A combined separating and throttling calorimeter recorded the following observations :

Pressure in the steam main \(=15\) bar Mass of water drained from the separate \(=0.55 \mathrm{~kg}\)

Mass of steam condensed after passing through the throttle valve \(=4.20 \mathrm{~kg}\)

Pressure and temperature after throttling \(=1 \mathrm{bar}, 120^{\circ} \mathrm{C}\)

Calculate the dryness fraction of steam in the main.