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Laminar and Turbulent Flows | What is Reynolds Number

Laminar and Turbulent Flows – Introduction
When speaking of fluid flow, one refers to the flow of an ideal fluid. Such a fluid is presumed to have no viscosity. This is an idealized situation that does not exist. When referring to the flow of a real fluid, the effects of viscosity are introduced into the problem. This results in the development of shear stresses between neighboring fluid particles when they move at different velocities. In the case of an ideal fluid flowing in a straight conduit, all the particles move in parallel lines with equal velocity. In the flow of a real fluid, the velocity adjacent to the wall is zero; it increases rapidly within a short distance from the wall and produces a velocity profile such as shown in Figure

ideal fluid vs real fluid – Velocity Profile

There are two types of flow in pipes:

1. Laminar flow:

This is also known as streamline or viscous flow and is illustrated in Fig. In streamline flow, the fluid appears to move by sliding of laminations of infinitesimal thickness relative to adjacent layers; that is, the particles move in definite and observable paths or streamlines. The flow characteristic of a viscous fluid is one in which viscosity plays a significant part.

2.Turbulent flow:

It is illustrated in Fig.. It is characterized by a fluid flowing in random way. The movement of particles fluctuates up and down in a direction perpendicular as well as parallel to the mean flow direction.
This mixing action generates turbulence due to the colliding fluid particles. This causes a considerable more resistance to flow and thus greater energy losses than those produced by laminar flow. A distinguishing characteristic of turbulence is its irregularity, there being no definite frequency, as in wave motion, and no observable pattern, as in the case of large eddies.

Reynolds Number

In the flow of a fluid through a completely filled conduit, gravity does not affect the flow pattern. It is also obvious that capillarity is of no practical importance, and hence significant forces are inertial force and fluid friction due to viscosity. The same is true for an airplane traveling at speed below that at which compressibility of air is appreciable. Also, for a submarine submerged far enough so as not to produce waves on the surfaces, the only forces involved are those of
friction and inertia.
Considering the ratio of inertial forces to viscous forces, the parameter obtained is called the Reynolds number, in honor of Osborne Reynolds, who presented this in a publication of his experimental work in 1882. He conducted a series of experiments to determine the conditions governing the transition from laminar flow to turbulent flow. Reynolds came to a significant conclusion that the nature of the flow depends on the dimensionless parameter, that is

Reynolds Number formula

Where

ν is the fluid velocity,

D is the inside diameter of the pipe,
ρ is the fluid density and
μ is the absolute viscosity of the fluid.

1. If Re is less than 2000, the flow is laminar.
2. If Re is greater than 4000, the flow is turbulent.
3. Reynolds number between 2000 and 4000 covers a critical zone between laminar and turbulent flow.

It is not possible to predict the type of flow that exists within a critical zone. Thus, if the Reynolds number lies in the critical zone, turbulent flow should be assumed. If turbulent flow is allowed to exist, higher fluid temperatures occur due to greater frictional energy losses. Therefore, turbulent flow systems suffering from excessive fluid temperature can be helped by increasing the pipe diameter to establish laminar flow.