Saturated water$/$steam mixture at temperature$$T$=537\mathrm{.}09$ K $$flows through a horizontal uniformly$$heated pipe with diameter$110$ mm and length $35$ m$.$

Calculate the total pressure change $$p $=$ p$2-$ p$1$over the pipe length when the mass flow rate of$$saturated water at the inlet is $4\mathrm{.}5$ kg$/$s and exit$$thermodynamic equilibrium quality is xex$=0\mathrm{.}65.$

Assume the same water$/$steam properties everywhere.

Assume wall roughness $0\mathrm{.}01$ mm$.$

Neglect the local inlet and outlet losses.