Laminar and Turbulent Fluid Flows & Reynolds Number

While traveling in an airplane we hear pilot instructing to fasten the seat belts because of the turbulence at the time of severe weather conditions or airflow over high mountains. There may be some other firsthand experience about the flow patterns. Fluid flow patterns are generally divided into laminar and turbulent fluid flows. Now, try to open the valve on a garden used without nozzle by just a little amount and notice what happens. Water streams getting out of it in an orderly fashion. There isn’t change in the shape of the flow of water from moment to moment. It is one of the classic examples of laminar fluid flow. If the valve is gradually opened, you’ll ultimately find a point where a smooth stream of water starts to vacillate and becomes turbulent. The water lost its glassy-looking appearance because of the disruption.

Please Read Fluid mechanics fundamentals and application.

Laminar and Turbulent Flows

Smooth fluid flow around an object is known to be laminar ( as shown in figure a ). Laminar flow occurs when a relatively slow movement of the fluid is observed. When the flow is moving faster the pattern surrounding the sphere starts to break and a random irregular pattern is observed. This irregular pattern is shown in figure b is known as turbulent. Behind the sphere, we found some small eddies and whirlpool and the flow at the downstream experiences a disturbance.

laminar flow turbulent flow and Reynolds number

Figure : (a) Laminar and (b) turbulent flow of a fluid around a sphere.

How to determine the characteristics of the flow – Reynold’s Number

Several factors are needed to be taken into consideration while analyzing the characteristics of the flow. These are

British engineer Osborne Reynolds discovered the exact relationship between these parameters in the nineteenth century. His experiments involved the transition between laminar and turbulent flow while flowing through pipes.

A dimensionless number,  recognized as being the most significant variable in fluids mechanics, was found to describe that transition. The Reynolds number (Re) is defined by this relation –

Re = ρvl/μ

in terms of the fluid’s density and viscosity, its speed v, and a characteristic length l that is representative of the problem at hand. For crude oil that is being pumped through a pipe, the characteristic length l is the pipe’s diameter; for water flowing past the sphere in Figure, l is the sphere’s diameter; for the ventilation system in a building, l is the diameter of the air duct; and so forth.
The Reynolds number has the physical interpretation of being the ratio between the inertia and viscous forces acting within a fluid; the former is proportional to density (Newton’s second law), and the latter is proportional
to viscosity. When the fluid moves quickly, is not very viscous or is very dense, the Reynolds number will be large, and vice versa. The inertia of fluid tends to disrupt it and to cause it to flow irregularly. On the other hand, viscous effects are similar to friction, and, by dissipating energy, they can stabilize the fluid so that it flows smoothly. From the standpoint of calculations, situations that arise in mechanical engineering involving laminar flow often can be described by relatively straightforward mathematical equations; that is generally not the case for turbulent flows. The usefulness of those equations, however, will be limited to low speeds and ideal shapes such as spheres, flat plates, and cylinders. Experiments and detailed computer simulations are often necessary for engineers to understand the complexity of fluids flowing in real hardware and at actual operating speeds.

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