E3.14 Adiabatic Mixing of Air Streams

Example 3.14: A stream of 2500 cfm of outdoor air at 40 °F dry-bulb temperature and 35 °F wet-bulb temperature is adiabatically mixed with 7500 cfm of recirculated air at 75 °F dry-bulb temperature and 50% relative humidity (rh). Find the dry-bulb temperature and thermodynamic wet-bulb temperature of the resulting mixture.

Solution

Locate state 1 and read the properties

υ₁ = 12.65 ft³/lb_a

υ₂ = 13.68 ft³/lb_a

Mass flow rates of air streams are

m_a1 = 2500/12.65 = 197.5 lb_a/min

m_aw = 7500/13.68 = 548 lb_a/min

(Line 3-2)/(Line 1-3) = m_a1/m_a2 = 197.5/548 = 0.36

The length of line segment 1-3 is 1/(1+0.36) = 0.735 times the length of entire line 1-2.

Using a ruler, locate state 3

t₃ = 65.9 °F, and t₃^* = 56.6 °F