Unformatted text preview: ace ∙ The mass flow through an area A is so has units of mass per unit time per unit area so the total rate of mass flowing into V thorough S is ∙ and ∙ point out so this is the rate at which mass leaves the volume. So the rate at which mass inside grows has to equal the rate at which mass flows in ∙ so ∙ 0 ∙ 0 And This is an integral form of the continuity equation We can apply the divergence theorem to the second term and get ∙ 0 And ∙ 0 This has to be true for any dV we can think of, so the think inside the integral has to be zero everywhere ∙
This is the differential form of the continuity equation 0 Momentum Equation Newton’s second law is Newton’s second Law First we work on an expression for the right side of the equation Consider some volume V The mass within the volume is The momentum within the volume is So the rate of change of momentum within the volume is That is what happens to the fluid initially within the volume. What happens as more fluid enters...
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- Fall '10
- Noncototient, January 20, total rate