# laminar flow

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## Laminar flow

A smooth, streamline type of viscous fluid motion characteristic of flow at low-to-moderate deformation rates. The name derives from the fluid's moving in orderly layers or laminae.

The chief criterion for laminar flow is a relatively small value for the Reynolds number, Re = &rgr;*VL*/μ, where &rgr; is fluid density, *V* is flow velocity, *L* is body size, and μ is fluid viscosity. Laminar flow may be achieved in many ways: low-density flows as in rarefied gases; low-velocity or “creeping” motions; small-size bodies such as microorganisms swimming in the ocean; or high-viscosity fluids such as lubricating oils. At higher values of the Reynolds number, the flow becomes disorderly or turbulent, with many small eddies, random fluctuations, and streamlines intertwining. *See* Creeping flow, Reynolds number, Turbulent flow, Viscosity

Nearly all of the many known exact solutions of the equations of motion of a viscous fluid are for the case of laminar flow. These mathematically accurate descriptions can be used to give insight into the more complex turbulent and transitional flow patterns for which no exact analyses are known. *See* Navier-Stokes equation

The theory of viscous lubricating fluids in bearings is a highly developed area of laminar flow analysis. Even large Reynolds number flows, such as aircraft in flight, have regions of laminar flow near their leading edges, so that laminar flow analysis can be useful in a variety of practical and scientifically relevant flows. *See* Boundary-layer flow, Fluid flow

## Laminar Flow

an ordered flow of a liquid or gas, in which the fluid moves in layers parallel to the direction of flow. Laminar flow is observed in very viscous fluids. It also occurs when the velocity of flow is sufficiently low and during the slow flow of a liquid around small objects. Specifically, laminar flow occurs in narrow (capillary) tubes, in the lubricant layer in bearings, and in the thin boundary layer that forms near the surface of a body over which a fluid is flowing. If the velocity of flow of a given fluid is increased, the laminar flow, at a certain instant, may undergo a transition to a disordered turbulent flow. As this occurs, the resistance to the motion of the fluid is changed drastically. The mode of flow of a fluid depends on the Reynolds number *Re.* If the value of *Re* is smaller than a certain critical value *Ren,* then laminar flow occurs. If Re > Re_{cr}, then the flow can become turbulent. The value of Re_{cr} depends on the type of flow being considered. For instance, for flow through circular tubes, Re_{cr} ≈ 2,200 (if it is assumed that the characteristic velocity is the velocity averaged across the cross section of the tube and that the characteristic dimension is that of the tube’s diameter). Consequently, at Re_{cr} < 2,200, the flow of the fluid in the tube will be laminar. The output of liquid from a tube during laminar flow is determined by the Poiseuille law.

### REFERENCES

Targ, S. M.*Osnovnye zadachi teorii laminarnykh techenii.*Moscow-Leningrad, 1951.

Loitsianskii, L. G.

*Mekhanika zhidkosti i gaza,*3rd ed. Moscow, 1970.

## laminar flow

[′lam·ə·nər ′flō]## streamline flow

## laminar flow

*laminar boundary layer*.