Reynolds Number

A Reynolds number is a quantity that has no dimension. Reynolds number is used to find out the type of flow pattern as laminar or turbulent during flow through a pipe. Reynolds number is determined by the ratio of inertial forces to the viscous forces. In fluid mechanics the Reynolds number is a basis for deciding whether the flow of fluid is perfectly steady or has slight unsteady variations on turbulence. In a fluid, the Reynolds number refers to the relationship (ratio) between internal forces and viscous forces. This relationship is affected by several factors which include internal movements caused by different fluid velocities. The Reynolds number is important in mechanics; however, it is a dimensionless quantity. which means it has no units.

History about Reynolds Number

In fluid mechanics, the Reynolds number is a criterion for determining whether a fluid (liquid or gas) flow is perfectly steady (streamlined, or laminar) or has minor unsteady variations on average (turbulent). Flow in a pipe is generally laminar when the Reynolds number is less than roughly 2,000, and turbulent when the Reynolds number is larger than 2,000. Actually, the transition from laminar to turbulent flow happens over a wide range of Reynolds numbers, mainly between 1,000 and 2,000 and rising to between 3,000 and 5,000. Osborne Reynolds, a British engineer and physicist, demonstrated in 1883 that the value of a mathematical quantity equal to the average velocity of flow times the diameter of the tube times the mass density of the fluid divided by its absolute viscosity determines the transition from laminar to turbulent flow in a pipe. The Reynolds number was named after this mathematical quantity, which was a pure number with no dimensions. It was later extended to various types of flow that are totally contained or include a moving object completely submerged in a fluid.

Reynolds number formula

According to Osborne Reynolds the turbulent flow is less frequent for viscous fluid which flows at low rates. He gives a dimensionless number called the Reynolds Number. The value of Reynolds number gives a rough notion of whether the flow will be turbulent or not.
The Reynolds number formula is given as
R_e=(ρVD)/ν
Here, R_e= Reynolds number
ν= viscosity of fluid
ρ= density of fluid
V = velocity
D = Diameter of pipe
The Reynolds number formula is also given as
R_e=inertial force / force on viscosity

Critical Velocity

The critical velocity is the velocity up to which the flow of a liquid is laminar or streamlined. When the velocity of a liquid is more than the critical velocity then the flow of liquid will be turbulent.
The critical velocity formula is given as
v=(K×ν)/(ρ×r)

Turbulent and Laminar flows

When the value of Reynolds number is more than 2000 then the flow is turbulent. When the value of Reynolds number is less than 2000 then the flow is laminar. These values are numerically accepted. But the laminar flow and turbulent flow are categorized on the basis of a range. The range of Laminar flow falls under 1100 of Reynolds number and the range of turbulent flow is more than 2200. Laminar flow is a type of flow in which the fluid covers regular paths. Turbulent flow follows an irregular path.

Significance of Reynolds Number

• The flow of fluids through pipe is turbulent when the calculated value of Reynolds number is above 2000.
• The flow of fluid is laminar when the calculated value of Reynolds number is small.
• Laminar flow is a flow in which the movement of fluid is in straight lines.

For specific flow conditions, the Reynolds number quantifies the relative importance of the two types of forces and is used to predict when turbulent flow will occur. The Reynolds number is used to scale fluid dynamic problems and to determine the dynamic similarity between two different cases of the flow of fluid like between a model airplane and the original version. This ability to predict the onset of turbulent flow is an important design tool for devices such as piping systems or airplane wings. Since such scaling is non-linear, scaling factors can be produced by implementing Reynolds numbers to both scenarios.

Conclusion

In a fluid, the Reynolds number refers to the relationship (ratio) between internal forces and viscous forces. This relationship is affected by several factors which include internal movements caused by different fluid velocities. The Reynolds number is important in mechanics; however, it is a dimensionless quantity. which means it has no units.
The Reynolds number formula is given as
R_e=(ρVD)/ν
R_e=inertial force / force on viscosity
The flow of fluids through pipe is turbulent when the calculated value of Reynolds number is above 2000.
The flow of fluid is laminar when the calculated value of Reynolds number is small.
Laminar flow is a flow in which the movement of fluid is in straight lines. Turbulent flow follows an irregular path.