Air flowing with a speed of 0.4 m/s in the direction of a vector $[-1,-1,1]$ goes through a closed loop C joined by the following points in order: $(1,1,0) \rightarrow (1,0,0) \rightarrow (0,0,0)\rightarrow(0,1,1)\rightarrow(1,1,1)\rightarrow(1,1,0)$
Calculate the volume of air flowing through C per second.
The answer to this problem should be √3/5 m$^3$/s, I calculated the flow to be 3/5 m$^3$/s. Where did I go wrong?
My solution: Noting that the divergence of the vector field of flow is 0 everywhere (seeing that it is uniform), I split the unit cube in the first octant into two parts split by the curve C and both parts of the cube gave 3/2 and -3/2 for the top and bottom halves respectively. Hence multiplying this value by 0.4 m/s gave me my answer of 3/5 m$^3$/s.