Page 358 - Bird R.B. Transport phenomena
P. 358

Cont.         —                    | p = - ( V - p v )                                                       3.1-4             For p = constant, simplifies  to
                                                                                                                                        (K)                  (V • v)  = 0


                           Motion        General              jpv=    -[V-pw]-Vp-[V- ]           + pg                                   3.2-9             For т  = 0 this becomes Euler's
                                                              t                               T
                                                                                                                                        (L)                  equation

                                         Approximate          j  pv  = -[V  • pvv]  -  Vp  -  [V •  T] + pg  -  pg/3(T -  T)                              Displays  buoyancy term
                                                               t
                                                                                                                                        (M)

                           Energy        In terms of          ^p(X+    1> + Ф) = -(V-p(K     + H +   <I>)v)-(V«q)-(V4T-v])              11.1-9            Exact only  for  Ф time independent
                                         X+   й  +  Ф         ot                                                                        (N)

                                         In terms of          j-p(K  + Ф) = -(V-p(X     + Ф)у) -  ( v  Vp)  -  ( v  [V-T])              3.3-2             Exact only  for  Ф time independent
                                                               t
                                         K + Ф                                                                                          (O)               From equation   of motion

                                         In terms of          j  t  p(K + II) = -  (V • p(X + H)v) -  (V • q) -  (V •  [T • v)]  + p(v • g)11.1-7
                                         X+ U                                                                                           (P)


                                         In terms of          j  t  pK = -  (V • pkv)  -  (v • Vp) -  (v •  [V • T])  4- p(v • g)       3.3-1             From equation   of motion
                                         к  = h 2                                                                                       (Q)


                                         In terms of          ^  pQ  =  -(V  • pUv)  -  (V  •  q)  -  p(V  • v)  -  (T:VV)              11.2-1            Term containing   (V • v) is zero  for
                                         U                                                                                              (R)                 constant p

                                         In terms of          ^ p H  =  -(V-pHv)   -  (V  •  q)  -  (T:VV) +  Щ                                           H  =  U  +  {pip)

                                         H                                                                                              (S)

                           Entropy       —                    fpS  = -(V-pSv)     "  (^  - | )  -  ^ ( q -  VT)  -  1(T:VV)             11D.1-1           Last two terms describe entropy
                                                              t
                                                                                                                                        (T)                 production
   353   354   355   356   357   358   359   360   361   362   363