  The paper shows how to optimize a water level sensor consisting of a cylinder
with spiraling metal stripes on the side, using a powerful Python library
FEniCS. It is shown how to reduce a 3D Laplace equation to a 2D, using a
spiraling coordinate system; how to specify the correct boundary conditions for
an open region; how to convert the partial differential equation to a
variational form for FEniCS; and how to calculate the capacitance. Then the
FEniCS code is shown that solves the Laplace equation and calculates the
capacitance. The further numeric experiments show that there is an optimal
combination of the spiral frequency and the width of the stripes that maximizes
the sensitivity of the sensor. The Python code is given to calculate the
optimum.
