Summary

This chapter developed the mechanics of fluids -- both their motion and their surface behaviour -- along exactly the topics WBCHSE's Unit 7 SUB TOPIC 2 lists:

• Streamline and turbulent flow, and the critical velocity (Section 9.2): in streamline flow every fluid particle follows the same path (streamline) as the one before it, with no crossing of layers; above the critical velocity this breaks down into chaotic, eddy-filled turbulent flow.
• Viscosity and Newton's law of viscosity (Section 9.3): $F = \eta A\,(dv/dx)$, where $\eta$, the coefficient of viscosity (SI unit $\text{Pa·s}$), is the viscous force per unit area needed to maintain a unit velocity gradient; liquid viscosity falls with rising temperature, gas viscosity rises with it.
• Stokes' law and terminal velocity (Section 9.4): the viscous drag on a small sphere is $F = 6\pi\eta r v$; balancing weight, buoyancy, and viscous drag gives the terminal velocity $v_t = \dfrac{2r^2(\rho-\sigma)g}{9\eta}$.
• Reynolds' number (Section 9.5): the dimensionless number $Re = \rho v d/\eta$ predicts, from its numerical value, whether a flow will be streamline (low $Re$) or turbulent (high $Re$).
• Bernoulli's theorem (Section 9.6): for an ideal (incompressible, non-viscous) fluid in steady flow along a streamline, $P + \tfrac12\rho v^2 + \rho g h = \text{constant}$ -- pressure, kinetic, and gravitational potential energy per unit volume together stay constant.
• Applications of Bernoulli's theorem (Section 9.7): the venturimeter (flow-speed measurement), dynamic lift on an aerofoil, the atomizer, and two sheets of paper drawn together by a stream of air blown between them -- all arise from the same speed-pressure trade-off.
• Surface energy and surface tension (Section 9.8): a surface molecule's net inward pull makes a liquid surface behave like a stretched membrane; surface tension $T = F/l$ and surface energy per unit area are numerically equal.
• Angle of contact (Section 9.9): small (acute) when adhesion to the solid exceeds the liquid's own cohesion (water on glass); large (obtuse) when cohesion dominates (mercury on glass). …