A streamline flow or laminar flow is defined as one in which there are no turbulent velocity fluctuations. In consequence, the only agitation of the fluid particles occurs at a molecular level. In this case the fluid flow can be represented by a streamline pattern defined within an Eulerian description of the flow field. These streamlines are drawn such that, at any instant in time, the tangent to the streamline at any one point in space is aligned with the instantaneous velocity vector at that point. In a steady flow, this streamline pattern is identical to the flow-lines or path-lines which describe the trajectory of the fluid particles within a Lagrangian description of the flow field, whereas in an unsteady flow this equivalence does not arise.
The definition of a streamline is such that at one instant in time streamlines cannot cross; if one streamline forms a closed curve, this represents a boundary across which fluid particles cannot pass. Although a streamline has no associated cross-sectional area, adjacent streamlines may be used to define a so-called streamtube. This concept is widely used in fluid mechanics since the flow within a given streamtube may be treated as if it is isolated from the surrounding flow. As a result, the conservation equations may be applied to the flow within a given streamtube, and consequently the streamline pattern provides considerable insight into the velocity and pressure changes. For example, if the streamlines describing an incompressible fluid flow converge (i.e. the cross-sectional area of the streamtube contracts), this implies that the velocity increases and the associated pressure reduces.
Duncan, W. J., Thorn, A. S., and Young, A. D. (1970) Mechanics of Fluids, Arnold, London.
Batchlor, G. K. (1967) An Introduction to Fluid Mechanics, Cambridge University Press, Cambridge, UK.