一道英文微积分题,关于vector field里line integrals的,A horizontal square has sides of 800 km running north-south and east-west.A wind blows from the west and decreases in magnitude toward the north at a rate of 10 m/s for every 400 km.Comp

一道英文微积分题,关于vector field里line integrals的,A horizontal square has sides of 800 km running north-south and east-west.A wind blows from the west and decreases in magnitude toward the north at a rate of 10 m/s for every 400 km.Comp
一道英文微积分题,关于vector field里line integrals的,
A horizontal square has sides of 800 km running north-south and east-west.A wind blows from the west and decreases in magnitude toward the north at a rate of 10 m/s for every 400 km.Compute the circulation of the wind counterclockwise around the square with the correct units!

一道英文微积分题,关于vector field里line integrals的,A horizontal square has sides of 800 km running north-south and east-west.A wind blows from the west and decreases in magnitude toward the north at a rate of 10 m/s for every 400 km.Comp
这是你们大学(SLU)的MATH 371 - Vector Analysis?
First of all,setup a coordinate system:
Let the positive x axis be west,+ yaxis be north.
From "A wind blows from the west and decreases in magnitude toward the north at a rate of 10 m/s for every 400 km" we can deduce that the horizontal velocity is constant,Vx,while the vertical velocity is Vy-10×(y/400),where Vx and Vy are constants thus we have a parametrization for the velocity field F(x,y)=.
The circulation,which is the line integral around the square,can be computed using Green's Theorem.Therefore circulation=double integral over 800*800 square of dQ/dx-dP/dy dxdy
dQ/dx=0,dP/dy=0,thus we end up with 0.
Another way to think of it is that the field is conservative.
Or else you could compute the line integral the slow way be definition,it depends on which stage of the game ur in right now.
Green's Theorem is just a handy dandy shortcut.
I hope I'm doing the right thing,cuz honestly,I'm taking the equivalent vector calc course at UBC,in Canada,...