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## Mixing of Air Streams at Different Pressures – A Graphical Approach

**Introduction**

Mixing air streams is a common scenario in many engineering applications. For the purposes of this discussion, let the two input streams be A and B, and the resulting (output) stream C. Normally, we would know the conditions of A & B and the requirement would be to determine the conditions of C. However, sometimes the requirement would be to determine B, knowing A and C .

Air properties that are relevant for the analysis of such situations are:

Temperature – measurable

Pressure – measurable

Density (or specific volume) – not measurable

Moisture content (also referred to as specific humidity, relative humidity, percent saturation, vapor pressure) – relative humidity is measurable.

**Background of the problem**

One basic assumption is that energy losses due to flow behavior can be neglected, which leads to the premise that the energy (specific enthalpy * mass) of the output stream is equal to the sum of the energies of the input streams. It is also assumed that there is no mass loss during the mixing process.

Direct measurement of enthalpies is not possible. Therefore, they must be calculated using psychrometric relationships. Mass flow rates can be derived from volumetric flow rates and densities. Density, which is not directly measurable, must be calculated from pressure, temperature and relative humidity. So, the measurable parameters are pressure, temperature and relative humidity, and the parameters that need to be determined are enthalpy and mass flow. It is obvious that psychrometric relations must be used to solve such problems.

**Variations of the problem**

1. A, B and C are under the same pressure (the temperatures of A and B can be the same or different)

2. A and B are under the same pressure, but C is under different pressure (same or different temperature)

3. A, B and C are under different pressures. (same or different temperatures)

**General solution method**

For** Type 1** problem, knowing the temperature and relative humidity of the inlet streams (A & B) it is possible to mark points (say P & Q) corresponding to the conditions of A & B. Draw a line between P & Q and find a point X such that the distances between X and P and X and Q correspond to the mass flow rates of B & A. The psychrometric values at point X would then indicate the state of the outlet stream. This type of situation is easy to show on a normal psychrometric chart because the pressures of all three streams are the same.

For** Type 2 **problem, where the inlet streams are at the same pressure, the procedure is identical to that of type 1, up to the stage of finding point X. However, since the outlet stream is at a different pressure, the psychrometric properties at point X, as indicated on that psychrometric map, do not would be correct for stream pressure C. In this case the solution would be to superimpose the chart for pressure C over the previous chart and read the values from the new chart.

For **Type 3 **problem, we would need 3 cards, one for each of the 3 involved pressures. The same approach could be used because enthalpy does not depend on pressure.

**Conclusion**

A graphical solution to the problem of mixing currents would be much easier if the psychrometric relations at all three pressures could be available from the same map. Although superimposing complete psychrometric charts on top of each other will be so confusing as to make the scheme impractical, it is possible to draw only the relevant lines for each of the two or three pressures concerned on the same chart and use the dynamic readout mechanism to display a set of values of the psychrometric properties of the three streams concerned.

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