## Reynolds Number

For a fluid flow through a straight, smooth pipe, what is the general Reynolds Numbers for laminar, transitional, and turbulent flows?

Hint
The Reynolds number is a dimensionless value that expresses the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces.
Hint 2
$$Re=ratio=\frac{Inertia\:Force}{Viscous\:Force}=\frac{vD\rho }{\mu }=\frac{vD}{\vartheta }$$$where $$v$$ is fluid velocity, $$\rho$$ is mass density, $$D$$ is pipe diameter, $$\mu$$ is dynamic viscosity, $$\vartheta$$ is kinematic viscosity, and $$Re$$ is Reynolds number. The Reynolds number is a dimensionless value that expresses the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces. $$Re=ratio=\frac{Inertia\:Force}{Viscous\:Force}=\frac{vD\rho }{\mu }=\frac{vD}{\vartheta }$$$
where $$v$$ is fluid velocity, $$\rho$$ is mass density, $$D$$ is pipe diameter, $$\mu$$ is dynamic viscosity, $$\vartheta$$ is kinematic viscosity, and $$Re$$ is Reynolds number.

High values of the parameter indicate that viscous forces are small and the flow is essentially inviscid. The Euler equations can then be used to model the flow. Low values of the parameter indicate that viscous forces must be considered.

Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.
Flow through a pipe is generally characterized as laminar for Re < 2,100, fully turbulent for Re > 10,000, and transitional flow for 2,100 < Re < 10,000.