Wall Gradient Calculator

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Instructions

Thermal Gradient and Vapor Pressure in a Wall Assembly - Overview

This workbook calculates and displays several items commonly needed when dealing with

assemblies. It uses standard methods, but most specifically uses the methods defined in:

Thermal and Moisture Protection Manual - Christine BeallMcGraw Hill1998. The o

included are:

- Thermal gradient across a wall- Saturation vapor pressure across a wall

- Actual vapor pressure across a wall- Joint width necessary to address component movements and construction tolerances.

- Thermal Bridging

- Wind pressure on a wall in both PSF and inches of water

The main worksheet is the Wall Gradients worksheet. It is protected so that you won't

unecessary mistakes while entering data. If you wish to make changes you can unprotect t

since there is no password.

The Saturation Pressure Worksheet shows the coefficients of the polynomial that is usedapproximate the Saturated Water Pressure in the range -50c to 50c for which this equation

Notes:

- The worksheet is set up to accept up to 8 materials in the wallplus the airfilms on eitheshould work from the left side entering material names, thickness and properties. The wor

work properly if you enter fewer than 8 materials.

- For thermal resistance the sheet is set up to expect Resistance per inch and then to calcularesistance based on the thickness of the material. If you are given a specific Resistance (as

film) then you can overide the calcuation.

- Similarly, for Vapor Resistance the sheet is set up to accept permeability and then calcula

resistance per inch and the actual vapor resistance. You can override these last two.

Latest update 10/19/2003

J. Mitchell

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Instructions

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Wall Gradients

Thermal & Vapor Pressure Gradient Calculator

Temp DegF TempDegC Rh Wind Sat VP Actual VP

Inside Conditions 68 20 50% 0.691 0.345

Outside Conditions 17 -8 73% 15 0.096 0.070

Delta -51 -28 -0.274907

Total Wall Thickness 12.9 Inches

Total Wall R 13.7

Total Wall Rep 2.8

AirFilm_In Mat1 Mat2 Mat3 Mat4 Mat5 Mat6

Material Name Gypsum onc Block Polyst Ins AirSpace Brick

Thickness in 0.5 6 1.5 1 3.875

X_Distance 0.5 6.5 8 9 12.875 12.875

R/in 1 0.255 6.2533333 0.97 0.11

R 0.68 0.5 1.53 9.38 0.97 0.42625

Permeabilty 120 18.75 19.2 1.2 120 3.2

Vapor Resistance/In 0.008 0.053 0.052 0.833 0.008 0.313Vapor Resistance 0.008 0.027 0.313 1.250 0.008 1.211

Temp on On Right 65 64 58 23 19 18 18

Temp (DegC) 18.6 18 14 -5 -7 -8 -8

Saturated Vap Press 0.6325 0.5926 0.4838 0.1238 0.1061 0.0991 0.0991

Actual Vap Press 0.344 0.342 0.311 0.189 0.188 0.070 0.070

Delta Vap Press 0.288032246 0.2507048 0.1724728 -0.065158 -0.081983 0.0295344 0.0295344

0

10

20

30

40

50

60

70

0 5 10 15

TempDegF

Wall X-Distance

Thermal Gradient in Wall

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 5 10VaporPressure-inchesofHG

Wall X_Distance

Vapor Pressure in

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Wall Gradients

Mat7 Mat8 Airfilm_out

12.875 12.875

0.17

18 18 17

-8 -8 -8

0.0991 0.0991 0.0964

0.070 0.070 0.070

0.0295344 0.0295344 0.0268536

15

all

Saturated Vap Press

Actual Vap Press

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Joint Width

Material Marble Name of Material Considered

JL 300 Inches Material Length in Inches

JTW 35 DegF Extreme Winter Wall Temperature

Jta 100 DegF Dry bulb Extreme summer air temperature

JX 75 Constant for heat capacity of material (table 9.2)

JS 0.8 Solar absorption coefficient (table 9.3)

JCT 8.6 Thermal Expansion Coefficient

JCM 8 Moisture Movment Coefficient

Sm 25% Pct Sealant Movement Capacity

SSF 80% Pct Sealant Safety Factor

JC 0.25 Inches Construction Tolerance

JTS 160 DegF Extreme Summer Wall Surface Temperature

JdeltaT 125 DegF Change in TemperatureJmt 0.3225 Inches Thermal Movement of Joint

JT 1.6125 Inches Joint minimum width for thermal movement

JM 0.0024 Inches Joint minimum width for moisture movement

J 1.8649 Inches Design Joint minimum width

The necessary width for a joint is addressed in Chapter 9 of Thermal and Moisture Protection Manual components that must included to determine the design width.

Jt = Thermal movement

Jm = Moisture movement

Jc = Construction Tolerances

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Joint Width

. There are 3

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Saturation Pressure

Saturation Pressure of Water CalculationRange Good -58 to 122 DegF

TinF 69 Coefficients of Polynomial for

TinC 20.55555556

a1 6.11E+000

EsPoly 24.204 Mb a2 4.44E-001

Sat_Water_In 0.7147 In of HG a3 1.43E-002

a4 2.65E-004

a5 3.02E-006

a6 2.04E-008

a7 6.39E-011

Calculating Mb to inches of Mercury

1 Mb 0.7500617

1 MM 0.03937008

1 Mb 0.029529989The saturation pressure of water vapor is a complicated

physical function. Good approximations to it are given at

http://hurri.kean.edu/~yoh/calculations/satvap/satvap.html

This spreadsheet uses the Polynomial approximation good

from -50c to 50c, approximately -58f to 122f.

This worksheet shows the coefficients of the polynomial and

how it is actually calculated. The main worksheet uses the

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Saturation Pressure

Mm of Hg

Inches

Inches of HG

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Thermal Bridging Calculation

Insulation Values Dimensions

ValueR1 1 a 10.5 inches

ValueR2 1 b 1.5 inches

ValueR3 1

ValueR4 18

ValueR5 6

a+b = 12 in

Total Insulation Calculation

Insulation Stud Path

R1 1 1

R2 1 1

R3 1

R4 18

R5 6Total 21 8

Effective Insulation

Reff 17.5Decrease 3.5

Decrease% 17%

R1

R2

This sheet allows you to calculate the decrease in effIt assumes a stud-like material with insulating materi

Vary the dimensions and the insulation values to see

You can see that the formula in B24 is=((Insulation_R*Stud_R)*(a+b)) / (a*Stud_R+b*InsulaThis is derived from equating the sum of the heat floan "effective" resistance over the total width path and

Note that when you have metal bridging the calculatimuch small of the metal. In this case you must calculcalculations.


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a

b

R3

R5

ective insulation value due to simple thermal bridging.l filling between the studs.

the decrease in effective insulation value.

tion_R)s through the two separate paths to the heat flow ofsolving for the effective resistance.

n is more complex because the dimensions are solate a tributary area. See 3.4.2 of Beall for those


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Wind Pressure as a function of wind speed in MPH

The pressure on a building is q=0.00256v^2

Gust Coeff 1

MPH q PSF q inches water

0 0.0 0.010 0.3 0.0

20 1.0 0.2

30 2.3 0.4

40 4.1 0.8

50 6.4 1.2

60 9.2 1.8

70 12.5 2.4

80 16.4 3.2

90 20.7 4.0

100 25.6 4.9

110 31.0 6.0

120 36.9 7.1

0.0

5.0

10.015.0

20.0

25.0

30.0

35.0

40.0

0 50 100 150PressureP

SF&InWater

Speed MPH

Wind Pressure

q PSF

q inches water


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Wall Gradient Calculator

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