Supplemental Materials for "Extension of a Quasi-Two-Dimensional Time-Domain Analytical Solution for Transient Pressurized Flow to Viscoelastic Pipes"

This additional text serves to enhance the main paper titled "Extension of a Quasi-Two-Dimensional Time-Domain Analytical Solution for Transient Pressurized Flow to Viscoelastic Pipes", but is not considered vital to support the science presented in the paper. It includes the proof of some equations and appendices. These elements are provided separately to prevent the original manuscript from becoming overly lengthy.