This concept was introduced by George Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds who popularized its use in 1883.
The Reynolds Number is a dimensionless quantity that helps to predict fluid flow patterns in different situations such as liquid flow in a pipe or air over an aircraft wing. It is the ratio of inertial forces to viscous forces within a fluid.
It's used to determine whether a fluid flow is laminar (smooth and orderly), turbulent (chaotic and irregular), or transitional.
When water first comes out of a tap, it often has a smooth, clear appearance (laminar flow). As the water falls further, it starts to become more disturbed and splash (turbulent flow).
In smaller blood vessels, flow is laminar, while in larger arteries, it may become transitional or turbulent.
Reynolds Number is calculated using the formula:
$$R_e = \frac{\rho \cdot v \cdot L}{\mu}$$Where:
$\rho$ = Fluid density
$v$ = Flow velocity
$L$ = Length or diameter of pipe
$\mu$ = Dynamic viscosity of the fluid
- Re < 2000: Laminar flow (smooth layers).
- Re > 4000: Turbulent flow (chaotic with eddies).
- 2000 ≤ Re ≤ 4000: Transitional flow.
Determine the flow of fluid having a density of 100 kg/m3 and viscosity of 0.5 Ns/m2 flowing at a velocity of 5 m/s through a pipe of diameter 0.2 m.
Given:
Velocity ($v$) = 5 m/s
Diameter ($L$) = 0.2 m
Density ($\rho$) = 100 kg/m3
Viscosity ($\mu$) = 0.5 Ns/m2
Substituting into $R_e = \frac{\rho \cdot v \cdot L}{\mu}$:
$$R_e = \frac{(100)(5)(0.2)}{0.5} = 200$$
Since $R_e < 2000$, the fluid flow is laminar.