ASHRAE Journal - November 2019 - 34

TECHNICAL FEATURE

Formulas for Cooling
With Exhaust Fans
BY MIRZA M. SHAH, PH.D., P.E., FELLOW/LIFE MEMBER ASHRAE

Exhaust fans drawing outdoor air are widely used for cooling industrial and commercial facilities. Air drawn into the room picks up the room heat before leaving through
the exhaust fans. Examples are electrical rooms, boiler rooms, manufacturing shops,
etc. Consider a room with sensible heat gain H with an exhaust fan with volumetric
flow rate Q. Outside air at temperature TOA enters the room, picks up heat to rise to a
temperature TROOM
M and is exhausted by the fan. Neglecting the moisture in air, which
has very little effect as its quantity is very small, heat balance gives:
TROOM = TOA +

H
C p DROOM
OO Q

(1)

Where DROOM
M is the density of air leaving the room and
Cp is the specific heat of air. During the analysis and
evaluation of existing systems, it is often required to
find the room temperature that will be maintained by
an exhaust system with a fixed flow rate. To calculate
the room temperature TROOM
M with Eq. (1), the density
of air DROOM
is
required.
This
density depends on room
M
temperature, which is unknown. Thus tedious trial and
error calculations are needed. Calculations are often
simplified by assuming the room air density to be the
same as the outside air density or that at standard conditions. The approximate formula most commonly used
according to ASHRAE Handbook1 is:
H = 1.1 Q (TROOM
M - TOA)
This can result in considerable error if the

(2)

temperature rise in room is large. To enable easy calculation of room temperature without trial and error,
the author has developed the formulas presented here.
Formulas are also given for easier accurate calculation of
required fan capacity.
As most calculations are done at sea level, formulas
for sea level are given below. Their derivation is given
in Appendix 1 of this article. Formulas for use at other
elevations are given in Appendix 2.

Formulas for Room Temperature
In customary I-P units, the formula is:
TROOM =

572TOAQ
572Q − H

(3)

In SI units, the formula is:
TROOM =

0.353TOAQ
0.353Q − H

(4)

These formulas are derived from Eq. (1) by using the

Mirza M. Shah, Ph.D., P.E., is director of Engineering Research Associates. He is active in research, design, and analysis in mechanical engineering, including heat transfer, fluid
flow, HVAC, refrigeration, plumbing, fire protection, energy conservation, and renewable energy systems.
34

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ASHRAE Journal - November 2019

Table of Contents for the Digital Edition of ASHRAE Journal - November 2019

Contents
ASHRAE Journal - November 2019 - Intro
ASHRAE Journal - November 2019 - Cover1
ASHRAE Journal - November 2019 - Cover2
ASHRAE Journal - November 2019 - 1
ASHRAE Journal - November 2019 - Contents
ASHRAE Journal - November 2019 - 3
ASHRAE Journal - November 2019 - 4
ASHRAE Journal - November 2019 - 5
ASHRAE Journal - November 2019 - 6
ASHRAE Journal - November 2019 - 7
ASHRAE Journal - November 2019 - 8
ASHRAE Journal - November 2019 - 9
ASHRAE Journal - November 2019 - 10
ASHRAE Journal - November 2019 - 11
ASHRAE Journal - November 2019 - 12
ASHRAE Journal - November 2019 - 13
ASHRAE Journal - November 2019 - 14
ASHRAE Journal - November 2019 - 15
ASHRAE Journal - November 2019 - 16
ASHRAE Journal - November 2019 - 17
ASHRAE Journal - November 2019 - 18
ASHRAE Journal - November 2019 - 19
ASHRAE Journal - November 2019 - 20
ASHRAE Journal - November 2019 - 21
ASHRAE Journal - November 2019 - 22
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ASHRAE Journal - November 2019 - 33
ASHRAE Journal - November 2019 - 34
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ASHRAE Journal - November 2019 - Cover3
ASHRAE Journal - November 2019 - Cover4
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