Question

Let T be the triangular region with vertices (1,0,0)(1,0,0), (0,1,0)(0,1,0), and (0,0,1)(0,0,1) oriented with upward-pointing normal vector.

A fluid flows with constant velocity field v=4i+6j m/sv=4i+6j m/s. Calculate:
(a) The flow rate through T
(b) The flow rate through the projection of T onto the xyxy-plane [the triangle with vertices (0,0,0)(0,0,0), (1,0,0)(1,0,0), and (0,1,0)(0,1,0)]

Assume distances are in meters.

(a) ∬Sv⋅dS=∬Sv⋅dS=  
(b) ∬Sv⋅dS

Answer 1