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Introduction
This wiki page deals with the two types of Flows in Fluid Mechanics that is Laminar and Turbulent Flows. It also shows the variation of Reynolds Number for different kinds of channel.

Laminar Flow
In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection. The resistance to flow in a liquid can be characterized in terms of the viscosity of the fluid if the flow is smooth. In the case of a moving plate in a liquid, it is found that there is a layer or lamina which moves with the plate, and a layer which is essentially stationary if it is next to a stationary plate.

There is a gradient of velocity as you move from the stationary to the moving plate, and the liquid tends to move in layers with successively higher speed. This is called laminar flow, or sometimes "streamlined" flow. Viscous resistance to flow can be modeled for laminar flow, but if the lamina break up into turbulence, it is very difficult to characterize the fluid flow.

The common application of laminar flow would be in the smooth flow of a viscous liquid through a tube or pipe. In that case, the velocity of flow varies from zero at the walls to a maximum along the centerline of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements and applying the viscous force to them.

Turbulent Flow
Turbulent flow, type of fluid (gas or liquid) flow in which the fluid undergoes irregular fluctuations, or mixing, in contrast to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow the speed of the fluid at a point is continuously undergoing changes in both magnitude and direction. The flow of wind and rivers is generally turbulent in this sense, even if the currents are gentle.

Flow descriptions such as Poiseuille's law are valid only for conditions of laminar flow. At some critical velocity, the flow will become turbulent with the formation of eddies and chaotic motion which do not contribute to the volume flowrate. This turbulence increases the resistance dramatically so that large increases in pressure will be required to further increase the volume flowrate. Experimental studies have characterized the critical velocity for a long straight tube in the form


 * $$ \mathrm{v_c} = {{ {\mathbf R} \mu} \over {\rho D}}.$$

which depends upon the viscosity in poise, the density in gm/cm^3, the radius of the tube in cm. The script R is an experimental constant called the Reynold's number. The reported Reynolds number for blood flow is about 2000. Modeling blood flow in the human aorta according to this criterion leads to the expectation of some turbulence in the center of the flow.

Relation with Reynold's Number
The Reynolds ( Re ) number is a quantity which engineers use to estimate if a fluid flow is laminar or turbulent. This is important, because increased mixing and shearing occur in turbulent flow. This results in increased viscous losses which affects the efficiency of hydraulic machines. A good example of laminar and turbulent flow is the rising smoke from a cigarette. The smoke initially travels in smooth, straight lines (laminar flow) then starts to “wave” back and forth (transition flow) and finally seems to randomly mix (turbulent flow).

Flow in Pipes
The typical criterion for whether pipe flow is laminar or turbulent is the value of the Reynolds Number. The Reynolds number for pipe flow is defined as Re = DVρ/μ, where D is the pipe diameter, V is the average flow velocity in the pipe, ρ is the density of the flowing fluid and μ is the dynamic viscosity of the flowing fluid. Re is a dimensionless number. Any consistent set of units can be used for D, V, ρ and μ, and will result in Reynolds number being dimensionless. The generally accepted criteria for laminar flow and turbulent flow in terms of Re are as follows:

For Re < 2100, it is laminar flow. For Re > 4000, it is turbulent flow. For 2100 < Re < 4000, the flow is in the transition region.

Flow in an Open Channel
The value of Reynolds number for laminar and turbulent flow in open channel is different than that of a pipe.

For Re < 500, it is laminar For Re > 2000, it is turbulent For 500 < Re < 2000, the flow is in the transition region.