P4 [30 pt]: A 2D velocity field is
$$u(x, y,t) = \frac{U}{L^2}x^2 cos\omega t$$
$$v(x, y, t) = \frac{U}{L^2}xy sin\omega t$$
U, L, and $$\omega$$ are constant.
a) Find the acceleration field [a = ?]
b) Find the equation for streamlines that passes through x = y = 1 at t = 0
[y(x) = ?]
*Note: for question (a), only x-component of a is required [ax =?]; you will get an extra +5
points if you also calculate y-component of a