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Unformatted text preview: s with a different choice of constant. So we have some room to choose how we construct our stream functions. We can chose our stream functions in such a way that for two constants c1 and c2 the value of the mass flow between ab and cd is equal to ∆ We still have some room for arbitrariness, but if we pick the c value for any one streamline, the rest can be determined from the mass flow rule Flow velocities from stream functions Consider two stream functions close together Since they are very close together we can assume V is constant along Δn between them ∆1 ∆ψ So ∆ ∆ Consider the limit ∆ lim ≡ ∆→ ∆ We can break down Δn into ‐Δx and Δy and the mass flow through these must be the same, so ∆ ∆ ∆ ∆ Taking the limit again we find that We also know by the chain rule that So we can see that So if is known we can calculate u and v everywhere For an incompressible case we can define another stream function / And we have for incompressible flows Since we have divided by ρ instead of mass fl...
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This note was uploaded on 01/19/2014 for the course AEEM 2042C taught by Professor Munday during the Fall '10 term at University of Cincinnati.

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