Consider an incompressible fluid with known veocity components v1 = 3x1^2*X2^2*x3*t^3 and v2 = x1^2*x2^2*x3^2*t^3.
Find the remaining component v3; assume the fluid is incompressible.
Work:
v3 = v1 X v2, where X = cross product of v1 and v2
i column = 3x^2, x^2
j column = x^2, x^2
k column = x, x^2
i, j, k = Cartesian coordinates
v1 X v2 = (x^4-x^3)i - (3x^4 - x^3)j + (3x^4 - x^4)k
Solution:
v3 = xi - 3xj + 3k