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Liquids and Solids by M. T. Sprackling (auth.)

By M. T. Sprackling (auth.)

6. 2 Creeping viscous move in a semi-infinite channel one hundred forty 6. three Poiseuille movement in tubes of round cross-section one hundred forty four 6. four movement of a Newtonian liquid among coaxial cylinders 148 151 6. five our bodies in beverages 6. 6 liquid circulate and intermolecular forces 154 Non-Newtonian beverages 157 6. 7 6. eight Viscometers one hundred sixty bankruptcy 7 floor results 163 7. 1 creation 163 7. 2 extra floor loose strength and floor stress of drinks 163 7. three the entire floor power of drinks 167 7. four floor pressure and intermolecular forces 168 7. five reliable surfaces 171 7. 6 particular floor loose strength and the intermolecular strength 172 7. 7 liquid surfaces and the Laplace-Young equation 174 7. eight liquid spreading 178 7. nine Young's relation 181 7. 10 Capillary results 184 7. eleven The sessile drop 187 7. 12 Vapour strain and liquid-surface curvature 189 7. thirteen The dimension of floor unfastened energies 191 bankruptcy eight excessive polymers and liquid crystals 197 eight. 1 advent 197 eight. 2 excessive polymers 197 eight. three The mechanisms of polymerisation 198 eight. four the scale and form of polymer molecules 199 eight. five The constitution of good polymers 201 eight. 6 The glass transition temperature 203 eight. 7 Young's modulus of strong polymers 205 Stress-strain curves of polymers eight. eight 206 eight. nine Viscous stream in polymers 209 liquid crystals 8.

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A bar of uniform cross-section a and unstretched length Lo becomes of length L when acted on by balanced forces, Fa applied uniformly over the end sections. The extension is L - Lo and the linear strain e, which here is homogeneous, is (L - Lo}/Lo. Since the stress 0, which here is also homogeneous, is given by Fa/a, when Hooke's law is obeyed o = Fa/a = Ee = E(L - Lo}/Lo . 11 ] E is a material constant, at constant temperature, known as Young's modulus. When a cube of material is subject to a uniform hydrostatic stress as a result of equal forces Fa being applied in the same sense to each surface, of area a, a change in volume from Vo to V is produced.

They refer to room temperature measurements and in the case of crystalline materials, to isotropic (frne-grained) specimens. 8 The theorem of superposition When the state of stress in a body is other than a simple, normal shear or hydrostatic stress, the resulting strain may be determined by application of the theorem of superposition, which may be stated as follows. For a deformed body, in the linear elastic range of behaviour, the strain produced by a complex system of stresses (of the same type) is given by the sum of the strains produced by the component stresses acting separately.

41] = Je' Fa de. I If Hooke's law is obeyed and the rod has an unstretched length Lo and area of cross-section at, then: stress, 0 = Ee = Oat extension, e = do load,Fa where e is the linear strain and E is Young's modulus of the material. 42] provided that at may be treated as a constant. 44] . 12 The tonion of a right circular cylinder This is a simple example of a situation where the stress and strain are not homogeneous. The problem is tackled by considering an element in which stress and strain can be considered as homogeneous and then integrating over the complete solid.

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