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Aerodynamics Notes 08 - InclassProblem(Andersonexample2.4...

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In class Problem (Anderson example 2.4) Given ݑ ൌ ݕ/ሺݔ ൅ ݕ ݒ ൌ െݔ/ሺݔ ൅ ݕ Calculate the vorticity ߦ ൌ ׏ ൈ ܸ ሬറ ൌ ൦ ଓ̂ ଔ̂ ݇ ߲ ߲ݔ ߲ ߲ݕ ߲ ߲ݖ ݑ ݒ ݓ ൪ ൌ ۏ ێ ێ ێ ێ ۍ ଓ̂ ଔ̂ ݇ ߲ ߲ݔ ߲ ߲ݕ ߲ ߲ݖ ݕ ݔ ൅ ݕ െݔ ݔ ൅ ݕ 0 ے ۑ ۑ ۑ ۑ ې ൌ ଓ̂ሺ0 െ 0ሻ ൅ ଔ̂ሺ0 െ 0ሻ ൅ ݇ ߲ ߲ݔ െݔ ݔ ൅ ݕ ߲ ߲ݕ ݕ ݔ ൅ ݕ ൌ ݇ ሺݔ ൅ ݕ ሻሺെ1ሻ െ ሺെݔሻሺ2ݔሻ ሺݔ ൅ ݕ ሺݔ ൅ ݕ ሻሺ1ሻ െ ݕሺ2ݕሻ ሺݔ ൅ ݕ ൌ ݇ െሺݔ ൅ ݕ ሻ ൅ ݔሺ2ݔሻ െ ሺݔ ൅ ݕ ሻ ൅ ݕሺ2ݕሻ ሺݔ ൅ ݕ ൌ ݇ െ2ሺݔ ൅ ݕ ሻ ൅ 2ݔ ൅ 2ݕ ሺݔ ൅ ݕ ൌ ݇ െ2ሺݔ ൅ ݕ ሻ ൅ 2ሺݔ ൅ ݕ ሺݔ ൅ ݕ ൌ ݇ ሺ0ሻ This flow has a name. It is called an irrotational vortex
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Streamtubes Can a fluid parcel ever cross a streamline? No, there can be no component of velocity perpandicular to the streamline, since the velocity is tangent to the streamline If chose a closed curve C and find the streamlines through every point on the curve these streamlines will form a tube. All the mass that passes through C will stay in the tube forever by definition.
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