Part of ME-07 — Properties of Solids & Liquids

Ten-Sentence Concise Review

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Elasticity describes how materials deform under stress (F/A, Pa) and recover; Hooke's Law states stress is proportional to strain within the elastic limit. Young's modulus (Y), Bulk modulus (B), and Shear modulus (G) quantify resistance to linear, volumetric, and tangential deformations respectively, all in Pascals [M1M^{1} L1L^{-1} T2T^{-2}]. The stress-strain curve progresses through five points: proportional limit, elastic limit, yield point, ultimate stress, and breaking point. Pascal's Law states that pressure in an enclosed fluid is transmitted equally in all directions, forming the basis of hydraulic presses. For ideal fluid flow, the equation of continuity (A1A_{1}v_{1} = A2A_{2}v_{2}) and Bernoulli's equation (P + ½ρv2v^{2} + ρgh = constant) govern motion, with higher velocity producing lower pressure. Viscosity (η, Pa·s) measures internal fluid friction, and Stokes' Law gives viscous drag as F = 6πηrv on a sphere. Terminal velocity v_t = 2r2r^{2}(ρ − σ)g/(9η) is proportional to r2r^{2}, so doubling the radius quadruples the terminal velocity. Surface tension (S = F/L, N/m) produces excess pressure ΔP\Delta P = 2S/R inside a liquid drop (one surface) and ΔP\Delta P = 4S/R inside a soap bubble (two surfaces). Capillary rise h = 2S cosθ/(ρgr) causes water to rise in glass tubes and mercury to be depressed. Heat conduction follows Fourier's Law (Q/t = KA ΔT\Delta T/L) and radiation follows the Stefan-Boltzmann Law (P = σAT4AT^{4}, T in Kelvin).

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