Chapter 19

Q. 19.2

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}

19.1
19.4

Step-by-Step

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}.
3. Determine cooling coil load.

\dot{Q}_{cc,tot} = \dot{m}_{a} (h_{1}  –  h_{3}) = 17,140  lb_{a}/h \times (33.4  –  22.6) Btu/lb_{a}

= 185,112  Btu/h = 15.4 tons

Comments
The cooling coil load has increased by 3.4% from the previous case. This example illustrates the fact that the airstream heating due to the fan is small but not negligible and needs to be considered in accurate design and analysis calculations.

19.3