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Analyzing Flow through Surfaces in Regional Integration

This study examines the flow through an elemental surface by integrating the z-direction components of velocity. Through this regional integration approach, we derive the flow rates across upper and lower surfaces in all three spatial directions. By computing flow through the element of the surface, we can accurately quantify the overall flow rates resulting from velocity components, enhancing our understanding of fluid dynamics in various regional contexts.

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Analyzing Flow through Surfaces in Regional Integration

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  1. Vz Vy Area = δar Vx Flow through an element of the surface(Regional Integration) Computing by integration over the region, we get, for the flow through one surface resulting from the z-direction components of velocity: The expanding for upper and lower surfaces and for all three directions we get Rate of flow through the element

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