## Q. 19.3

Peak Design for High Latent Load Spaces

We shall use the same design specifications as that of the CAV system analyzed under peak-load condition in Example 19.1 with one major difference. Instead of the space SHR being equal to 0.7, we are specified a value of 0.5, i.e., the sensible and latent loads are equal. The cooling coil leaving air temperature is as before, at 58°F and 80% RH. We will determine the supply air mass flow rate, and cooling coil and reheat coil loads in this case.
Figure: See Figures 19.5a and 19.7.
Assumptions: The location is at sea level. The duct heat transfer and the fan air temperature rise are ignored for simplicity.
Given: $SHR_{space} = 0.50, \dot{Q}_{space,tot} = 120,000 Btu/h, \dot{Q}_{space,sen} = \dot{Q}_{space,lat} = 60,000 Btu/h$

Outdoor air conditions:$T_{db,o} = 95°F, \phi_{o} = 0.55, \dot{V}_{0} = 1000 ft^{3}/mi$

Cooling coil leaving air conditions:    $T_{db,3} = 58°F$ and  $\phi_{3} = 0.8$.

Space condition: $T_{db,7} = 78°F$ and $\phi_{7} = 0.5$.
Find: $\dot{m}_{a}, \dot{Q}_{cc,tot}, \dot{Q}_{cc,sen}$, and $\dot{Q}_{hc,tot}$
Lookup values: Specific volume $v_{0} = 14.4 ft^{3}/lb_{m}$, humidity ratio $W_{0} = 0.0197 lb_{w}/lb_{a}, h_{0} = 44.52 Btu/lb_{a}, W_{3} = 0.0082 lb_{w}/lb_{a}, h_{3} = 22.85 Btu/lb_{a}, W_{7} = 0.0103 lb_{w}/lb_{a}, h_{7} = 30 Btu/lb_{a}$.

## Verified Solution

The solution via the graphical procedure is adopted.
1. Locate specified points 0, 3, and 7 on the psychrometric chart (see Figure 19.7),  which are specified from the problem statement.
2. Locate supply air point 5.
Previously, the slope of line 5–7 was determined from the inner scale of the protractor. The location of point 6 is the intersection of the line drawn from point 7 with a slope equal to 0.5 and the horizontal line drawn from point 3.
This is found to be $T_{db,5} = 69.1°F$ and $h_{5} = 25.5 Btu/lb_{a}$ and $W_{5} = 0.0082 lb_{w}/lb_{a}$.
3. Determine space supply airflow rate.
The enthalpy balance equation (Equation 19.1) is rearranged to yield

$\dot{Q}_{cc,tot} = \dot{m}_{a} (h_{cc,in} – h_{cc,out})$           (19.1)

$\dot{m}_{a} = \frac{\dot{Q}_{space,cool}}{h_{7} – h_{5}}$

$= \frac{120,000 Btu/h}{(30 – 25.5) Btu/lb_{a}} = 26,667 lb_{a}/h$

4. Determine mixed air condition point 1.
The outdoor air mass ow is the same as before $\dot{m}_{a,0} = 4170 lb_{a}/h$.
The ratio of air mass flows is (4,170/26,667) = 0.156. Therefore, point 1 is located 15.6% of the distance from point 7 along line segment 7–0. The properties at point 1 can be read from the psychrometric chart or determined by calculation. The dry-bulb temperature could be calculated by using the weighted average rule, e.g., the mixed-air temperature $T_{db,1} = [0.156 × 95°F + (1 − 0.156) × 78°F)] = 80.65°F$. Similarly, we find and the humidity ratio $W_{1} = 0.0118 lb_{w}/lb_{a}$ and enthalpy $h_{1} = 32.31 Btu/lb_{a}$.
$\dot{Q}_{cc,tot} = \dot{m}_{a} (h_{1} – h_{3}) = 26,087 lb_{a}/h \times (32.31 – 22.85)$

$Btu/lb_{a} = 246,783 Btu/h (20.6 tons)$

$\dot{Q}_{hc} = \dot{m}_{a} (h_{4} – h_{3})$
$= 26,087 lb_{a}/h \times (25.5 – 22.85) Btu/lb_{a}$
Note the substantial increase in supply airflow rate (from 17,140 to 26,667 $lb_{a}/h$ and the substantial additional reheat). The primary reason for the need of reheat is that the $SHR_{space}$ line is so steep that it does not intersect the saturation curve, and so no feasible apparatus dew point temperature value can be deduced. The practical connotation is that it is not possible to simply circulate chilled water through the cooling coil and achieve the desired cooling and dehumidification process in one step. Thus, if a CAV system is used, one is forced to provide reheating even at peak load, i.e., under design conditions. This is a major energy penalty in hot and humid locations in several coastal locations worldwide.