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Chain-rule issue on Laplacian equation
Thanks for the advice, it was spot on! The correct formula for the Laplacian in polar coordinates is Δ2ψ = r-1δ/δr(r*δψ/δr) + r-2(δ2ψ/δθ2) Plugging in, we have: r-1δ/δr[-r*cαr(α-1)sin(αθ)] + r-2[cα2rαsin(αθ)] Differentiating the first term and simplifying, we have -cαr(α-2)sin(αθ) -...- NinjaPeanut
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- Forum: Calculus and Beyond Homework Help
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Chain-rule issue on Laplacian equation
Homework Statement "The flow of a fluid past a wedge is described by the potential ψ(r,θ) = -crαsin(αθ), where c and α are constants, and (r,θ) are the cylindrical coordinates of a point in the fluid (the potential is independent of z). Verify that this function satisfies Laplace's...- NinjaPeanut
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- Laplacian
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- Forum: Calculus and Beyond Homework Help