Reynolds Number , Reynolds Experiment , Working , Significance

Reynolds Number :

- Reynolds number is a dimensionless number used in fluid dynamics to find out fluid flow ( laminar or turbulent ) .

- It is the ratio in between inertial forces which favour turbulent flow , and viscous flow  , which is favour laminar flow .

Re = DV(rho) / Viscosity of liquid

Re = Reynolds Number  .

D = Pipe diameter

V = Velocity through Pipe

(rho) = density of the fluid .

Reynolds Experiment :

- To study the behaviour of fluid flow through a closed channel ( pipeline ) , Osborne Reynolds in 1880 preformed an experiment which led to the creation of Reynolds number  . 

- Apparatus for Reynolds experiment are as mentioned here :

1.  A tank containing water at constant head .

2. A small tank containing some dye .

3. A glass tube with bell-mounted entrance at one end and a  regulating value at other end  .

Working :

- water is allowed to pass through the glass tube from the water tank , regulating valve is provided to vary the velocity of water flowing through the glass tube .

- A liquid dye is introduced of having same specific weight of water , in to the glass tube as displayed in figure .

- When velocity of water flow is low , dye filament ( thread structure ) will be in the form of straight line in the glass tube , indicating laminar flow or viscous flow or streamline flow.

- At moderate velocity , a point is reached ( the critical velocity ) at which thread begin to waver , although no mixing occur , this is known as transitional flow .

- when the velocity of flow is increased further with the help of regulating valve the threads of color solution disappear and the entire mass of the water gets uniform colored , this flow is known as turbulent flow .

Significance :

- It is used to predict the nature of flow .

- For a fluid flow through a pipe

1. Re up to 2000  =  flow remain laminar flow .

2. Re > 4000 =  flow become turbulent .

3. Re > 2000 =  and < 4000 =  transitional flow