I have 3 problems I need solved with step by step solutions. Thanks

Question

Robert · Accepted Answer

1.A two dimensional steady flow has velocity components ?=?, ?=? ;Show that the streamlines are 
rectangular hyperbolas ?2− ?2=?????.  
 Sketch the flow patterns. 
Solution 
 
For a two dimensional flow The equation for stream line is   
dx dy
u v
  
Given u=y and and v=x 
Substituting in the above equation 
dx dy
y x
xdx ydy


 
 
Integrating on both sides 
 
2 2
2 2
xdx ydy
x y C
x y C

 
 
 
 
This is the equation for rectangular hyper bola. 
 
Flow patterns are Rectangular hyper bolas are 
 
 
 
 
 
 
 
 
Q2 )  If a velocity field is given by u = ay, compute the circulation around a circle of radius r =1 about 
the origin. Check the result by using Stokes theorem.

I have 3 problems I need solved with step by step solutions. Thanks

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