The speed of water in a pipe

Water flows through a level pipe whose diameter changes along its length: wide, then narrow, then wide again. You will make the program find the speed and the pressure all along it, and where the pressure is lowest.

The idea. Continuity: $v = \dfrac{Q}{A}$ with $A = \pi\left(\dfrac{d}{2}\right)^2$. Bernoulli in a level pipe: $p = p_1 + \tfrac12\rho(v_1^2 - v^2)$, where $p_1$ and $v_1$ are at the start.

Your tasks.

1. Work out the area A at every point along the pipe.
2. Work out the speed v at every point.
3. Work out the pressure p at every point, and the lowest pressure.