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⟩

Question

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⟩

diskusje5 · Accepted Answer

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=cos⁡t,y=sin⁡t  dx=−sin⁡tdt,dy=cos⁡tdt  the flux of F→ across the curve C is  ∫CF→n^ds=∫Cpdy−Qdx  ∫CF→n^ds=∫Cxdy−ydx  ∫CF→n^ds=∫01(cos⁡t)cos⁡tdt−sin⁡(−sin⁡t)dt  ∫CF→n^ds=∫011dt=1  b) F→=⟨−y,x⟩  Here  p=-y, Q=x  ∫CF→nds=∫C−ydy−xdx  ∫CF→nds=∈it01−sin⁡tcos⁡tdt−cos⁡t(−sin⁡tt)dt  ∫CF→nds=∫010dt=0

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>>

Answered question

Answer & Explanation

New Questions in High school geometry