Ever wonder how the flow of water in a pipeline is different from the flow of water in a river? 

Does the vortex we often see in violent rivers occur in the pipe that supplies water in our home? To answer such a question we may take count of many physical quantities which we see later in our article but the net result is a simple number called Reynold’s number. This number is named after Osborn Reynolds by Arnold Sommerfeld but The concept was introduced by George Stokes in 1851. This number basically gives us an idea about the kind of flow of the fluid.

REYNOLDS NUMBER FORMULA

The formula for the Reynolds number could be written as:

Re= VL

Where,

ρ = density of fluid

V = velocity of fluid

μ = viscosity of fluid

L = length or diameter of the fluid.

Based on the different values of Re, we can infer that:

1. If Re < 2000, the flow is called Laminar
2. If Re > 4000, the flow is called turbulent
3. If 2000 < Re < 4000, the flow is called transition.

REYNOLDS NUMBER UNITS

The variables in Reynolds number possess different units. These are as follows:

• R in the Reynolds number is unitless
• ρ in the fluid density is taken in kilograms-per-cubic-meter (kg/m3)
• v in the velocity is taken in meters-per-second (m/s)
• D in the diameter of the pipe is always in meters (m)
• μ in the viscosity of the fluid is taken in pascal-seconds (Pa⋅s)

Reynolds number value

Reynolds number, in liquid mechanics, is a model of whether the liquid (fluid or gas) stream is consistent (smoothed out, or laminar) or on the normal consistent with little temperamental changes (tempestuous). At whatever point the Reynolds number is not exactly around 2,000, the stream in a line is by and large laminar, though, at values more noteworthy than 2,000, the stream is normally violent. The change among laminar and tempestuous streams happens not at a particular worth of the Reynolds number yet in a reach typically starting between 1,000 to 2,000 and stretching out vertically to somewhere in the range of 3,000 and 5,000.                                                            

Reynolds number and the definition.

Reynolds number is defined as a  dimensionless quantity which is used to understand the type of flow pattern such as laminar or turbulent while flowing in a pipe. Reynolds number can be found by taking the ratio of inertial forces and viscous forces. 

The Reynolds number has wide applications, going from a fluid stream in a line air entry over an aeroplane wing. It is utilised to anticipate the change from laminar to tempestuous stream and is utilised in the scaling of comparative yet unique estimated stream circumstances, for example, between an aeroplane model in an air stream and the standard rendition. The forecasts of the beginning of disturbance and the capacity to ascertain scaling impacts can be utilised to assist with anticipating liquid conduct for a bigger scope, for example, in a neighbourhood or worldwide air or water development and subsequently the related meteorological and climatological impacts.

3. Factors Affecting Reynolds Number

The main factors that affect the value of Reynolds Number are can be seen from the formula-:

Re = (ρVL)/μ

• The flowing geometry of the fluid 
• V = Fluid Flow velocity; with an increase in flow velocity the Reynolds number value increases and with a decrease in flow velocity the value of Reynolds number decreases that is Reynolds number is directly proportional to fluid flow
• L = Characteristic Dimension; with an increase in characteristic dimension the Reynolds number value increases and with a decrease in characteristic dimension the Reynolds number value decrease that is Reynolds number is directly proportional to the characteristic dimension
• ρ = Fluid Density;  Reynold’s number decreases with decrease in fluid density and with an increase in fluid density the Reynolds number increases, that is Reynolds number is directly proportional to the fluid density.
• μ = Viscosity;  the value of the Reynolds number value decreases with an increase in viscosity and with the decrease in viscosity the number increases, that is Reynolds number is inversely proportional to the viscosity of fluid. The viscosity of a fluid is the property that maximum affect the value of Reynolds number

4. Application 

The Reynolds number has a large spectrum of applications in the field of physics varying from fluid flow in a pipe to the passage of air flowing around an aircraft wing. It is used to know  the transition of  fluid  from laminar to turbulent flow and used for scaling of comparable but different-sized flow circumstances, such as between an airplane model in a wind tunnel and the actual airplane. The forecasts of the onset of turbulence and the capacity to calculate scaling effects can be used to help us in anticipating fluid behavior on a larger scale, such as in regional or international air or water movement and thereby the associated meteorological and climatological effects.

For pipes Reynolds number must be in a range  such that the flow of fluid must tend to laminar this will save time  and also reduce the material loss of inner wall of pipes due to turbulent flow which means the pipes should have longer life time .

Conclusion:

From the above, we have learnt about Reynold’s principle and its universal usage in science and different fields of daily life. The Reynolds number is the proportion of inertial force to viscous force  inside a liquid, exposed to relative interior development because of various liquid speeds.