Lecture #3 Governing Equations Ehsan Roohi Ferdowsi...

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Lecture #3 Governing Equations Ehsan Roohi Ferdowsi University of Mashhad 1

Transcript of Lecture #3 Governing Equations Ehsan Roohi Ferdowsi...

Page 1: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

Lecture #3

Governing Equations

Ehsan Roohi

Ferdowsi University of Mashhad

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Page 2: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Read Vector algebra

Don’t Cover

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Page 4: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Read the next

Page 5: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Page 6: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Page 7: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Page 8: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Read Example 2.1

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Page 10: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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Page 11: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

11 For Incompressible flow: div (V)=0

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Page 13: Lecture #3 Governing Equations Ehsan Roohi Ferdowsi ...e.roohi.profcms.um.ac.ir/imagesm/1019/stories/PDFs/Aerodynamics/... · p(x, y, z) p(r, e, The gradient of p, V p, at a given

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mv

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Divergence Theorem

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HW: Derive Bernoulli's

Eq.

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CV

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P=P_Inf on the CV U1=Cte., U2= F(y)

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Body force is negligible

Consider momentum Equation in integral form

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