Psychrometric Properties
A mixture of dry air (molecular weight 28.966) and water vapour (molecular weight 18.015) is known as moist air. Degree of freedom of moist air is 3.
1. Specific Humidity / humidity ratio
Humidity ratio (w) is defined as mass of water available in moist air per kilogram of dry air.
\[ w = \frac{mass of vapour}{mass of dry air} = \frac{m_v}{m_a}\]
Assuming both water vapour and dry air is perfect gas,
\[ \boxed{w = 0.622 \frac{P_v}{P_a} = 0.622\frac{P_v}{P_t - P_a}}\]
Here, Pv : Partial Pressure of vapour
Pa : Partial Pressure of air
Pt : Total pressure
2. Relative Humidity
Relative humidity (φ) is defined as the ratio of mass of vapour to the mass of vapour under saturation condition in the same volume and temperature.
\[ \boxed{φ = \frac{m_v}{m_{vs}} = \frac{P_v}{P_{vs}}}\]
In case of relative humidity is 100% then
- Dry bulb temperature (DBT),
- Wet bulb temperature (WBT),
- Dew point temperature (DPT),
- Saturation temperature will be equal.
If unsaturated moist air is cooled at constant pressure, then the temperature at which the condensation starts is known as dew-point temperature (DPT) of air.
3. Degree of Saturation (μ)
The ratio of actual specific humidity to specific humidity of saturated air at same temperature is known as degree of saturation.
\[ μ = \frac{w}{w_s} = φ \Big(\frac{P_t - P_{vs}}{P_t - P_v}\Big)\]
4. Enthalpy of Moist Air
Total enthalpy will be sum of enthalpy of dry air and vapour.
\( H = H_a + H_v = m_ah_a + m_vh_v\)
moist air enthalpy per kg of dry air = \( \frac{H}{m_a} = h = h_a + w.h_v\)
\[h = 1.005 t + w(2500 + 1.88 t) \]
where, h is in kJ / kg dry air
t is dry bulb temperature in °C
Psychrometric Chart
- The chart is plotted for one barometric pressure (Atmospheric pressure).
- Constant enthalpy lines and Wet Bulb Temperature doesn't coincide but practical purpose we can assume them as parallel.
Basic Process in Air Conditioning
- Process of heating/cooling air at constant specific humidity(w) is called sensible heating/cooling.
- Process of increasing/decreasing specific humidity at constant DBT is called humidification/dehumidification.
- All other process are combination of these two as shown in above figure.
Sensible Heat Factor
Sensible heat factor (SHF) is defined as the ratio of sensible heat to the total heat.
\[ SHF = \frac{sensible \quad heat}{total \quad heat} = \frac{h_2 - h_1}{h_3 - h_1}\]
- SHF = 1 for sensible cooling/heating
- SHF = 0 for humidification/dehumidification
Chemical Dehumidification
This process is done using hygroscopic material which absorbs water vapour from moist air. If process is thermally isolated then enthalpy of air remains constant which causes increases in temperature of air as its moister content decreases.
Mixing of Two Streams
1. Without Condensation
mass balance of vapour and dry air:
\[m_{a1} + m_{a2} = m_{a3}\]
\[m_{a1}.w_1 + m_{a2}.w_2 = m_{a3}.w_3\]
Energy balance:
\[m_{a1}.h_1 + m_{a2}.h_2 = m_{a3}.h_3\]
from above equations,
Specific humidity of mixture:
\[\boxed{w = \frac{m_{a1}.w_1 + m_{a2}.w_2}{m_{a1} + m_{a2}}}\]
Enthalpy of mixture:
\[\boxed{h = \frac{m_{a1}.h_1 + m_{a2}.h_2}{m_{a1} + m_{a2}}}\]
Temperature of mixture can be approximated:
\[\boxed{t = \frac{m_{a1}.t_1 + m_{a2}.t_2}{m_{a1} + m_{a2}}}\]
2. With Condensation
After condensation some amount of water (Wc) leaves system as liquid water. Due to this, specific humidity of resulting mixture (point 4) will be less than that at point 3. Temperature of air increases due to the release of latent heat of condensation.
\[w_4 = w_3 - w_c\]
\[w4 = \frac{m_{a1}.w_1 + m_{a2}.w_2}{m_{a1} + m_{a2}} - w_c\]
\[h4 = \frac{m_{a1}.h_1 + m_{a2}.h_2}{m_{a1} + m_{a2}} - w_c.h_{f4}\]
By-Pass Factor (BPF)
If Air is heated from temperature t1 to t2 by coils (ts) then BPF is defines as:
\[ BPF = \frac{Actual \quad loss}{Ideal \quad gain} = \frac{t_s - t_2}{t_s - t_1}\]
Efficiency of Coil = 1 - BPF
If 'n' number of coils with BPF x in a row then equivalent BPF is $x^n$.
- For sensible heating, coil temperature (ts) should be greater than DBT of air.
- For sensible cooling, coil temperature should be less than DBT but more than DPT.
- For cooling and dehumidification $t_s < DPT < DBT$.
