# Question #ed062

Dec 1, 2017

Explained below ...

#### Explanation:

A liquid can be seen as made up of multiple layers each moving relative to the other. When the fluid flow rate is not very high, these multiple layers do not intersect. Such a flow is called laminar flow.

But if the flow rate increases beyond a certain value then the layers start mixing up and the flow is called turbulent flow.

The transition to turbulent flow was studied by Osborne Reynolds. Two forces that govern the dynamics of a fluid are - the inertial force (which is due to fluid's momentum) and the viscous force. The nature of flow depends on which is dominant. The ratio of inertial force to the viscous force is called the Reynold's Number.

$R e = {F}_{\text{inert}} / {F}_{v i s c} = \frac{\setminus \rho . {v}^{2}}{\setminus \mu \frac{v}{L}} = \frac{\setminus \rho v L}{\setminus} \mu$

$\setminus \rho$ and $\setminus \mu$ are, respectively, the fluid density and viscosity.
$v$ is the speed of flow and $L$ is the length scale of the system.

At low Reynold's number ($R e < 2000$) the flow is dominated by the viscous force and is laminar. At high Reynold's number ($R e > 2000$), the flow is dominated by inertial forces and gives rise to turbulent flow dominated by eddies and vortices.