## Q. 19.2

Effect of Fan Heat

We will rework Example 19.1 but include the effect of airstream heating of the supply fan. The supply fan pressure drop is 3 inWG (750 Pa). The efficiency of the supply fan is 70%, while the fan motor efficiency is 84%—both of them are located within the airstream.

Figure: See Figures 19.1 and 19.4.

Assumptions: The location is at sea level. The supply air condition to the space is the same as that in Example 19.1 (58°F and $0.0084 lb_{w}/lb_{a}$).
The duct heat gains/losses are ignored.
Given: $Δp_{fan} = 3 inWG, \eta_{fan} = 0.7, \eta_{motor} = 0.84$

$SHR_{space} = 0.70, \dot{Q}_{space,cool} = 120,000 Btu/h, \dot{V}_{0} = 1,000 ft^{3}/min = 60,000 ft^{3}/h$

$T_{db,5} = 58°F$, outdoor and indoor air conditions are identical to those in Example 19.1.
Find: $\dot{m}_{a}, \dot{Q}_{cc,tot}, SHR_{cc}$

## Verified Solution

1. Locate specified points 0 and 6 on psychrometric chart. Note that the state points 3
and 4 are no longer the same as in Figure 19.3 because of the supply fan reheat. The supply airow rate remains unchanged since $T_{5}$ is the same. Consequently, point 1 is also unchanged.
2. Locate point 3. Using Equation 19.9 IP but including the motor efficiency (since the motor is located in the airstream), we can calculate the supply fan reheat:

$\Delta T_{db} (°F) = 0.63 \times \frac{\Delta p (inWG)}{\eta_{fan}}$         (19.9  IP)

$T_{db,5} – T_{db,3} = 0.363 \times \left\lgroup \frac{3 inWG}{0.7 \times 0.84} \right\rgroup = 1.85 °F$

The cooling coil set point temperature has to be lower to compensate for the airstream heating Thus, point 3 is specified given $T_{db,3} = 58 − 1.85 = 56.15°F$ and humidity ratio $W_{3} = W_{5} = 0.0084 lb_{w}/lb_{a}$.
Then, the enthalpy at point 3 is determined as $h_{3} = 22.6 Btu/lb_{a}$.
$\dot{Q}_{cc,tot} = \dot{m}_{a} (h_{1} – h_{3}) = 17,140 lb_{a}/h \times (33.4 – 22.6) Btu/lb_{a}$