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6155-Conservation of Momentum

6155-Conservation of Momentum - Conservation of Momentum...

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Conservation of Momentum: Rate of momentum accumulation in control volume equals rate of momentum entering control volume less rate of momentum leaving control volume plus summation of forces acting on control volume X-momentum: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 y x z z zx y x z zx z x y y yx z x y yx z y x x xx z y x xx z y x x P z y x P z y x y x z z uw y x z uw z x y y uv z x y uv z y x x uu z y x uu z y x u t + + - + + - + + - + - + Χ + + - + + - + + - = τ τ τ τ τ τ ρ ρ ρ ρ ρ ρ ρ Noting That: ( 29 ( 29 ( 29 x x uu x x uu x x uu + = + ρ ρ ρ . . . x x x P x P x x P + = + . . . ( 29 ( 29 ( 29 x x xx x x xx x x xx + = + τ τ τ . . . Insert in Momentum Equation
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X-momentum: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 Χ + + + + - = + + + zx z yx y xx x x P uw z uv y uu x u t τ
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