Question 13.7: Use of the Psychrometric Chart Find the five listed properti......
Use of the Psychrometric Chart
Find the five listed properties for atmospheric air in a building maintained at 70°F (21°C). The wetbulb temperature is measured to be 60°F (15.5°C), a typical interior condition in winter in heating climates.
Given: T_{db} = 70°F and T_{wb} = 60°F.
Figure: See Figure 13.6
Assumptions: The atmospheric pressure is the standard atmosphere, 14.696 psia.
Find: \phi, h, v, T_{dp}, and p_{vap}
This problem can be solved easily by using the IP psychrometric chart. Note that only one of the two independent variables (T_{db}) used to plot the chart is known, but two different independent properties are known. Hence, the problem can be solved.
First, nd the intersection of the 70°F dry-bulb vertical line and the 60°F wet-bulb line. This intersection is approximately at the 57% RH point.
At the same intersection point, the following values can be read by interpolation. The humidity ratio is 0.0088 lb_{w}/lb_{a}. The enthalpy is read from the scales at the upper left and bottom of the chart and determined as 26.5 Btu/lb_{a}. By interpolation the specific volume is 13.55 ft³/lb_{a}. A better approach than this rough interpolation is to calculate the specific volume from the partial pressure p_{vap} and the dry-bulb temperature by using the ideal gas law:
The partial pressure of water vapor p_{vap} cannot be found from the chart but is easy to find from Equation 13.14 since the humidity ratio W is already known:
W = 0.622 \times \left\lgroup \frac{ p_{vap}}{p_{tot} – p_{vap}} \right\rgroup (13.14)
p_{vap} = \frac{p_{tot}}{1 + 0.622/W} = \frac{14.696 psia}{1 + 0.622/0.0088} = 0.21 psiaAn alternate method of finding p_{vap} is to use the basic equation for the RH (Equation 13.6)
\phi = \frac{p_{vap}}{p_{sat}} (13.6)
p_{vap} = \phi \cdot p_{sat} = 0.57 \times 0.3633 psia = 0.21 psiain which the saturation pressure has been determined from the second column of Table 12.3.
The value of p_{vap} can be used in the aforementioned ideal gas law to find a more accurate value of the specific volume. The dew point is found at the intersection of the humidity ratio line (0.0088) and the saturation curve. The dew point is 54°F.
Comments
The psychrometric chart can be read to about a few percent accuracy. For better accuracy, the online HCB software, tables, or psychrometric equations can be used.
Although the availability of computer programs allow for more accurate and faster determination of the moist-air properties (as well as the conversion of different system of units and arbitrary atmospheric pressures), the psychrometric chart is still used extensively by HVAC professionals in several aspects of design and analysis.
| TABLE 12.3 | ||
| Values of Coefficients Appearing in Equation 12.12 | ||
| Coefficient | SI Units | IP Units |
| a | −5.8002206 × 10³ | [atex]−1.0440397 × 10^{4}[/latex] |
| b | 1.391499 | −1.1294650 × 10¹ |
| c | −4.8640239 × 10^{−2} | −2.7022355 × 10^{−2} |
| d | 4.1764768 × 10^{−5} | 1.2890360 × 10^{−5} |
| e | −1.4452093 × 10^{−8} | −2.4780681 × 10^{−9} |
| f | 6.545967 | 6.545967 |
\ln p_{sat} = a/T + b + c \cdot T + d \cdot T^{2} + e \cdot T^{3} + f \cdot \ln T (12.12)