1. Given a solenoidal velocity field and a body force field defined as
$\vec{V} = u(x, y)\hat{i} + v(x, y)\hat{j} + 0\hat{k}$
$u(x, y) = \frac{y^3}{3} + 2x - x^2y$
$v(x, y) = xy^2 - 2y - \frac{x^3}{3}$
$\vec{f} = 0\hat{i} + 0\hat{j} - g\hat{k}$
a.) Assuming inviscid flow, find the pressure field $p(x, y, z)$
b.) Find a function $f(x, y) = 0$ on which an inviscid surface boundary condition would be
satisfied. Hint – this is a particular value of $\psi(x, y) = \text{constant}$, where $\psi$ is the stream
function. Explain why this is the case.
c.) Calculate $\nabla p \cdot \hat{n}$ along this surface, where $\hat{n}$ is the surface normal.
