CHARACTERIZATION OF WINDINDUCED PRESSURE DIFFERENTIALS AS
DRIVING FORCES AFFECT INDOOR RADON ENTRY AND REMOVAL
Kaiss K. AlAhmady
State of Florida, Department of Health and Rehabilitative Services
Office of Environmental Toxicology, Radon and Indoor Air Toxics
Tallahassee, FL
ABSTRACT
Windinduced pressure differentials acting on a structure shell may affect both radon entry into the structure
and indoor radon removal from the structure depending on the wind speed, direction, frequency, wave span, and
structure features. Wind blowing directly toward a side of a structure may cause an increase in pressure at the
structure wall in order to conserve the change in the momentum initiated by the change of wind velocity from the
free stream area to almost zero at the wall side. A mechanistic model has been developed to predict pressure
differentials generated in response to different configurations of wind movements around a structure. Parametric
analysis has been performed to characterize pressure differentials generated from different wind configurations. The
effect of windinduced pressure differentials on indoor radon entry and removal were characterized using general
approach to entry and ventilation modeling and applied using constant values exhibited by the University of Florida
Radon Research House. The model and approach developed in this application can be used to quantify an
acceptable range of wind conditions in which shortterm indoor radon testing should be performed.
INTRODUCTION
The most significant convective component of radon transport from substructure area into the interior, and
from the interior into the outdoors, is due to the pressuredriven air flow processes. Mechanisms which generate
pressure gradients depend on environmental and indoor operational factors. The environmental factors that induce
pressure differences include temperature differences, wind, meteorological conditions, and atmospheric pressure
changes. The indoor operational factors can be divided into two parts: the human and nonhumaninduced indoor
operational factors. The nonhuman factors result from mechanicallyinduced pressurization or depressurization of
the indoor environment by household appliances, as well as heating, ventilation, and air conditioning (HVAC)
systems. Other cases can be represented by the humaninduced indoor operational factors, which are characterized
by effects such as opening windows and doors (AlAhmady 1995).
Wind blowing directly toward a side of a structure may cause an increase in pressure at the structure's wall
in order to conserve the change in the momentum initiated by the change of the wind velocity from the free stream to
almost zero at the wall, neglecting the effect of the ground. However, windinduced pressure differentials usually
fluctuate rapidly and the determination of the fluctuation frequency has been considered an important parameter
(Nazaroff et al. 1988). Van der Hoven (1957) utilized Fourier transform analysis to obtain the frequency distribution
of wind speed for a 100 m range. Fukuda (1955) had developed a theoretical treatment to obtain the windinduced
pressure frequency when such pressures are much smaller than atmospheric pressure.
The general scheme of characterizing the windinduced pressures on radon entry can be connected to the
soil permeability, the frequency of the developed pressure, and the magnitude of the developed pressure differential.
More effects are expected to be observed when the frequency of the windinduced pressure wave is long enough to
propagate in the soil and large enough to produce a differential pressure across the structure slab and envelope. The
indoor operational factor pressure generating mechanisms have been investigated by researchers using both
experimental and mathematical models. These factors are more difficult to address since they include the effects of

1996 International Radon Symposium IIP 3.1
the occupants. The irregular opening of windows causes a decrease in the pressure difference, as well as an increase
in the infiltration air.
In this paper, a mechanistic model to predict windinduced pressure differentials across the structure shell
was developed. Characterization of these pressure differentials on radon entry and removal rates were evaluated by
integrating the model into basic mathematical representations of indoor radon entry and removal. Predictions for an
actual structure were developed by using constants' values for the model based on measurements previously
conducted at the University of Florida Radon Research House (UFRRH).
MODEL DEVELOPMENT
Starting from the physics of a fluid in motion, in this case air, the fundamental equation for conservation of
fluid energy can be utilized to establish a correlation between wind speed and pressure. In this application, wind is
assumed to be represented by an incompressible stream of air that has a Reynolds number much greater than one.
Such conditions for this case are always satisfied.
Neglecting the shear stress between the wind stream and the ground surface, the conservation of energy
(Bernoulli's equation) indicates that the total air energy under steadystate conditions must be constant at any point in
the stream, therefore
where P is the air pressure in Pa, h is the height of the point in meters relative to a horizontal reference, p is the air
density (kg/m3), g is the acceleration constant due to gravity (m/s2), and
v is the air speed (ds).
If the above equation is applied for two points in the air system, one point in the air stream around the
structure when the pressure is not affected yet by the existence of the flow obstruction, and the other point at the
surface of the structure wall, then
For the height encountered in single family residential structures and short structures measured from the ground
surface around the structure, the difference between the two quantities (h p g), and (h p g)2 is small enough to be
neglected. Then Equation 2 can be written as,
When the wind blows on the structure wall, its speed can be reasonably assumed to be zero at the surface of
the wall. Therefore, if point 1 is selected to represent the area on the wall, the above equation reduces to,
where v is the directional velocity of the wind stream measured by the weather station, and AP is the pressure
difference between the wall outer surface and the pressure of the wind stream surrounding the structure. The wind
stream pressure can be reasonably represented by the atmospheric pressure measured at the site, therefore the
immediate pressure on the wall will be equal to,
I996 International Radon Symposium IIP  3.2
The windinduced differential pressure across the structure may then be calculated from,
MODEL PREDICTIONS AND DISCUSSION
Assumptions made during the preceding derivation neglect the effect of shear stress between the wind
stream and the ground, the compressibility of air (particularly at the wall surface), and other factors that contribute to
reduce the value of the pressure difference estimated by Equation 6. Therefore, this equation represents the
maximum pressure difference that can be induced from wind blowing on the structure for the specific configuration.
To account for the effects of the neglected factors, a constant, Cw(pressure or drag coefficient) is introduced into the
equation that has a theoretical value ranging from zero to one.
The value of Cw is usually empirically determined through wind tunnel experimentation and is highly
dependent on the particular cases of structure/wind configurations. Equation 6 is then written as,
Figures 1, 2, and 3 illustrate the model predictions of windinduced pressure differences developed across
the wall of a structure when the indoor pressure is constant and equal to the barometric pressure. The wind is
blowing with a range of speed (from 0 to 25 m/s) with wind drag coefficients of 0.56 (windward side wall), 0.49
(side wall), and 0.15 (leeward side wall), respectively. Figure 4 illustrates the model predictions for windinduced
pressure differences across the structure shell for wind speeds of 1, 3, 5, and 10 mls, and the fall range of drag
coefficients. As seen from the graphs, the drag coefficient has a negligible effect for the small range of wind speeds.
Figures 5 and 6 illustrate the model prediction of windinduced pressure differences generated in response to
temporal variations in barometric pressure and indoor pressure equal to the timeaveraged value of the barometric
pressure for 1 and 14 m/s wind on the windward side wall and the leeward side wall of the structure, respectively.
To characterize the effect of pressure differentials generated by winds across the structure, indoor radon
ventilation and entry rates need to be considered. The effects of natural and forced ventilation air on indoor radon
concentrations can be generally attributed to the dilution of indoor radon through mixing with the ambient air which
has a much lower radon concentration. Once the steady state radon concentration in the indoor environment reaches
a high level, reduction of this concentration by ventilation is the only effective radon removal mechanism that can be
employed. Ventilation forced by pressure differences between the indoors and outdoors needs to be employed to
cause air change rates that dilute the elevated indoor radon concentration.
For the scope of this application, representation of structure variation rate can be quantified by the
utilization of a blower door test, following the standard blower door testing protocols (ASTM 1987). This technique
provides accurate measurements of indoor/outdoor differential pressures and the corresponding ventilation rates over
the range of 2 to 50 Pa. The relationship between the structure ventilation expressed by the air volumetric flow rate
across the shell, and pressure differentials can be written as,
where Q is the volumetric ventilation (or leakage) flow rate into or out of the structure in (m3/s), APShell is the
pressure differential across the structure shell in (Pa), n is the flow exponent and has a value between 0.5 and 1, and
K is the flow coefficient for the structure in (m3/pan.s). Incorporating the windinduced pressure differential model
into Equation 8 yields,

1996 International Radon Symposium IIP 3.3
Equation 9 can then be used to predict wind effects on structure ventilation and, consequently, indoor radon removal
rate from structures. The values of K and n are empirically determined by the best linear regression. For the
UFRRH, the flow coefficient was 0.0566 Â 0.0006, and the flow exponent was found to be equal to 0.69 Â 0.04.
Figures 7, 8, and 9 illustrate predictions of different winds configurations on indoor radon removal rates using the
above constant values.
Determination of the generic radon convective entry from the substructure area into the indoor can be
determined by computing the correlation between simultaneous monitoring of indoor radon concentration and
pressure differentials across the slab for a period of time. Experimental observations suggest that high linear
correlation exists between the pressure differentials across the structure and the radon entry rate (AIAhmady 1995).
The latter can be expressed as,
where hOnv
is the convective flow of soil gasradon into the structure in Bqls, and B is the correlation constant
(Bq/s.pa) empirically determined for a specific structure. To evaluate windinduced pressure differentials across the
slab, a proportional coefficient needs to be applied to relate pressure difference across the structure shell to pressure
difference across the slab as the following,
and
where Bw is the proportional constant between pressure differences across the slab and across the shell. This
constant is equal to I when barometric pressure is constant over a period of time greater than the time needed by the
subslab air volume pressure to equalize with the change in barometric pressure due to the damping response of the
soil system (AlAhmady 1995).
The value of the constant B can be computed from a least square fit to differential pressure across the
structure slab and indoor radon concentration measurement. For the UFRRH this value was computed as 13.23
(Hintenlang and AlAhmady 1994). Figure 10 illustrates predictions of windinduced pressure differentials across
the slab on the convective radon entry rate. It should be noted that these pressure differences depend on complexity
interacting parameters including slablfoundation joints, soil characteristics, and wind characteristics. For practical
concerns, the influence of windinduced pressure differentials generated from wind movement around the structure
on indoor radon entry is minimal when compared with their influence on the indoor radon removal rate.
CONCLUSIONS
Pressure differentials affecting radon entry from the substructure area into the indoor and indoor radon
removal from the indoor to the outdoor, that generated from wind movements around the structure are interacting
with many parameters including: wind speed and direction, wind wave fluctuation and span, structure shell and
foundation details, and soil characteristics. A mathematical approach based on the conservation of wind momentum
between wind stream and the structure shell, neglecting the share stress with the ground, can be used to develop a
mechanistic model predicting pressure differentials generated in response to different windlstructure configurations.
These windinduced pressure differentials may then be integrated into mathematical representations of the structure
ventilation and radon entry to characterize winds effects on radon removal and entry rates. It has been observed that
windinduced pressure differentials generated from different wind configurations have a minimal effect of soilgas
radon transport from substructure area into the interior when compared with their effects on structure ventilation and,
consequently, indoor radon removal rates. The mathematical approach and model developed in this work may be
1996 International Radon Symposium IIP  3.4
used to quantify wind conditions upon which minimal effects are anticipated for the purpose of shortterm indoor
radon concentration testing.
REFERENCES
AlAhrnady, K.K. "Measurements and Theoretical Modeling of Radon Driving Forces and Indoor Radon
Concentration and The Development of Radon Prevention and Mitigation Technology", Ph.D. Dissertation,
University of Florida. Gainesville, Florida; 1995.
ASTM (American Society for Testing and Materials). "Standard Test Method for Determining Air Leakage Rate by
Fan Pressurization". Philadelphia: ASTM; ASTM E77987; 1987.
Fukuda, H. "Air and Vapor Movement in Soil Due to Wind Gustiness", Soil Sciences, 79: 249; 1955.
Hintenlang D.E.; AlAhmady, K.K.,"Influence of Ventilation Strategies on Indoor Radon Concentrations Based on a
SemiEmpirical Model for FloridaStyle Houses", Health Physics, 66: 427, 1994.
Nazaroff, W.W.; Feustal, A.; Nero, A.; Revzan, K.L.;Grimsrud, D.T.; Essling, M.A.; Toohey, R.E. "Radon
Transport into a Detached OneStory House with a Basement", Atmospheric Environment, 19: 3 1; 1988.
Van der Hoven, I. "Power Spectrum of Horizontal Wind Speed in the Frequency Range from 0.0007 to 900 cycles
per hour", Journal of Meteorology, 14, 160, 1957.

1996 International Radon Symposium IIP 3.5
10 !
0
5
10
Wind Speed (m/s)
15
 (056
I
20
25
mph)
Figure I: The windinduced pressure differential predictions for a range of wind speed blowing on the windward side
wall of a structure when the indoor pressure equals the barometric pressure.
70
1
0
3
5
10
Wind Speed (m/s)
1
15
 (056
20
25
mph)
Figure 2: The windinduced pressure differential predictions for a range of wind speed blowing on the leeward side
wall of a structure
when the indoor pressure equals the barometric pressure.
"
1996 International Radon Symposium IIP  3.6
15
10
Wind Speed (rn/s)
 (056
20
rnph)
Figure 3: The windinduced pressure differential predictions for a range of wind speed blowing on the side wall of a
structure when the indoor pressure equals the barometric pressure.
10
1

!
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
\
1
Wind Drag Coefficient
1 rn/s
wind
+3 rn/s
wind
5 m/s wind
+
* 10
m/s
wind
1
Figure 4: The model predictions of windinduced pressure differences generated for several wind speeds blowing on
the windward side wall of a structure as a function of the wind drag coefficient.
1996 International Radon Symposium IIP  3.7
300
1
0
720
,
,
1440
2160
2880
3600
4320
Time (min.)
Figure 5: Prediction of windinduced pressure differences in response to temporal variations in barometric pressure
and indoor pressure equal to the average barometric pressure for I (lower curve) and 14 m/s wind on the windward
wall.
v
100 :
0
7 20
1440
2160
2880
I
3600
4320
Time (min.)
Figure 6: Prediction of windinduced pressure differences in response to temporal variations in barometric pressure
and indoor pressure equal to the average barometric pressure for 1 (upper curve) and 14 rn/s wind on the leeward
wall.

1996 International Radon Symposium IIP 3.8
0
5
10
Wind Speed ( r n / s )
15
 (056
20
25
mph)
Figure 7: Predictions of the windinduced pressure differential effects on the UFRRH ventilation for a range of wind
speed blowing on the windward wall of the structure.
Figure 8: Predictions of the windinduced pressure differentials effect on the UFRRH ventilation for a range of wind
speed blowing on the side wall of the structure.
1996 International Radon Symposium IIP  3.9
LJ
1

0
0.~2
0.~1
0.~3
0.~4
0.~5
0.~6
0.~7
0.~8
0.~9
1
Wind Drag Coefficient
1 +I
rn/s
wind
+3 m/s
wind
+5
wind
m/s
6
10 rn/s
wind
1
Figure 9: Predictions of the effect of wind speed on the UFRRH ventilation for all the possible interaction
configurations developed by the wind direction and fluctuations across the structure.
1
Q
s
10
15 20
25
30
35
40
45
50
55
60
.(
SubSlob to Indoor Pressure Oiff. (Pa)
Figure 10: Predictions of the convective radon entry rate from the substructure area into the indoor for interior
depressurization of 2 to 60 Pa.

I996 International Radon Symposium [IP 3.10