User:
Leakage problem on windows and doors
Description 
When the wind flows around an obstacle, it deflects, creating areas of higher and lower velocity. Specifically:
• When the flow is perpendicular to the obstacle, a bifurcation occurs in the flow. There is a current that deflects to the left (blue zone - upward perpendicular velocity) and another to the right (red zone - downward perpendicular velocity). Between these zones, there is a green zone corresponding to an area without velocity.
• When the obstacle is rotated towards the flow, the bifurcation is less pronounced. In particular, there is no green zone without flow.
To understand the effect of the flow, it is important to understand that the pressure is lower when the flow is faster and is maximum in areas without velocity. Therefore, in the first obstacle, a high-pressure zone is created in front of the obstacle. This pressure pushes the windows inward, creating gaps through which water penetrates.
Therefore, there are two strategies to combat leakage:
Avoid situations of frontal flow that create high-pressure zones. This is achieved through the study of currents and proper design.
Ensure that the pressure inside the house is high to create a force opposite to the one pushing the window/door inward. This is achieved by sealing the house and preventing air leakage from the interior to the exterior.
When modeling these effects, it is important to keep in mind that:
The airflow is turbulent, and vortices can form at the rear of the house.
These vortices can lead to high-pressure points in areas that may not intuitively be exposed.
ID:(481, 0)
Classification of the window water tightness
Description
The window's air tightness classification is measured by exposing it to a pressure difference and spraying it with water while measuring the time it retains water without penetrating the window. The EN 12208:2001 standard defines how to conduct the measurement and establishes the following classes:
| Pressure [Pa] | Class | Time [min] |
| 0 | 1A | 15 |
| 50 | 2A | 20 |
| 100 | 3A | 25 |
| 150 | 4A | 30 |
| 200 | 5A | 35 |
| 250 | 6A | 40 |
| 300 | 7A | 45 |
| 450 | 8A | 50 |
| 600 | 9A | 55 |
| 750 | 10A | 60 |
| 900 | 11A | 65 |
| 1050 | 12A | 70 |
ID:(756, 0)
Pressure on the surface
Concept
The pressure on the surface ($p_z$), which acts vertically to the surface:
and is generally smaller than the atmospheric pressure ($p_0$) due to the effects of air displacement from the air density ($\rho_a$) with the wind speed with height ($V_z$).
In this case, we can model it using the Bernoulli equation with its kinetic energy term:
$\displaystyle\frac{1}{2} \rho_a V_Z^2$
This factor is corrected with a factor depending on the shape of the body, the aerodynamic shape factor ($C_a$), and a factor originating from fluctuations due to turbulence vortices, the surface pressure reduction ($q_z$), resulting in:
| $ q_z = \displaystyle\frac{1}{2} \rho_a V_z ^2 C_d C_a$ |
Thus, the pressure on the surface ($p_z$) can be calculated resulting in:
| $ p_z = p_0 - q_z $ |
ID:(768, 0)
Filtration mechanism
Concept
Windows and doors are exposed to the surface pressure difference ($\Delta p$) between the surface pressure reduction ($q_z$) existing outside and the minimum pressure ($p_{min}$) inside.
When there are drops in pressure around the house and it is not airtight, the pressure inside tends to drop below the external pressure values. Therefore, the surface pressure difference ($\Delta p$) is defined as:
| $ \Delta p = p_z - p_{min} $ |
the surface pressure difference ($\Delta p$) fluctuates over time and at times may exceed the pressure limit that defines the window's airtightness.
Each time this occurs, the window or door begins to leak, and the volume of water can be estimated by assuming laminar flow through a channel between two surfaces with a microscopic length of the seal and a width equal to the perimeter of the window or door.
ID:(770, 0)
Model
Concept
Parameters
Variables
Calculations
to 
, then, select the variable: 
to 
Calculations
Calculations
Variable 
Given Calculate 
Target : Equation To be used 
Equations
$ C_a = 0.3445 \theta ^2 - 1.4961 \theta + 0.8$
C_a = 0.3445* theta ^2 - 1.4961* theta + 0.8
$ \Delta p = p_z - p_{min} $
Dp = p_z - p_min
$ J_V = \displaystyle\frac{ h ^3 L }{12 \eta }\displaystyle\frac{ \Delta p }{ d }$
J_V = h ^3* L * Dp /(12* eta * d)
$ p_z = p_0 - q_z $
p_z = p_0 - q_z
$ q_z = \displaystyle\frac{1}{2} \rho_a V_z ^2 C_d C_a$
q_z = rho_a * V_z ^2* C_d * C_a /2
$ V_z = \displaystyle\frac{2}{5} u \ln\left(\displaystyle\frac{ z }{ z_o }\right)$
V_z = 2* u * log( z / z_o )/5
ID:(767, 0)
Speed with height
Equation
The wind speed with height ($V_z$) depends on the height above ground ($z$). Typically, it is virtually negligible at the surface and reaches the value reported in meteorological reports at a height of 10 meters. Its variation is influenced by the terrain roughness, expressed by the roughness length ($z_o$), and by the friction speed ($u$), as follows:
| $ V_z = \displaystyle\frac{2}{5} u \ln\left(\displaystyle\frac{ z }{ z_o }\right)$ |
ID:(757, 0)
Aerodynamic form factor model
Equation
The aerodynamic shape factor ($C_a$) can be modeled as a function of the wind angle ($\theta$) to estimate the contributions to the pressure from the different surfaces of the object. This model is based on constants derived from measurements taken on various different objects:
| $ C_a = 0.3445 \theta ^2 - 1.4961 \theta + 0.8$ |
ID:(761, 0)
Reduction of pressure on the surface
Equation
The surface pressure reduction ($q_z$) is the pressure per unit area by which it decreases on the surface of the body. It is modeled as a modification of the Bernoulli's principle, characterized by the air density ($\rho_a$) and the wind speed with height ($V_z$), correcting for dynamics with the dynamic response factor ($C_d$), and geometry with the aerodynamic shape factor ($C_a$):
| $ q_z = \displaystyle\frac{1}{2} \rho_a V_z ^2 C_d C_a$ |
ID:(759, 0)
Pressure on the surface of a body
Equation
The pressure on the surface ($p_z$) is equal to the atmospheric pressure ($p_0$) reduced by the surface pressure reduction ($q_z$):
| $ p_z = p_0 - q_z $ |
ID:(776, 0)
Surface pressure difference
Equation
The pressure inside tends to be equal to the minimum pressure ($p_{min}$), so the surface pressure difference ($\Delta p$) is obtained by subtracting the minimum pressure ($p_{min}$) from the surface pressure reduction ($q_z$):
| $ \Delta p = p_z - p_{min} $ |
ID:(769, 0)
Water flow in windows
Equation
The filtration flow ($J_V$) is estimated assuming a model where the airtightness is achieved with two surfaces of a thickness the distance in flow direction ($d$) from a distance between contacts ($h$) with a width corresponding to the surface perimeter ($L$). The flow is propelled by the surface pressure difference ($\Delta p$) to move the water with a viscosity ($\eta$) and is calculated through:
| $ J_V = \displaystyle\frac{ h ^3 L }{12 \eta }\displaystyle\frac{ \Delta p }{ d }$ |
ID:(771, 0)