This requires a numerical differential equation solver for a thorough study. An open-ended extension of the original problem. This is enough for a full term project. Similar to the original problem, but movement is by angle instead of along a straight line. Another inverse problem.
Honest attempts deserve high praise.
Give this only to motivated students. A willingness to try many things. A thorough understanding of the preceding problems. For example, you might consider a pipe with a equilateral triangular cross section and a rectangular valve covering.