Introduction

SUB TOPIC 1 of WBCHSE's Unit 7 ("Properties of Bulk Matter") ended with a single, sharp observation: a fluid -- a liquid or a gas -- has a shear modulus of rigidity of exactly zero. Unlike a solid, which pushes back with an internal restoring force when its shape is distorted, a fluid offers no lasting resistance at all to a shearing force; it simply flows to accommodate it, and once the force is removed the fluid does not spring back to any earlier shape. This single fact is the starting point of SUB TOPIC 2, which studies exactly how fluids behave once they are set flowing, and how a fluid's own free surface behaves when it is left alone.

This sub-topic falls naturally into two halves, matching the two halves of WBCHSE's own syllabus line for it.

The first half is about fluids in motion. Section 9.2 opens with the two basic patterns a flowing fluid can follow -- orderly, layer-by-layer streamline (laminar) flow, and chaotic, eddy-filled turbulent flow -- and the critical velocity that marks the boundary between them. Section 9.3 introduces viscosity, a fluid's own internal friction, and Newton's law of viscosity, which quantifies it. Section 9.4 uses viscosity to explain why a small sphere falling through a viscous fluid eventually settles into a constant terminal velocity (Stokes' law). Section 9.5 gives the Reynolds number, a single dimensionless number used to predict, in advance, whether a given flow will be streamline or turbulent. Sections 9.6-9.7 then turn to Bernoulli's theorem -- essentially, the conservation of energy applied to a moving, ideal fluid -- and its wide range of everyday and instrumental applications, from the venturimeter to the lift that keeps an aircraft's wing in the air.

The second half is about a fluid's free surface. Sections 9.8-9.11 explain why a liquid's surface behaves almost like a stretched elastic membrane (surface tension and surface energy), why different liquids meet a solid surface at different angles (the angle of contact), why the pressure inside a small drop or bubble is always higher than the pressure outside it (excess of pressure), and why a liquid rises -- or, for some liquids, falls -- inside a sufficiently narrow tube (capillarity). WBCHSE's own syllabus note is explicit that this very last topic, capillary rise and fall, is to be treated only analytically here, using the stated formula directly, without working through its derivation -- a treatment this chapter follows exactly.