Circulation of two-dimensional flows Let C be the unit circle with counterclockwise orientation. Find the circulation on C of the following vector fields. a. The radial vector field F = <<x, y>> b. The rotation vector field F = << -y, x>>

facas9 2021-02-05 Answered
Circulation of two-dimensional flows Let C be the unit circle with counterclockwise orientation. Find the circulation on C of the following vector fields.
a. The radial vector field F=x,y
b. The rotation vector field F=y,x
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diskusje5
Answered 2021-02-06 Author has 82 answers
Similar to circle sphere is a two dimensional space where the set of points that are at the same distance r from a given point in a three dimensional space. In analytical geometry with a center and radius is the locus of all points is called sphere.
a) F(x,y)=x,y
Here the curve C is the unit circle x1+y2=1
The parametric equations are
x=cost,y=sint
dx=sintdt,dy=costdt
the flux of F across the curve C is
CFn^ds=CpdyQdx
CFn^ds=Cxdyydx
CFn^ds=01(cost)costdtsin(sint)dt
CFn^ds=011dt=1
b) F=y,x
Here
p=-y, Q=x
CFnds=Cydyxdx
CFnds=∈it01sintcostdtcost(sintt)dt
CFnds=010dt=0
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