Cátedra de Mecánica del Continuo – FI-UNER Cursado: Primer cuatrimestre de 2008 Material de Estudio Tema V: Balance Macroscópico de cantidad de movimiento y ecuación de Euler Introducción ! " # $ % # " & $ ! ' # $ " ρ ρ ρ # ( $ ρ = * " # " + " " # ) # + # + # , ! , + % " % # , ρ # ( # # . " )- ρ = , )- " $ # # % # " / # # # # " , 1 ) = # )0 # )0 % ! 2 ρ * " ρ = " & + )3 " # " " " " & ! , ! # 4 " 5% " , # , # 6 7 )" 8 - 8 7 6 ) 2$ # ! " &" # , " % " # # # / " ( # # + # # # 1 " # # # ! 9: " )) # " ! # % " # 9: )< # 9> # % # ; ( = &# & = )) " 9 / " # # 0 7 " / ! # #& )3 3.1 Balance macroscópico de cantidad de movimiento 9 9 > > ;∆ 9 6 ) -2$ + # $ )3 / # " & ! # + # ! / + " ' " " & 6 # ' ! )0 ( + ! " " 3 ! # ( & )3 = ρ = + ρ = # ! 2 @ = )? % ( ρ = @ 2 > > " ρ = @ # 9 @ + > > 9 @ > > % 9 @ )A > $ ! " + 2 > ;∆ ≠ @ > ;∆ > ;∆ ≠ @ > ;∆ > ;∆ ≠ @ > ;∆ ( % ! 2 = = @ = = > @ ∆ →> > > ∆ →> > +∆ − ∆ @ ≠ = B ) > +∆ − ∆ > = > @ ∆ →> > +∆ − ∆ > @ ) > = > )? ) ρ + = ρ = ∂(ρ ∂ = ( ρ ' ⋅ ) ∂(ρ ∂ ) + ρ ( ⋅ ) + ρ ( ⋅ ) ) ) # ρ $ + ∂(ρ ∂ = = ∂(ρ ∂ ρ + ) ) ρ / + ρ ( ⋅ ) + ρ ( ⋅ + ρ ( ⋅ ) + ρ ( − ρ + ( − )⋅ = + " B ⋅ ) ) # " ( )⋅ ! & ρ − ! " + / # , = # , − " # # + 7 , ! " + , ) - # " , # " ) C 2DDEEE D D D DF G G D, G # < 3.2 Balance diferencial de cantidad de movimiento para un fluido invíscido # & )? ρ H ρ = 1 − ) 0 / ρ (ρ = ) 0 −∇ ) ) 3 3 > # - << (ρ ) −∇ = ∂(ρ ∂ ) + ∇ ⋅ (ρ ) = ∂ρ ∂ +ρ ∂ + ∇ ⋅ (ρ ∂ ∂ρ + ∇ ⋅ (ρ ∂ = ) +ρ ) + ρ ⋅∇ ∂ + ⋅∇ ∂ ρ = ρ >= ( 3 ) − ρ +∇ ) ) " 2 ρ $ − ρ +∇ = > ) ρ = ρ −∇ / # # ) < # & 3.3 Movimiento de fluidos como cuerpo rígido & & ! # ? # " # 1 # # 2 9 " 9 " D H 9> ! # 9 ( ) < ∇ = ρ[ − . # ( )] ) ? " # ? ! & # " I ! 1 ) / # # & " / )) 4 " ) ? " : J ! K" & # " " & " J # &" " # 1 ! # , • K " &" &" : & & # * # & 2 & • * • * & " & ) ? $ # &" ! # % A