The stream function for a flow field is given as: p= K (x y) +...
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The stream function for a flow field is given as: p= K₁ (x² − y²) + K₂ ln(x² + y²) where K₁ and K₂ are constant. a) Find the stagnation point(s) coordinates in terms of K₁ and K₂ i.e. where u=0 and v=0. b) Is this flow incompressible? Why? c) Is this flow irrotational? Why? d) Derive the velocity potential function in polar coordinate system. e) Derive the velocity components in polar coordinate system. f) Derive the stream function in Cartesian and in polar coordinate systems. g) Sketch a few streamlines and a few velocity potential lines for K₁=K₂=1. Using the polar forms might be easier. Separate r and 0, vary from 0 to 27 with a small increment (0.01 rad) and calculate r. The stream function for a flow field is given as: p= K₁ (x² − y²) + K₂ ln(x² + y²) where K₁ and K₂ are constant. a) Find the stagnation point(s) coordinates in terms of K₁ and K₂ i.e. where u=0 and v=0. b) Is this flow incompressible? Why? c) Is this flow irrotational? Why? d) Derive the velocity potential function in polar coordinate system. e) Derive the velocity components in polar coordinate system. f) Derive the stream function in Cartesian and in polar coordinate systems. g) Sketch a few streamlines and a few velocity potential lines for K₁=K₂=1. Using the polar forms might be easier. Separate r and 0, vary from 0 to 27 with a small increment (0.01 rad) and calculate r.
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a To find the stagnation points we need to solve for the values of x and y where the velocity components u and v are both equal to zero Given the stream function Kx yK lnx y we can find the velocity c... View the full answer
Related Book For
Fundamentals Of Momentum Heat And Mass Transfer
ISBN: 9781118947463
6th Edition
Authors: James Welty, Gregory L. Rorrer, David G. Foster
Posted Date:
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