Turbulent flow

When the speed of a moving fluid exceeds its critical speed $v_c$, the motion becomes TURBULENT. In turbulent flow, the velocity of the fluid at a given location changes both in magnitude AND in direction from one particle to the next passing through it, so individual particles no longer trace out smooth, well-defined streamlines the way they do in streamlined flow. Instead, the path taken by each particle becomes erratic, and the fluid develops whirlpool-like circular patterns called EDDY CURRENTS or eddies. The turbulent wake of water just behind a moving boat, or the turbulent wake of air just behind a moving bus, are familiar everyday examples of turbulent flow. The transition between streamlined and turbulent flow can be demonstrated directly by injecting a thin jet of ink axially into a wide tube through which water is flowing: at low flow velocities, the ink stays a straight, well-defined thread (streamlined flow); once the water's velocity is increased beyond the critical value, the ink instead spreads out and becomes disordered, visibly showing that the flow has become turbulent -- this zig …