Question

A fluid is flowing through space following the vector field F(x, y, z) = yi −...

A fluid is flowing through space following the vector field F(x, y, z) = yi − xj + zk. A filter is in the shape of the portion of the paraboloid z = x^2 + y^2 having 0 <= x <= 3 and 0 <= y <= 3, oriented inwards (and upwards). Find the rate at which the fluid is moving through the filter.

PLEASE SOLVE ON MATLAB, when I did it by hand I got 18.

Math   Calculus   
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Answer #1

% matlab code

% Flow Rate Inward is given by double integral;
f=@(x,y) -2.*y.*x.^3-2.*y.^3;
q = integral2(f,0,1,0,1);
disp('The Flow Rate Inwards in units^3/sec : ')
disp(q)
disp('The Flow Rate Outwards in units^3/sec : ')
disp(-q)

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