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By R. T. Lahey Jr., D. A. Drew (auth.), Jeffery Lewins, Martin Becker (eds.)

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K=l mil V ai~,t) 1. V [e k JJ k - Pk] dS Pk [q" + P n· a. (x,t) -k -k 1. - V k -k i [E~ + q"'] 1. (81 ) R. 1. · - q" A'" k=l ki i d • -k. v 1. + V T -k EO + q'" i R. s' " -k • i (82 ) 1. i aS 2 Using Equations (76b), and (79), and noting that at we can rewrite Equation (82) as f2 «e2>. - · ) - q" 1. 1. 2i -«p 2. 1. + Md -2. 1. V T -1. 1. > -

1. • T =k i k. 1. S". + -k. 1. A' i 1. " qk " • v d -k + i (109) Alii W k W In terms of these variables, the jump conditions become: D. Mass o (110a) 34 E. R. T. LAHEY AND D. A. DREW Momentum -2 =1. ~ F. d ~2 + Mnd i T =1. ~ q" 1. A~" ~ i -1. 0 (P2. - Pl. ) 3t II ~ v nd ~ S' " -2 + ~2 d d + M v -1. -2. + Md -2. -1. o i • SI T =2. ~ 0 d ~l ~ ~ ~ T ~ ~ ~ ~ i A'. I I -2. ~ a E. + ~ i q'" R. ~ (110c) 7. CLOSURE AND CONSTITUTIVE EQUATIONS The equations of motion, Equations (107)-(109) for each phase, and the jump conditions in Equations (110) represent fifteen scalar equations.

IT R2. 0 -¢ e -r R 0 de or S' " -2 w [J¢ 1 'IT R 0 -¢ cose de e + -y J¢ -¢ sine de e 1 -x THREE-DIMENSIONAL CONSERVATION EQUATION Figure 3. 37 Stratified flow in a pipe Thus 2 S' " -2 w 'IT R 0 e sin¢ -y (115a) Hence S" -lw , - 8'" -2 w 2 --'IT R 0 sin¢ e -y (115b) The phasic densities may be given in terms of the following state equations: (116a) (116b) where the liquid phase can be subcooled and the vapor phase superheated. For the special case of saturated two-phase flows, and P2 (117 ) 38 R.

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