Mixing steam at different pressures

[Morey]

Homework Statement

steam flow through a line is 3.5 kg/s at 650 kps and .9 dry. It enters a mixing line where it exits at 800kpa, dry and saturated. The mixing steam is throttle from 2000kps to 800kpa. What is the mass of throttling steam added to have a final mixture of 800 kpa dry steam.

Homework Equations

steam tables
q=mcΔT

The Attempt at a Solution

@650: hf=684 hfg=2076 hg=2552
@800: hf=721 hfg=2048 hg=2769
@2000:hf=908 hfg=1890 hg=2798

 

[Chestermiller]

To do this, we need to assume that the throttled steam was saturated. Otherwise the problem can't be solved.

Enthalpy rate of entering 650 kpa stream = 3.5((0.1)(684)+(0.9)(2552))=8278.2 kJ/s
Specific enthalpy of 2000 kPa steam = 2798 kJ/kg
Specific enthalpy of 800 kPa product steam =2769 kJ/kg

From heat balance on system, 8278.2 + 2798 w = (3.5+w) 2769

w = 48.7 kg/s