Consider the two-dimensional flow given by V = (x1 + x2)i1 + (x12 - x2)i2. Is th

Question

Consider the two-dimensional flow given by V = (x1 + x2)i1 + (x12 - x2)i2. Is the flow compressible or incompressible? Is the flow irrotational? Determine the circulation around a square defined by x1 = 1, x2 = 1, x3 = 0; Verify the Stokes theorem for the current problem (X V).ndGamma = V. dI Consider the two-dimensional flow given by V = (x1 + x2)i1 + (x12 - x2)i2. Is the flow compressible or incompressible? Is the flow irrotational? Determine the circulation around a square defined by x1 = 1, x2 = 1, x3 = 0; Verify the Stokes theorem for the current problem (X V).ndGamma = V. dI

Explanation / Answer

1) u=x1+x2 ;
v=x1^2-x2 ;
for continous flow du/dx1 + dv/dx2 = 0 ;
1-1=0 hence continous flow ;

2) for irrotational flow ;
dv/dx1=du/dx2 ;
2x1 is not equal to 1 hence rotaional flow ;

3) = integration(0.5**dA) = -4

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