How to Factor Perms into Mold Risk - public

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q
1		Seeking a formula for how vapor retarders affect mold risk, I ended up converting a printed spreadsheet into a functioning spreadsheet - almost.
2		The source calculates vapor pressure and condensation through a wall.
3		How were the highlighted-yellow parts calculated? .... The blue font parts (+two formulae images on line 13) were added by me. Black is identical to the source. Italics means now calculated (vs just printed).
4		(If you want the source, it's "Vapour Pressure and Condensation", in Canadian Building Digest.)						https://nrc-publications.canada.ca/eng/view/ft/?id=897fca5e-67e2-46e0-9e83-c2c456faadf1
5
6		"Consider a wall of 4-inch reinforced concrete with an inside finish of winch plaster over 1 inch of foamed plastic insulation that separates
7		an internal environment of 73°F and 35 per cent RH from an outside environment of 0°F and 80 per cent RH.
8		The actual vapour pressures are, respectively, 0.818 x 0.35 = 0.286 in. Hg and 0.038 x 0.80 = 0.030 in. Hg, and the total pressure difference is 0.256 in. Hg."
9		Interior Temp	73	°F	22.8	°C						Exterior Temp	0	°F	-17.8	°C
10		Interior RH	35%									Exterior RH	80%
11		Saturation Vapor Pressure	0.818	in.Hg	2.7743	kPa, by Buck Approximation						Saturation Vapor Pressure	0.038	in.Hg	0.1275	kPa	by Huang, sub-zero version
12			0.8193	by converting kPa to in.Hg (inches of mercury)									0.038	by converting kPa to in.Hg
13		Buck Approximation							Huang Approximation						0.1517	kPa	by Buck, not right for sub-zero
14									sub-zero-°C version
15
16		The pressure difference must be apportioned among the various components of the envelope in proportion to their resistance to vapour flow.
17		Table I. Tabulated Vapour and Temperature Calculations
18			Interior	Air Film		Plaster		Insulation		Concrete		Air Film	Exterior	Total
19		Thickness n		-		0.75		1		4
20		Permeance M		-		15		-		-		-
21		Permeability µ		-		-		1.6		3.2		-
22		Vapour Resistance 1/M , n/µ				0.07		0.63		1.25				1.94
23		% of drop		0%		3.43%		32.19%		64.38%		0%		100%
24		Vapour Pressure Drop for Continuity (in.Hg)		0		0.009		0.082		0.165		0		0.256	(row calculated by either (1) measuring the interior and exterior actual vapor pressures, then multiplying the difference by the % of resistance at that layer, or (2) as some unit conversion from line 22 (dividing line 22 by 7.58 matched the printed #s in line 24)
25		Vapour Pressure for Continuity ("pc") (in.Hg)	0.286		0.286		0.278		0.195		0.030		0.030			Vapour permeability can be expressed in several ways:
26																- vapour resistivity of a material, measured in GNs/kgm (giga Newton seconds per kilogram metre) or MNs/gm (mega Newton seconds per gram metre)
27		Thermal Conductance C		1.46		6.66		-		-		6				- vapour resistance for a given thickness of material, in GNs/kg or MNs/g
28		Thermal Conductivity k		-		-		0.25		12		-				- vapour resistance factor, also known as th µ-value, which is the resistivity of a material relative to that of still air. It is a factor, and has no units.
29		Thermal Resistance 1/C , n/k		0.68		0.15		4.00		0.33		0.17		5.34		- "perms", short for permeability, used commonly in North America, measured in grains/(ft2 ·h·inHg)
30		Temperature Drop °F		9		2		55		5		2		73
31		Temperature °F	73		64		62		7		2		0
32		Temperature °C	22.8		17.6		16.4		-14.0		-16.5		-17.8
33
34		Saturation Vapor Pressure	2.7743	kPa	2.0100		1.8697		0.1816		0.1436		0.1275	* intermediary calculation in kPa to get to source's unit (inches of mercury, in.Hg)
35		Saturation Vapour Pressure ("ps")	0.819	in.Hg	0.594		0.552		0.054		0.042		0.038	(calculated matches printed)
36		Actual Vapour Pressure ("pa")	0.287	in.Hg	0.286		0.264		0.054		0.03		0.030
37		Actual Vapor Pressure (calc'd: SVP x calculated-RH)	0.287	in.Hg	0.2077477914		0.193239512		0.01876448531		0.01484500392		0.01318083873	How did they calculate mid-assembly RH? My calc's in this row don't match the printed data (the row above) because I can't properly calculate mid-assembly RH.
38		Actual Vapor Pressure (calc'd: SVP x given-RH )	0.287		(RH not given)		(RH not given)		(RH not given)		(RH not given)		0.030
39
40		Vapour Flow = Vapour Pressure Difference / Vapour Flow Resistance
41		The vapour flow to point A is
42		(0.286 - 0.054) / (0.07 + 0.62)	0.286	0.054	0.232	0.34	grain / sq ft / hr
43		(0.286 - 0.054) / (0.07 + 0.62)	0.07	0.63	0.69	0.34	grain / sq ft / hr
44		and that from point A
45		(0.054 - 0.030) / 1.25	0.054	0.030	0.024	0.02	grain / sq ft / hr
46		(0.054 - 0.030) / 1.25	1.25		1.25	0.02	grain / sq ft / hr
47		giving a condensation rate of
48		0.34 - 0.02 = 0.32 grain/sq ft/hr.	Condensation Rate:			0.32	grain / sq ft / hr				1 perm = 1 grain/(hr ft2 inHg)
49
50		Does knowing the condensation rate enable us to factor vapor pressure into calculations of relative humidity?
51
52	* How did they calculate "Actual Vapor Pressure"?
53	The paper only includes RH inside and outside - it does not include RH (or dewpoint) mid-assembly.
54	Actual Vapor Pressure can be calculated from RH and Temperature. RH can be calculated from Dewpoint and Temperature, but Dewpoint is calc'd from RH and Temp, so: circular reasoning.
55		Temperature °C	22.8		17.6		16.4		-14.		-16.5		-17.8
56		Dewpoint	6.5		1.9		0.9		-26.2		-28.4		-29.6		formula source: https://bmcnoldy.rsmas.miami.edu/Humidity.html
57		r.h.	35.0%		35.0%		35.0%		35.0%		35.0%		35.0%		formula source: https://bmcnoldy.rsmas.miami.edu/Humidity.html
58		Dewpoint (by sub-zero version of formula)	8.5		3.8		2.8		-25.		-27.3		-28.4
59		r.h. (by sub-zero version of formula)	35.0%		35.0%		35.0%		35.0%		35.0%		35.0%
60		r.h. (given)	35.0%										80.0%
61		Why are the r.h. calculations all 35% at every point of the assembly? Circular reasoning / calculating.
62		I used the same indoor RH for the Dewpoint calculations at every point of the assembly. Was there a now-forgotten good reason for that?
63
64	About the formula for "Saturation Vapor Pressure":
65
66	Psat in kPa and T in °C. Where A, B, and C are the coefficients of the August-Roche-Magnus approximation.
67	For above-zero temperatures, A = 6.112, B= 17.625 and C= 243.04.
68	For sub-zero temperatures, A = 6.112, B=22.46 and C=272.62.
69
70	Psat2008 EVAL [ 6.112 * EXP(17.62*Temperature/(243.12+Temperature)) ]
71	PsatSub0 EVAL [ 6.112 * EXP(22.46*Temperature/(272.62+Temperature)) ]
72	-- https://cumuluswiki.org/a/Charts_Definition_Language_(CDL)
73
74
75
76
77
78
79
80		Where A = 6.1094, B= 17.625 and C= 243.04 are the coefficients of the August-Roche-Magnus equation as found here. Psat in hPa and T in °C
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100