Reynolds number

Reynolds number is a dimensionless quantity used to determine the type of flow. From the value of Reynolds number one can tell whether flow is laminar or turbulent or flow is in transition.

The flow in which fluid flows smoothly such that fluid layers are parallel to each other or no to streamlines intersect each other, such type of flow is known as laminar flow

The flow in which fluid flows in zig-zag manner and fluctuate irregularly in such a way that its velocity changes irregularly, such type of flow is known as turbulent flow

To know more about different types of fluid flow check out this post

Osborne Reynolds studied various conditions for types of flow such as Turbulent flow, Laminar flow and flow in transition. Osborne Reynolds described dependency of flow on Reynolds number.

Osborne Reynolds - Wikimedia

Reynolds numbers is defined as ratio of inertial forces to viscous forces.

Numerically Reynolds number can be given by,

    Re is Reynolds number

    ρ is the density of the fluid (kg/m3)
    u is the velocity of the fluid with respect to the object (m/s)
    L is a characteristic linear dimension (m)
    μ is the dynamic viscosity of the fluid (Pa.s or N.s/m2 or kg/(m.s))
    ν is the kinematic viscosity of the fluid (m2/s).

For flow of fluid through pipe through fixed diameter D,

When value of Reynolds number is approximately less than 2000, then flow is Laminar.

When value of Reynolds number is approximately in between 2000 to 4000, then flow is in Transition.

When value of Reynolds number is approximately more than 4000, then flow is Turbulent.

Behavior of fluid flow for various values of Reynolds number is shown

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For more information about Reynolds number Visit

https://en.wikipedia.org/wiki/Reynolds_number

https://www.grc.nasa.gov/www/BGH/reynolds.html