Momentum Balance3

Momentum Balance3 - Momentum Balance[Sum of the forces[rate of momentum in[rate of momentum out]=0 •[Sum of the forces o External forces o

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Unformatted text preview: Momentum Balance [Sum of the forces]+[rate of momentum in]-[rate of momentum out]=0 • [Sum of the forces] o External forces o Pressure force (use gauge pressure) • [rate of momentum in] o m’vin • [rate of momentum out] o m’vout δv + ρv • ∇v = − P + ∇τ + ρg ∇ δt δv ρ + ρv • ∇v ≡ Acceleration δt − ∇P ≡ Net Pr essure ∇τ ≡ Viscous ( Frictional Force) ρg ≡ Gravitational Force ρ Solve problems with microscopic momentum balance 1. Shell Balacne: Obtain DE by doing this 2. Simplify from the PDE ρ( ρ( δv x δv δv δv δP δ τ xx δ τ yx δ τ zx + vx x + v y x + vz x ) = − + + + + ρg x δt δx δy δz δx δx δy δz δv x δv δv δv δ 2v δ 2vx δ 2vx δP + vx x + v y x + vz x ) = − + µ ( 2x + + ) + ρg x δt δx δy δz δx δx δy 2 δz 2 ...
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This document was uploaded on 09/26/2010.

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