What do chemical engineers deal with while working that most people don't know?
Chemical Engineers work with dimensional analysis often. This is a form of mathematics mostly unknown to the non-engineer. The grandfather of these numbers is the Reynolds Number. Osborne Reynolds in the 1870's built a device to test fluid flow to determine laminar and turbulent flow and the transition between the two. His non-dimensional number N= (Dvρ)/ս That is: Diameter of the pipe, times velocity times density of the fluid and all that divided by the viscosity of the fluid. Reynolds gave a complete demonstration and lecture before the Royal Society. It has been the unique pleasure of mine of having seen the original Reynolds equipment in operation at The University of Manchester in England at the invitation of Professor Richards.
There are other forms of the Reynolds number used in open channel flow and mixing of fluids and other materials in a tank. Dimensional less numbers are used in gravitational influence on processes and heat transfer. Aerodynamics also uses dimensional less numbers for some calculations.
Einstein used dimensional analysis in the early study of specific heats of solids and their connection with quantum phenomena in 1911.
Matrix math is used to evaluate dimensional less formula. Cramer's rule is used to reduce any large matrix to a solvable 3x3 matrix.