C4_Isothermal_Equations_of_Change_1

C4_Isothermal_Equations_of_Change_1 - Equations of Change...

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Equations of Change for Isothermal Systems The equation of continuity Mass balance over a fixed elementary volume () xx x yy y zz z xyz t yz u u xz u u xy u u ρ ρρ ΔΔΔ ⎡⎤ =Δ Δ ⎣⎦ +Δ Δ ⎢⎥ ( ) . y u uu tx y z ⎛⎞ ∂∂ ⎜⎟ =− + + =− ∇ ⎝⎠ u ( ) is called divergence of , and for incompressible fluids .0 ∇∇ = Mass influx (inward arrows) Mass outflux (outward arrows) x y z x y z
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Equations of Change for Isothermal Systems The equation of continuity Mass balance over a moving elementary volume () ( ) ( ) ( ) D .. . tD t t ρ ρρ ∂∂ =− ∇ =− ∇ + + ∇ =− ∇ ⎡⎤ ⎣⎦ uu u u u is called material (also, substantial/particle) derivative is called local rate of change of at a given point D/ / Dt t u is called convective (or advective ) derivative, which is the change of as a result of convection of the particle from one location to another where is different ( ) Df .
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C4_Isothermal_Equations_of_Change_1 - Equations of Change...

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