Question

Oil at 20°C (density = 870 kg/m³ and velocity = 0.104 kg/m-s) flow at 1.1 m³/hr through a horizontal pipe with diameter d = 2 cm and length L = 12 m. Find the Reynolds number for the flow.

1. 104
2. 163
3. 208
4. 78

Answer 1

Correct Answer - Option 2 : 163

Concept:

Reynolds number is a dimensionless formula that is used to differentiate laminar flow from turbulent flow.

Reynolds number is given by, 

\(Re = \frac{{ρ VD}}{μ }\)

Calculation:

Given:

Dynamic viscosity of water μ = 0.104 kg/ms, density of oil ρ =870 kg/m3, Diameter of pipe = 2 cm = 0.02 m, Volume flow rate Q = 1.1 m³/hr = \(\frac{1.1}{{3600}}\) m³/sec.

\(\frac{1.1}{{3600}} = \frac{\pi }{4} \times {0.02^2} \times V\)

V = 0.9727 m/s

\(Re = \frac{{ρ VD}}{μ }\)

\(Re=\frac{{870 \times 0.9727 \times 0.02}}{0.104} = 162.72 \approx 163\)