fluid density,v = velocity, D = diameter of the pipe, μ = viscosity of the fluid.
Calculation:

Given:

μ = 0.5 N s/m2 , s = 0.6, ρ = 0.6 × 1000 = 600 kg/m³, D = 60 cm = 0.6 m, L = 500 m, V = 2 m/s

\(R = \frac{ρ v D}{μ} =\frac{600\times2\times0.6}{0.5} = 1440\)
The Reynolds number is 1440.