# Laminar flow

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A sphere in Stokes flow, at very low Reynolds number. An object moving through a fluid experiences a force in the direction opposite to its motion.

In fluid dynamics, laminar flow (or streamline flow) occurs when a fluid flows in parallel layers, with no disruption between the layers.[1] 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.[2] 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.[3] Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity of the fluid: laminar flow or turbulent flow. Laminar flow tends to occur at lower velocities, below a threshold at which it becomes turbulent. Turbulent flow is a less orderly flow regime that is characterised by eddies or small packets of fluid particles which result in lateral mixing.[2] In non-scientific terms, laminar flow is smooth while turbulent flow is rough.

## Relationship with the Reynolds number

The type of flow occurring in a fluid in a channel is important in fluid dynamics problems. The dimensionless Reynolds number is an important parameter in the equations that describe whether flow conditions lead to laminar or turbulent flow. The Reynolds number delimiting laminar and turbulent flow depends on the particular flow geometry, and moreover, the transition from laminar to turbulent flow can be sensitive to disturbance levels and imperfections present in a given configuration.

In the case of flow through a straight pipe with a circular cross-section, at a Reynolds number below a critical value of approximately 2040,[4] fluid motion will ultimately be laminar, whereas at larger Reynolds numbers, the flow can be turbulent. When the Reynolds number is much less than 1, Stokes flow occurs. This is an extreme case of laminar flow whereby viscous (frictional) effects are much greater than inertial forces.

## Examples

In the case of a moving plate in a liquid, it is found that there is a layer (lamina) that moves with the plate, and a layer next to any stationary plate that is stationary.
The streamlines associated with laminar flow resemble a deck of cards. This flow profile of a fluid in a pipe shows that the fluid acts in layers that slide over one another.

A common application of laminar flow is 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 cross-sectional centre 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.[5]

Another example is the flow of air over an aircraft wing. The boundary layer is a very thin sheet of air lying over the surface of the wing (and all other surfaces of the aircraft). Because air has viscosity, this layer of air tends to adhere to the wing. As the wing moves forward through the air, the boundary layer at first flows smoothly over the streamlined shape of the airfoil. Here, the flow is laminar and the boundary layer is a laminar layer. Prandtl applied the concept of the laminar boundary layer to airfoils in 1904.[6][7]

## Laminar flow barriers

Experimental chamber for studying chemotaxis in response to laminar flow.

Laminar airflow is used to separate volumes of air, or prevent airborne contaminants from entering an area. Laminar flow hoods are used to exclude contaminants from sensitive processes in science, electronics and medicine. Air curtains are frequently used in commercial settings to keep heated or refrigerated air from passing through doorways. A laminar flow reactor (LFR) is a reactor that uses laminar flow to study chemical reactions and process mechanisms.

## References

1. ^ Batchelor, G. (2000). Introduction to Fluid Mechanics.
2. ^ a b Geankoplis, Christie John (2003). Transport Processes and Separation Process Principles. Prentice Hall Professional Technical Reference. ISBN 0-13-101367-X.
3. ^ Noakes, Cath & Sleigh, Andrew (January 2009). "Real Fluids". An Introduction to Fluid Mechanics. University of Leeds. Retrieved 23 November 2010.
4. ^ Avila, K.; D. Moxey; A. de Lozar; M. Avila; D. Barkley; B. Hof (July 2011). "The Onset of Turbulence in Pipe Flow". Science 333 (6039): 192–196. Bibcode:2011Sci...333..192A. doi:10.1126/science.1203223.
5. ^ Nave, R. (2005). "Laminar Flow". HyperPhysics. Georgia State University. Retrieved 23 November 2010.
6. ^ Anderson, J.D. (1997). A history of aerodynamics and its impact on flying machines. Cambridge U. Press. ISBN 0-521-66955-3.
7. ^ Rogers, D.F. (1992). Laminar flow analysis. Cambridge U. Press. ISBN 0-521-41152-1.