Question 3.7: Two thousand cubic feet per minute (cfm) of air at 100 F db ......
Two thousand cubic feet per minute (cfm) of air at 100 F db and 75 F wb are mixed with 1000 cfm of air at 60 F db and 50 F wb. The process is adiabatic, at a steady flow rate and at standard sea-level pressure. Find the condition of the mixed streams.
A combination graphical and analytical solution is first obtained. The initial states are first located on Chart 1a as illustrated in Fig. 3-10 and connected with a straight line. Using Eq. 3-44b or another form of Eqs. 3-42 and 3-43, we obtain
\dot{m}_{a1} + \dot{m}_{a2} = \dot{m}_{a3} (3-42)
\dot{m}_{a1} W_{1} + \dot{m}_{a2} W_{2} = \dot{m}_{a3} W_{3} (3-43)
W_{3} = \frac{\frac{\dot{m}_{a1}}{\dot{m}_{a2}} W_{1} + W_{2}}{1 + \frac{\dot{m}_{a1}}{\dot{m}_{a2}}} (3-44b)
W_{3} = W_{1} + \frac{\dot{m}_{a2}}{\dot{m}_{a3}} (W_{2} – W_{1}) (3-46)
Using the property values from Chart 1a, we obtain
\dot{m}_{a1} = \frac{1000 (60)}{13.21} = 4542 lbma/hr
\dot{m}_{a2} = \frac{2000 (60)}{14.4} = 8332 lbma/hr
W_{3} = 0.0054 + \left[\frac{8332}{4542 + 8332}\right] (0.013 – 0.0054)
W_{3} = 0.0103 lbmv/lbma
The intersection of W_{3} with the line connecting states 1 and 2 gives the mixture state 3. The resulting dry bulb temperature is 86 F, and the wet bulb temperature is 68 F.
