Pressure Drop in Compressible Flow

This problem is a fundamental fluid mechanics problem that demonstrates pressure drop as liquid flows in a pipeline. The image below shows the work that solves for the outlet pressure of the following description of a system:

Methane gas is being pumped through a 305-m length of 52.5-mm-ID steel pipe at the rate of 41.0 kg/m2 · s. The inlet pressure is p1 = 345 kPa abs. Assume isothermal flow at 288.8 K. The viscosity is 1.04 × 10 –5 Pa · s.

The work below is a situation where a non-linear equation that is difficult to solve by hand is solved using numerical solutions, specifically Newton's Method in MATLAB.