By Joseph H. Spurk
This choice of over two hundred exact labored routines provides to and enhances the textbook "Fluid Mechanics" by means of an analogous writer, and, while, illustrates the instructing fabric through examples. The workouts revolve round using the basic strategies of "Fluid Mechanics" to acquire recommendations to various concrete difficulties, and, in so doing, the scholars' ability within the mathematical modelling of functional difficulties is constructed. moreover, 30 demanding questions with out specific suggestions were integrated. whereas academics will locate those questions compatible for examinations and checks, scholars themselves can use them to envision their realizing of the topic.
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Additional resources for Fluid Mechanics: Problems and Solutions
For example, if one is solving the gas momentum equations, the liquid phase velocity can be used for the interfacial velocity. For separated or counter-current ﬂow, the interfacial velocity should be calculated diﬀerently. The interfacial temperature used for computing the energy transfer between the phases can be chosen with the same fashion as the interfacial momentum transfer. Therefore, one will choose liquid temperature as the interfacial temperature to obtain the interfacial energy transfer for solving the gas energy equation.
The ﬁnite diﬀerence approximation of Eq. 136) is n (αg ρg Ig )n+1 i,j,k = (αg ρg Ig )i,j,k + Δt [ αg ρg ug Ig Δx n i− 12 ,j,k − αg ρg ug Ig + Δt [ αg ρg vg Ig Δy n i,j− 12 ,k + Δt [ αg ρg wg Ig Δz n i,j,k− 12 + n+1 n (αg )i,j,k pi,j,k Δt (ρg )i,j,k − (ρg )i,j,k (ρg )i,j,k Δt − αg ρg vg Ig n i,j+ 12 ,k ] − αg ρg wg Ig n i,j,k+ 12 ] n i+ 12 ,j,k ] March 4, 2013 13:42 52 World Scientific Book - 9in x 6in ws-book9x6 Computational methods for two-phase ﬂow and particle transport 1 ( ρg u g Δx 1 ( ρg vg + Δy n i+ 12 ,j,k − ρg u g n i− 12 ,j,k ) n i,j+ 12 ,k − ρg vg n i,j− 12 ,k ) + 1 ( ρg wg ni,j,k+ 1 − ρg wg ni,j,k− 1 ) 2 2 Δz n n (ug )i+ 1 ,j,k − (ug )i− 1 ,j,k 2 2 − (ρg )ni,j,k Δx + + (vg )ni,j+ 1 ,k − (vg )ni,j− 1 ,k 2 2 Δy + (wg )ni,j,k+ 1 − (wg )ni,j,k− 1 2 2 Δz + Δt[(Sg )ni,j,k + (Λg )ni,j,k ] + (Δt)Ri,j,k [(T )i,j,k − (Tg )i,j,k ] Δt n n [ kg αg ni+ 1 ,j,k (Tg,i+1,j,k − Tg,i,j,k ) 2 Δx2 n n − Tg,i−1,j,k )] − kg αg ni− 1 ,j,k (Tg,i,j,k + 2 + Δt [ kg αg Δy 2 − kg αg n n i,j+ 12 ,k (Tg,i,j+1,k n n i,j− 12 ,k (Tg,i,j,k n − Tg,i,j,k ) n − Tg,i,j−1,k )] Δt n n [ kg αg ni,j,k+ 1 (Tg,i,j,k+1 − Tg,i,j,k ) 2 Δz 2 n n − Tg,i,j,k−1 )] .
The drag functions for chunk ﬂow, plug ﬂow, and counter current ﬂow are more complicated and will not be addressed in this book. The viscous stresses appeared in Eqs. 80) for the gas phase. 83) for the liquid phase. The mean resistive velocity u for a phase and the eﬀective drag function for that phase K are deﬁned in terms of the interaction between phases Kn K ≡ K n with K n > 0. 85) K2 = K21 + K22 = K21 , since K22 = 0 . 86) Also Ku ≡ K n un . 88) K2 u2 = K21 u1 . 89) For the condition of momentum conservation, it is necessary K n = Kn ⇒ K12 = K21 etc.