Question

 A fluid flow is given by : V = x * y ^ 2 * i - 2y * z ^ 2 * j - (z * y ^ 2 - (2z ^ 3)/3) * k. Prove that it is a case of possible steady incompressible fluid flow Calculate the velocity and acceleration at the point [1, 2, 3] .

Answer 1

$\vec v=xy^2\vec i-2yz^2\vec j-(zy^2-\frac{2z^3}3)\vec k,$

$\vec v(1,2,3)=4\vec i-36\vec j+6\vec k,$

$\vec a=y^2\vec i-2z^2\vec j-(y^2-2z^2)\vec k,$

$\vec a(1,2,3)=4\vec i-18\vec j+14\vec k.$