Q.Distinguish between streamline (laminar) flow and turbulent flow in a moving fluid, and define the critical velocity of a fluid flowing through a tube.

Fluid flow can occur in several distinct patterns -- streamlined or turbulent being the two the chapter contrasts directly. STREAMLINED FLOW (also called steady or laminar flow) occurs when every particle of the liquid passing through a given point follows the SAME path with the SAME velocity as the particle immediately before it: picture a calm river, where the water's speed differs from place to place across its width (fastest at the centre, slowest near the banks) but, at any ONE fixed point, stays constant over time, so every particle crossing that point has identical speed and direction to its predecessor. The actual path a fluid particle follows in streamlined flow is a STREAMLINE -- a curve whose tangent at any point gives the local flow direction -- and a bundle of streamlines sharing the same velocity across a cross section forms a TUBE OF FLOW. Because fluid in one tube of flow can never mix with fluid in a neighbouring tube (each particle stays inside its own tube throughout its motion), TWO STREAMLINES CAN NEVER CROSS EACH OTHER: if they did, the fluid particle passing through the crossing point would have to be moving in two different directions with two different velocities at once, which is impossible for a single physical particle at a single point in time -- a direct consequence of the definition of a streamline as the unique tangent-direction path of the flow at that point. Streamlined flow persists only up to a CRITICAL VELOCITY $v_c$. Once the fluid's speed EXCEEDS $v_c$, the flow becomes TURBULENT: the velocity at a given location now varies in both magnitude and direction from particle to particle, individual particles no longer trace smooth streamlines, and the flow instead develops erratic, whirlpool-like EDDY CURRENTS (the visible wake behind a moving boat or bus). The transition is demonstrated by injecting a thin jet of ink into a wide tube of flowing water: at low speed the ink stays a straight thread (streamlined); past the critical speed it spreads out and becomes disordered (turbulent), and this disordered zig-zag motion, which forms the eddy currents, dissipates far more energy than smooth streamlined flow at a comparable average speed. Whether a particular pipe flow is streamlined or turbulent is predicted quantitatively by Reynold's number.