# Laminar flow

Last updated

In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. [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 particles close to a solid surface moving in straight lines parallel to that surface. [3] Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

## Contents

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 and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. The threshold velocity is determined by a dimensionless parameter characterizing the flow called the Reynolds number, which also depends on the viscosity and density of the fluid and dimensions of the channel. Turbulent flow is a less orderly flow regime that is characterized 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 and subsequently affects heat and mass transfer in fluid systems. The dimensionless Reynolds number is an important parameter in the equations that describe whether fully developed flow conditions lead to laminar or turbulent flow. The Reynolds number is the ratio of the inertial force to the shearing force of the fluid: how fast the fluid is moving relative to how viscous it is, irrespective of the scale of the fluid system. Laminar flow generally occurs when the fluid is moving slowly or the fluid is very viscous. As the Reynolds number increases, such as by increasing the flow rate of the fluid, the flow will transition from laminar to turbulent flow at a specific range of Reynolds numbers, the laminar–turbulent transition range depending on small disturbance levels in the fluid or imperfections in the flow system. If the Reynolds number is very small, much less than 1, then the fluid will exhibit Stokes, or creeping, flow, where the viscous forces of the fluid dominate the inertial forces.

The specific calculation of the Reynolds number, and the values where laminar flow occurs, will depend on the geometry of the flow system and flow pattern. The common example is flow through a pipe, where the Reynolds number is defined as

${\displaystyle \mathrm {Re} ={\frac {\rho uD_{\text{H}}}{\mu }}={\frac {uD_{\text{H}}}{\nu }}={\frac {QD_{\text{H}}}{\nu A}},}$

where:

DH is the hydraulic diameter of the pipe (m);
Q is the volumetric flow rate (m3/s);
A is the pipe's cross-sectional area (m2);
u is the mean speed of the fluid (SI units: m/s);
μ is the dynamic viscosity of the fluid (Pa·s = N·s/m2 = kg/(m·s));
ν is the kinematic viscosity of the fluid, ν = μ/ρ (m2/s);
ρ is the density of the fluid (kg/m3).

For such systems, laminar flow occurs when the Reynolds number is below a critical value of approximately 2,040, though the transition range is typically between 1,800 and 2,100. [4]

For fluid systems occurring on external surfaces, such as flow past objects suspended in the fluid, other definitions for Reynolds numbers can be used to predict the type of flow around the object. The particle Reynolds number Rep would be used for particle suspended in flowing fluids, for example. As with flow in pipes, laminar flow typically occurs with lower Reynolds numbers, while turbulent flow and related phenomena, such as vortex shedding, occur with higher Reynolds numbers.

## Examples

1. 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]
2. 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]
3. An everyday example is the slow, smooth and optically transparent flow of shallow water over a smooth barrier. [8]
4. When water leaves a tap with little force, it first exhibits laminar flow, but as acceleration by the force of gravity immediately sets in, the Reynolds number of the flow increases with speed, and the laminar flow can transition to turbulent flow. Optical transparency is then reduced or lost entirely.
5. In waterfalls a large scale version of examples 3 and 4 occurs, as now broad sheets of smoothly flowing water fall over a ridge or edge of the waterfall. Immediately the transition to turbulence sets in with speed due to acceleration (the Reynolds number crosses the threshold for turbulence) and foamy aerated water obscures the falling flow.

## Laminar flow barriers

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. A laminar flow design for animal husbandry of rats for disease management was developed by Beall et al 1971 and became a standard around the world [9] including in the then-Eastern Bloc. [10]

## Related Research Articles

In fluid mechanics, the Grashof number is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number.

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.

In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation.

In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition. The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer.

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference via the hydraulic conductivity.

In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or between a fluid and a solid surface.

In fluid dynamics, the Schmidt number of a fluid is a dimensionless number defined as the ratio of momentum diffusivity and mass diffusivity, and it is used to characterize fluid flows in which there are simultaneous momentum and mass diffusion convection processes. It was named after German engineer Ernst Heinrich Wilhelm Schmidt (1892–1975).

In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers.

In fluid dynamics, the law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid region. This law of the wall was first published in 1930 by Hungarian-American mathematician, aerospace engineer, and physicist Theodore von Kármán. It is only technically applicable to parts of the flow that are close to the wall, though it is a good approximation for the entire velocity profile of natural streams.

This page describes some of the parameters used to characterize the thickness and shape of boundary layers formed by fluid flowing along a solid surface. The defining characteristic of boundary layer flow is that at the solid walls, the fluid's velocity is reduced to zero. The boundary layer refers to the thin transition layer between the wall and the bulk fluid flow. The boundary layer concept was originally developed by Ludwig Prandtl and is broadly classified into two types, bounded and unbounded. The differentiating property between bounded and unbounded boundary layers is whether the boundary layer is being substantially influenced by more than one wall. Each of the main types has a laminar, transitional, and turbulent sub-type. The two types of boundary layers use similar methods to describe the thickness and shape of the transition region with a couple of exceptions detailed in the Unbounded Boundary Layer Section. The characterizations detailed below consider steady flow but is easily extended to unsteady flow.

In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, the turbulence kinetic energy is characterised by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.

The term friction loss has a number of different meanings, depending on its context.

The Dean number (De) is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. It is named after the British scientist W. R. Dean, who was the first to provide a theoretical solution of the fluid motion through curved pipes for laminar flow by using a perturbation procedure from a Poiseuille flow in a straight pipe to a flow in a pipe with very small curvature.

In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section. It can be successfully applied to air flow in lung alveoli, or the flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Léonard Marie Poiseuille in 1838 and Gotthilf Heinrich Ludwig Hagen, and published by Poiseuille in 1840–41 and 1846. The theoretical justification of the Poiseuille law was given by George Stokes in 1845.

In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows.

In fluid dynamics, the process of a laminar flow becoming turbulent is known as laminar–turbulent transition. The main parameter characterizing transition is the Reynolds number.

In fluid mechanics, the Reynolds number is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation.

In fluid dynamics, the entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed. Entrance length refers to the length of the entry region, the area following the pipe entrance where effects originating from the interior wall of the pipe propagate into the flow as an expanding boundary layer. When the boundary layer expands to fill the entire pipe, the developing flow becomes a fully developed flow, where flow characteristics no longer change with increased distance along the pipe. Many different entrance lengths exist to describe a variety of flow conditions. Hydrodynamic entrance length describes the formation of a velocity profile caused by viscous forces propagating from the pipe wall. Thermal entrance length describes the formation of a temperature profile. Awareness of entrance length may be necessary for the effective placement of instrumentation, such as fluid flow meters.

Skin friction drag is a type of aerodynamic or hydrodynamic drag, which is resistant force exerted on an object moving in a fluid. Skin friction drag is caused by the viscosity of fluids and is developed from laminar drag to turbulent drag as a fluid moves on the surface of an object. Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force.

Biofluid dynamics may be considered as the discipline of biological engineering or biomedical engineering in which the fundamental principles of fluid dynamics are used to explain the mechanisms of biological flows and their interrelationships with physiological processes, in health and in diseases/disorder. It can be considered as the conjuncture of mechanical engineering and biological engineering. It spans from cells to organs, covering diverse aspects of the functionality of systemic physiology, including cardiovascular, respiratory, reproductive, urinary, musculoskeletal and neurological systems etc. Biofluid dynamics and its simulations in computational fluid dynamics (CFD) apply to both internal as well as external flows. Internal flows such as cardiovascular blood flow and respiratory airflow, and external flows such as flying and aquatic locomotion. Biological fluid Dynamics involves the study of the motion of biological fluids. It can be either circulatory system or respiratory systems. Understanding the circulatory system is one of the major areas of research. The respiratory system is very closely linked to the circulatory system and is very complex to study and understand. The study of Biofluid Dynamics is also directed towards finding solutions to some of the human body related diseases and disorders. The usefulness of the subject can also be understood by seeing the use of Biofluid Dynamics in the areas of physiology in order to explain how living things work and about their motions, in developing an understanding of the origins and development of various diseases related to human body and diagnosing them, in finding the cure for the diseases related to cardiovascular and pulmonary systems.

## References

1. Streeter, V.L. (1951-1966) Fluid Mechanics, Section 3.3 (4th edition). McGraw-Hill
2. Geankoplis, Christie John (2003). Transport Processes and Separation Process Principles. Prentice Hall Professional Technical Reference. ISBN   978-0-13-101367-4. Archived from the original on 2015-05-01.
3. Noakes, Cath; Sleigh, Andrew (January 2009). "Real Fluids". An Introduction to Fluid Mechanics. University of Leeds. Archived from the original on 21 October 2010. Retrieved 23 November 2010.
4. Avila, K.; Moxey, D.; de Lozar, A.; Avila, M.; Barkley, D.; Hof, B. (July 2011). "The Onset of Turbulence in Pipe Flow". Science. 333 (6039): 192–196. Bibcode:2011Sci...333..192A. doi:10.1126/science.1203223. PMID   21737736. S2CID   22560587.
5. Nave, R. (2005). "Laminar Flow". HyperPhysics. Georgia State University. Archived from the original on 19 February 2011. Retrieved 23 November 2010.
6. Anderson, J. D. (1997). A History of Aerodynamics and Its Impact on Flying Machines. Cambridge University Press. ISBN   0-521-66955-3.
7. Rogers, D. F. (1992). Laminar flow analysis. Cambridge University Press. ISBN   0-521-41152-1.
8. sovereign578. "Laminar Flow in Nature". YouTube. Retrieved 17 December 2019.
9. Faith, Robert E.; Hessler, Jack R. (2006). "10. Housing and Environment". In Suckow, Mark A.; Weisbroth, Steven H.; Franklin, Craig L. (eds.). The Laboratory Rat (2 ed.). Amsterdam Boston: American College of Laboratory Animal Medicine (AP). p. 304/pp. 304–337/xvi+912. ISBN   978-0-08-045432-0. OCLC   162569241.
10. Trávníček, J.; Mandel, L. (1979). "Gnotobiotic techniques". Folia Microbiologica . Czechoslovak Society for Microbiology (Springer). 24 (1): 6–10. doi:10.1007/bf02927240. ISSN   0015-5632. PMID   374207. S2CID   6421827.