Water at $40^oc$ is continuously sprayed into a pipeline carrying 5 tons of steam per hour at 5 bar, $300^oc$. At a section downstream where the pressure is 3 bar, the quality is to be 95%.

Solution:

Enthalpy at inlet = enthalpy at outlet

Enthalpy of water + enthalpy of steam = enthalpy of mixture

$M1 × hf (at 40^oC) + M2 × hg (at 5bar ; 300^oC superheated) = (M1 + M2) (hf + x hfg) (at 3bar pressure)$

M1 (167.6) + 5 × 3061 = (M1 + 5) x (561 + 0.95 × 2164)

M1 = 0.9