Using EES (or other) software, calculate and plot the entropy change of air across the normal shock for upstream Mach numbers between 0.5 and 1.5 in increments of 0.1. Explain why normal shock waves can occur only for upstream Mach numbers greater than Ma 5 1.

Apiping systems consists of 6 m of 6-std type k and 12 m of 4-std type k, both drawn copper tubing. the system conveys ethylene glycol at a rate of 0.013 m3/s. the pressure drop across the system is to be calculated. there are two 90° elbows in the 6-in pipe, a reduction from the 6-in pipe to the 4-in pipe and four 90° elbows in the 4-in pipe. all fittings are soldered (same as flanged) and regular. the inlet and outlet of the system are at the same height.