Consider a potential vortex positioned a distance a above a horizontal wall, immersed in a free...

  

 

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Consider a potential vortex positioned a distance a above a horizontal wall, immersed in a free stream parallel to the wall with speed U as shown in the figure. The vortex has clockwise circulation I. The flow is steady, irrotational, and incompressible. (a) Write out the complex potential (z) for this flow, as well as the stream function (x, y) and velocity potential (x, y). Find the velocity components u (x, y) and v(x, y). (b) U a Find the net pressure distribution on the surface p(x,0) - Poo where po is the pressure far away from the vortex. (d) Compute the total net force (per unit depth) on the entire surface from - < x < x. What is the force in the limit as a ? You may find the values of these integrals useful, where C is a constant: C If x + dx = 2 C 1 ( + ) d = 50 dx 20 Consider a potential vortex positioned a distance a above a horizontal wall, immersed in a free stream parallel to the wall with speed U as shown in the figure. The vortex has clockwise circulation I. The flow is steady, irrotational, and incompressible. (a) Write out the complex potential (z) for this flow, as well as the stream function (x, y) and velocity potential (x, y). Find the velocity components u (x, y) and v(x, y). (b) U a Find the net pressure distribution on the surface p(x,0) - Poo where po is the pressure far away from the vortex. (d) Compute the total net force (per unit depth) on the entire surface from - < x < x. What is the force in the limit as a ? You may find the values of these integrals useful, where C is a constant: C If x + dx = 2 C 1 ( + ) d = 50 dx 20

Answer rating: 100% (QA)

a The complex potential z for this flow can be written as z Uz F 2 lnz a where z x iy is the c... View the full answer