# ASHRAE Journal - November 2019 - 36

```TECHNICAL FEATURE

In I-P units:

Re-arranging,
Q=

H
572(1 − TOA / TROOM )

(6)

In SI units:
Q=

H
0.353(1 − TOA / TROOM )

(7)

Example Three
A mechanical room has sensible heat gain of 120,000
Btu/h (35 169 W). The room temperature should not
exceed 104°F (40°C). Design outdoor temperature is
86°F (30°C). Calculate required capacity of exhaust fan.
TROOM = 104 + 460 = 564 R

TROOM =

TOAC p DST TST Q
TOAC p DST TST Q − H

In IP units, Cp= 0.24 Btu/lb °F. DST = 0.075 lb/ft3 at
TST =69°F=(69 + 460)=529 R.1 Airflow is usually expressed
in cfm and H in Btu/h. Hence Q is to be multiplied by 60.
Substituting these values in Eq. (3A1), Eq. (3) is obtained.
In SI units, Cp = 1 kJ/kg K, DST = 1.2 kg/m3 at TST = 21°C
= (273 + 21) = 294 K. Airflow is usually expressed in L/s
hence Q has to be divided by 1,000. Substituting these
values in Eq. (3A1), Eq. (4) is obtained.
Re-arrangement of Eqs. (3) and (4) yields Eqs. (6) and (7).

Appendix Two
Formulas for Other Elevations

TOA = 86 + 460 = 546 R

Using the perfect gas equation, the density of air at
elevations other than sea level may be calculated by:

Using Eq. (6),

D = DSL p / pSL

Q = 120,000/[572 × (1 - 546/564)] = 6,573 cfm

Conclusions
* A formula has been given with which room temperature can be determined easily and accurately for rooms
cooled by exhaust fans without tedious trial and error
calculations, which would otherwise be needed.
* Another formula has been given with which the
required capacity of exhaust fan for space cooling can
be easily and accurately determined without the tedious
calculations which are needed for accurate determination of air density.
1. ASHRAE Fundamentals Handbook 2017, page 18.15.

TROOM =

TOAC p DST p * TST Q
C p DST p * TST Q − H

(3A2)

0.353TOAQp*
0.353Qp* − H

(4A2)

In SI units,
TROOM =

Using the perfect gas law, density of air at any temperature can be related to the standard air density as below.
(1A1)

In I-P units,
H
572 p* (1 − TOA / TROOM )

(5A2)

H
0.353 p (1 − TOA / TROOM )

(6A2)

Q=

In SI units,

Substituting in Eq. (1),

ASHRAE JOURNAL

572TOAQp*
572Qp* − H

TROOM =

Derivation of Formulas for Sea Level

36

(2A2)

By substituting the values as in Appendix 1, the following formulas are obtained.
In customary I-P units,

Appendix One

TROOM = TOA +

(1A2)

Where the subscript "SL" means at sea level.
Inserting this relation in Eq. (3A1) with p* = p/pSL:

References

DROOM = DST × TST /TROOM

(3A1)

H
C p QDST TST / TROOM
ashrae.org

N O V E M B E R 2 0 19

(2A1)

Q=

*

```

# 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
ASHRAE Journal - November 2019 - 23
ASHRAE Journal - November 2019 - 24
ASHRAE Journal - November 2019 - 25
ASHRAE Journal - November 2019 - 26
ASHRAE Journal - November 2019 - 27
ASHRAE Journal - November 2019 - 28
ASHRAE Journal - November 2019 - 29
ASHRAE Journal - November 2019 - 30
ASHRAE Journal - November 2019 - 31
ASHRAE Journal - November 2019 - 32
ASHRAE Journal - November 2019 - 33
ASHRAE Journal - November 2019 - 34
ASHRAE Journal - November 2019 - 35
ASHRAE Journal - November 2019 - 36
ASHRAE Journal - November 2019 - 37
ASHRAE Journal - November 2019 - 38
ASHRAE Journal - November 2019 - 39
ASHRAE Journal - November 2019 - 40
ASHRAE Journal - November 2019 - 41
ASHRAE Journal - November 2019 - 42
ASHRAE Journal - November 2019 - 43
ASHRAE Journal - November 2019 - 44
ASHRAE Journal - November 2019 - 45
ASHRAE Journal - November 2019 - 46
ASHRAE Journal - November 2019 - 47
ASHRAE Journal - November 2019 - 48
ASHRAE Journal - November 2019 - 49
ASHRAE Journal - November 2019 - 50
ASHRAE Journal - November 2019 - 51
ASHRAE Journal - November 2019 - 52
ASHRAE Journal - November 2019 - 53
ASHRAE Journal - November 2019 - 54
ASHRAE Journal - November 2019 - 55
ASHRAE Journal - November 2019 - 56
ASHRAE Journal - November 2019 - 57
ASHRAE Journal - November 2019 - 58
ASHRAE Journal - November 2019 - 59
ASHRAE Journal - November 2019 - 60
ASHRAE Journal - November 2019 - 61
ASHRAE Journal - November 2019 - 62
ASHRAE Journal - November 2019 - 63
ASHRAE Journal - November 2019 - 64
ASHRAE Journal - November 2019 - 65
ASHRAE Journal - November 2019 - 66
ASHRAE Journal - November 2019 - 67
ASHRAE Journal - November 2019 - 68
ASHRAE Journal - November 2019 - 69
ASHRAE Journal - November 2019 - 70
ASHRAE Journal - November 2019 - 71
ASHRAE Journal - November 2019 - 72
ASHRAE Journal - November 2019 - 73
ASHRAE Journal - November 2019 - 74
ASHRAE Journal - November 2019 - 75
ASHRAE Journal - November 2019 - 76
ASHRAE Journal - November 2019 - 77
ASHRAE Journal - November 2019 - 78
ASHRAE Journal - November 2019 - 79
ASHRAE Journal - November 2019 - 80
ASHRAE Journal - November 2019 - 81
ASHRAE Journal - November 2019 - 82
ASHRAE Journal - November 2019 - 83
ASHRAE Journal - November 2019 - 84
ASHRAE Journal - November 2019 - 85
ASHRAE Journal - November 2019 - 86
ASHRAE Journal - November 2019 - 87
ASHRAE Journal - November 2019 - 88
ASHRAE Journal - November 2019 - Cover3
ASHRAE Journal - November 2019 - Cover4
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