The college of Science, in the Department of Mathematics, discussed a master’s thesis entitled “ numerical study of compressible Newtonian fluid flows” for postgraduate student Fatima Abdul Razzaq Muhammad. The aim of the thesis is to present numerical solutions to the partial differential equations governing the flow of compressed Newtonian fluids by developing an algorithm based on Galerkin's finite element method to understand the flow of compressible and incompressible fluids.