Cátedra de Mecánica del Continuo – FI-UNER Cursado: Primer cuatrimestre de 2008 Material de Estudio Tema VII: Balance macroscópico de energía Introducción + = + + ! # $ % & " ! " Energía interna Trabajo Calor + Energía cinética ' ( ) * Energía interna y calor $ ! + , - . / % ! ! " " 0 1 % 2 1 3 4 5 % 4 $ 6 + . + + . ρ " . 3 +. + . 3 +(& . + . + . 7 $ % + . + . 89 +(&7. +9. 6 + . 6 $ + 6 . + . 4 6 + . − ⋅ +(&:. Balance macroscópico de la energía 3 ) ρ + . 7 <7 ρ 8 7 7 + = ⋅ ⋅ + . + + . ρ ⋅ − + . 7 ⋅ +(&;. +(&;. 6 # = ;>+ % +(&;. 1 7 4 6 6 + . 8 ' ;&7. % + . 2 $ ? ⋅ ⋅ + + . + . ρ ⋅ ? − ⋅ + . + +:&@.. 7 ρ = 7 + . = = = + 7 ∂ + ρ ∂ 7 + . + 7 ∂ + ρ ∂ 7 + . + 7 ρ 7 + . ρ + . 5 7 + 7 ρ + ( + 7 + . (&> − + 7 ∂ + ρ ∂ 7 + . + 7 +(&;. )⋅ = ρ + . ρ + . ( + ρ + . − ⋅ ⋅ 7 7 7 7 7 + ( ⋅ ) + ( ⋅ ) + ( ⋅ ) )⋅ + + . 7 + . ρ ⋅ − + . ⋅ +(&>. 2 $ % 6 # 6 $ 89 ! φ8 ρ + . 7 + + . 8 9∇ φ $ ": ! 7 " + ρ + + . 7 7 + + +(&>. ( − )⋅ = ⋅ ⋅ + . − + . ⋅ +(&A. * & 1 8 1 8B ) ⋅ ⋅ = + . = − − ⋅ ⋅ + ⋅ ⋅ − + . + . ⋅ ⋅ + . + . − ⋅ + +(&(. ⋅ ⋅ + . 6 & 6 & +(&(. ⋅ ⋅ + . =− − ⋅ + . + ⋅ ⋅ +(&C. + . * ) =− +(&@. ⋅ +(& B. + . =− + ⋅ ⋅ + . (&@. 0 % + + 8B ρ + . D (& +(&(. +(& B.. . 7 7 +(&A. + + ρ + − 7 7 + + + ρ ( ⋅ ) + +(& . & . 6 & % : =− 6 + 1 & / # , 6 +(& . $ 8± + 7 8 . +(& . ρ : + 7 4 + + ρ − ρ : 7 + + + =− ρ + +(& 7. EF $ % ! − + ρ = : 7 : = 7 + + + + + + ρ : 7 : − ρ ρ − 7 + + + + + + +(& 7. ρ ρ +(& :. : = + 7 + + ρ : − + 7 + + ρ =ρ 6 ? % − + 7 ≈ 7 +(& :. 7 + + ) 7 + + + − ρ 7 2 7 2 + ρ − + + 2 7 7 + + + + + ρ =− +(& ;. ρ = + = . 7 7 + + + 7 − ρ + 7 3 + + =− ρ + +(& >. +(& >. % 6 ! " % 6 2 +(& >. " )ω= 3 ) • 6 "+ ω = ! • > B. 6 +ω = ! " < B. / % = ) % + (& (&:. 5 % − = + +(& A. + . 5 (& A ! +(& >. 7 7 D + + ρ (& ( − ) 7 7 + + ρ = −ω − + + (& >. " +(& (. . + (& A. ; 2 % (&; ω= ' , =B (& ( ) 7 7 + + = ρ 7 + 7 + +(& C. ρ ) . $ 2 2 . . & . 5 . 5 % . D % % 3.1 Pérdida de carga y potencia en el eje % 6 4 +(& (. ) = ! ! ; + 4 6 6 . +(& @. G ! G " ! " 2 +(& @. G 4 % 4 % + 6 . % + % . / ω= ω! +(&7B. ! 6 6 % Apéndice (&> φ8 ∇ ⋅ ( ρϕ ) = ∇(ρϕ ) ⋅ = ρ∇(ϕ ) ⋅ + ρϕ (∇ ⋅ ) = ρ∇(ϕ ) ⋅ + ϕ∇ ⋅ ( ρ ) (&A 4 8 9∇φ + ϕ∇( ρ ) ⋅ + ρϕ (∇ ⋅ ) = ρ∇(ϕ ) ⋅ + ϕ [∇( ρ ) ⋅ + ρ (∇ ⋅ (> ρ + . ρ + . ρ + . ρ + . = ⋅ ⋅ + . 7 7 7 7 7 7 7 7 + ρ + + . + ρ + + . + ρ + + . + ρ + + . − 1 + . 7 7 7 7 7 7 7 7 + ( − )⋅ − + ( − )⋅ + + ( − )⋅ + + ( − )⋅ + + . + . + . + . ρ ⋅ ρ∇ϕ ⋅ − ρϕ ( ⋅ ) + ' 2 2 (&A − ⋅ + . = ) 6 6 6 ⋅ ⋅ + . ∇ ⋅ ( ρϕ ⋅ 2 = + . ϕ∇ ⋅ ( ρ ∂ (ϕρ ) ∂ + . ) = = )]