Streamlined flow

The flow of a fluid can happen in several distinct ways -- steady (streamlined) or turbulent, compressible or incompressible, viscous or non-viscous. Picture a calm river: careful observation shows the water's velocity differs from place to place across the river's width (fastest at the centre, slowest near the banks), yet at any ONE fixed location the velocity of the water stays constant over time -- every successive particle passing through that same point has exactly the same velocity as the one before it. When a liquid flows so that each particle passing through a given point follows the SAME path with the SAME velocity as the particle immediately before it, the flow is called STREAMLINED flow (also called steady or laminar flow). The actual path traced out by a moving fluid particle is called a STREAMLINE -- a curve whose tangent at any point gives the direction of flow of the fluid at that point; it is called a streamline because, under ideal conditions, it looks exactly like the flow lines of a calm stream or river. A bundle of streamlines that all share the same velocity across any cross section perpendicular to the flow direction is called a TUBE OF FLOW; because every particle in a tube of flow always stays inside that same tube throughout its motion (it can never mix with the fluid in a neighbouring tube), the axis of a tube of flow always itself traces out a streamline, and streamlines therefore represe …