Integral of a Vector Field over a Surface

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Presentation transcript:

Integral of a Vector Field over a Surface Flux integrals

What is flux? Uniform fluid flow Volume of fluid passing through surface in time interval Dt Uniform fluid flow “Field” = velocity of fluid at each point Flat surface of area A, face on to flow “Flux” = volume rate of flow

What is flux? Volume of fluid passing through surface in time interval Dt Uniform fluid flow Flat surface of area A, tilted to flow

Why cos q ? Slice into thin horizontal disks and re-stack Volume of right-angle cylinder Slice into thin horizontal disks and re-stack Slantwise cylinder

What is flux? Volume of fluid passing through surface in time interval Dt Uniform fluid flow Flat surface of area A, tilted to flow Flux through surface:

Sign of F

Non-uniform flow, curved surfaces

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