ASHRAE Journal - November 2019 - 35

TECHNICAL FEATURE

Nomenclature
Cp = Speciﬁc heat of air at constant pressure,
Btu/lb R (J/kg K)
D = Density of air, lb/ft3 (kg/m3)
H = Sensible heat load of space being cooled,
Btu/h (kW)
P = Absolute atmospheric pressure at a
location, psia (Pa)
PSL = Absolute atmospheric pressure at sea level,
psia (Pa)
p* = =p/pSL
Q = Airﬂow at exhaust fan inlet, cfm (L/s)
T = Temperature, R (K)

Subscripts
OA
= Outside air
ROOM = Room air
ST
= Standard air
perfect gas equation and re-arrangement (Appendix 1).
They give exactly the same result as Eq. (1).

Example One
An electrical room has a sensible heat gain of 500,000
Btu/h (146 536 W). It is provided with an exhaust fan
of 10,000 cfm (4719 L/s) capacity on the west wall. Air
intake louvers are installed on the east wall. Outside air
is at 90°F (32°C) dry bulb and 30% relative humidity.
Calculate the room temperature.
TOA= 90 + 460 = 550 R

Using Present Formula
Using Eq. (3),
TROOM = 572 × 550 × 10,000/
(572 × 10,000 - 500,000) = 603 R = 143°F

By Trial and Error
If Eq. (2) is used as is the usual practice, TOA is calculated to be 135°F (57°C).
The next step for trial and error is to calculate the air density at 135°F (57°C). Plotting sensible heat gain from 90°F
(32°C) DB and 30% RH on psychrometric chart as a horizontal line to 135°F (57°C), air density is found to be 0.066
lb/ft3 (1 kg/m3). Note that air density can also be calculated

with software such as ASHRAE Duct Fitting Database (Air
Properties). Using Eq. (1) with this density, room temperature is calculated to be 142.6°F (61.4°C). This is close
to the correct value given by Eq. (3) but the person doing
calculations does not know it until further iterations
converge. Therefore, one more calculation using the air
density at 142.6°F (61.4°C) will be done to conﬁrm that
the correct value of room temperature has been found.
In many cases, more than two iterations may be needed.
It is thus clear that the new formula will signiﬁcantly
reduce the effort needed for accurate calculations.

Example Two
A diesel-generator room has a heat gain of 200 kW at
maximum load and 100 kW at part load. It is provided
with an exhaust fan of 10,000 L/s (21 189 cfm) at the roof
and air intake fans at the walls. Outdoor air temperature
is 30°C (86°C). Calculate the room temperature at maximum and part loads.
TOA = 30 + 273 = 303 K
Applying Eq. (4),
At full load,
TROOM = 0.353 × 10,000 × 303/
(0.353 × 10,000 - 200) = 321.2 K = 48.2°C
At part load,

TROOM = 0.353 × 10,000 × 303/
(0.353 × 10,000 - 100) = 312 K = 39°C

Formulas for Exhaust Fan Capacity
For calculating fan capacity, Eq. (1) may be re-arranged
to:
Q=

H
C p QDROOM (TROOM − TAir )

(5)

To use this formula, the density of room air DROOM
has to determined. While it can be done quickly with a
psychrometric chart, to get an accurate value this way is
difﬁcult as it requires interpolation between constant
speciﬁc volume lines. For accurate value of density, one
must use psychrometric tables and formulas or software
such as that in the ASHRAE Duct Fitting Database; this
is tedious. The following formulas allow calculation of
required fan capacity without the need to calculate room
air density; their derivation is given in Appendix 1.
N O V E M B E R 2 0 19

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ASHRAE Journal - November 2019

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