(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write a vector field equation which describes fluid flowing around a pipe of radiusrwhose axis is a circle of radiusRin the (x,y)-plane.

2. Relevant equations

x^{2}+y^{2}=r^{2}

Equation of a torus?

3. The attempt at a solution

What I've gathered from the question: the pipe is in the shape of a torus of radiusrand the circle of radiusRruns through the center of the inside of the pipe.

I know that two things describe this flow:

1. The magnitude of the flow decreases the farther away from the axis line on the inside of the torus that the point (x,y,z) is.

2. The flow goes either clockwise or counterclockwise around the origin in the (x,y)-plane. So the vector field equation for that piece is F(x,y)=<y,x> or F(x,y)=<y,-x>

Otherwise, I have no idea where to start.

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# Homework Help: Vector Field Describing Fluid Flow in a Torus

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