Question

What is Reynolds number? What is its significance?

Answer 1

Hint: The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities. The Reynolds number helps predict flow patterns in different fluid flow situations.

Complete answer:
The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluid systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. Mathematically, the Reynolds number is:
$\operatorname{Re} = \dfrac{{\rho uL}}{\mu }$
Where, $\operatorname{Re} = $Reynolds number
$\rho = $Density of the fluids
$u = $Flow speed
$L = $Characteristic linear dimension
$\mu = $Dynamic viscosity of the fluid.
 Reynolds number assumes a prominent part in anticipating the examples in a liquid's behavior. The Reynolds number is utilized to decide if the liquid stream is laminar or turbulent. The Reynolds number is likewise utilized in scaling of liquid elements problems, and is utilized to decide dynamic comparability between two distinct instances of liquid stream, for example, between a model aircraft, and its full-size form. Such scaling isn't straight and the utilization of Reynolds numbers to the two circumstances permits scaling variables to be created.

Note:
The ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full-size version. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed.