Quiz.II - relations If you are using a polar coordinate system use 29 29 1 1 v 1 = ∂ ∂-∂ ∂ = × ∇ = ∂ ∂ ∂ ∂ = ⋅ ∇ ∂ ∂-=

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AE 3003 Quiz II Closed Book and Notes - Fall 1998 1. Briefly define or explain the following terms. a) Vorticity b) Pathline c) Streamline d) Substantial derivative (also called Material derivative) e) Doublet 20% 2. Show that in 2-D flows, streamlines ( ) lines constant = ψ are orthogonal to velocity potential lines ( Φ =Constant lines). 30% 3. Given the velocity field for a doublet: θ sin r C = Determine if this field satisfies (a) continuity, and (b) irrotationality. Hint: This problem may be done in polar coordinates or the Cartesian coordinates. If you choose to use the Cartesian coordinate system, you may want to use the following
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Unformatted text preview: relations: If you are using a polar coordinate system, use: ( 29 ( 29 1 1 v 1 = ∂ ∂-∂ ∂ = × ∇ = ∂ ∂ + ∂ ∂ = ⋅ ∇ ∂ ∂-= ∂ ∂ = k v r rv r V v r rv r V r r v r r r & 50% : : : from v and u Compute sin cos = × ∇ = ⋅ ∇ ∂ ∂-= ∂ ∂ = = = V ality Irrotation V Continuity x v y u r y r x C...
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This note was uploaded on 10/23/2011 for the course AE 3003 taught by Professor Yeung during the Fall '08 term at Georgia Institute of Technology.

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