Reynold Experiment

Reynold was first to demonstrate that the transition from laminar to turbulent depends not only on mean velocity but on the quantity ρVD/ μ.  

This quantity ρVD/ μ is a dimensionless quantity and is called Reynolds number (Re).

In case of circular pipe if Re

 < 2000 the flow is said to be laminar and if Re

 > 4000, the

flow is said to be turbulent. If Re

 lies between 2000 to 4000, the flow changes from

laminar to turbulent.

Reynolds Experiment:

The type of flow determined Reynold number i.e., ρVD/ μ. This was demonstrated by Reynold in 1883. The apparatus shown in the figure as above. 

The apparatus consists of: 

i) A tank containing water at a constant head,

ii) A small tank containing some dye

iii) A glass tube having a bell- mouthed entrance at one end and a regulating valve at another end. The water from the tank was allowed to flow through the glass tube. The  velocity of flow was varied by the regulating valve. A liquid dye having same specific  

weight as water was introduce into the glass tube as shown in fig

The following observation were made by Reynold:

                          Fig.10

(i) when the velocity of flow was low, the dye filament in the glass tube was in the form

of a straight line. The straight line of dye filament parallel to the glass tube, which was

the case of laminar flow as shown in fig. 10(a)

(ii) with the increase of velocity of flow, the dye filament was no longer a straight line

but it became a wavy one as shown in fig. 10(b). This shows that flow is no longer

laminar.

(iii) with the increase of velocity of flow, the wavy dye filament broke-up and finally

diffused in water as shown in fig. 10(c). This means that the fluid particles of the dye at this higher velocity are moving in a random fashion, which shows the case of turbulent  flow. Thus, in case of turbulent flow the mixing of dye- filament and water is intense and  flow is irregular, random and disorderly.  

In case of laminar flow, the loss of pressure head was found to be proportional to the velocity but in case of turbulent flow, Reynold observed that loss of head is  approximately proportional to the square of velocity. More exactly the loss of head, hf ∝ Vn 

, where n varies from 1.75 to 2.0.

Critical Velocity: It is the velocity of fluid at which flow changes from laminar flow to

turbulent flow. Critical Velocity can be,

 (i) Lower critical velocity

 (ii) upper critical velocity

(i) Lower critical velocity: When flow of fluid changes from laminar to turbulen

there is some transition period, The velocity at which flow enters from laminar to  transition period, is called lower critical flow. 

(ii) upper critical velocity: The velocity at which flow enters from transition period to turbulent flow is called upper critical flow.