00:01
Hello, the question deals with application of partial derivatives given a velocity field if expressed as 3y square plus 2 i cap plus 6xy j cap.
00:17
First we find the curl of the given velocity field which is equal to determinant i cap, j cap, k cap, del del x, del by del by del y, del by del by del z, 3y plus 2, 6xy, 0, and on computing the derivative, it is equals to i -cap 0 minus 0, minus 0, plus k -cap 6x0, 6y, minus 6y and it is equals to 0.
01:07
So we have that the given velocity field is a conservative and path independent also the potential function exists and for this.
01:43
Compare del by del x of the given function f i cap plus del by del f with respect to y k cap plus del f by del s k cap is equals to three y square plus i cap plus six x y on comparing, we have del f by del x is equal to 3y square plus 2.
02:27
Integrating both sides, f is equal to integration of 3y square plus 2 with respect to x and it is equals to 3xy squared plus 2x plus a where a is integrating constant.
02:51
Also, del f by del y is equals to 6xy...