# Development and Application of a New Apparatus for Moisture Measurement in Building Composites
## 3 Methods
### Computation Model  
[PERSON] et al. [23] presented a method for determining the vertical and horizontal flow of water through the specimen of porous material, permeability test was used following the EN 12697-19  
Figure 2: (**A**) HP4 apparatus, (**B**) scheme of hydrostatic pressure on sample.  
standard. In this method, a column of water with a constant height (300 mm) is applied to the specimen for a controlled time (the range from 30 to 60 s) in either the vertical or horizontal direction, depending on the parameter being measured.  
The quantity of water flow in the vertical and horizontal directions, expressed as QV and QH, were determined and calculated from:  
\[Q_{(V,H)}=\frac{m}{t}\times 10^{-6}, \tag{1}\]  
where m is the mass of the flowed water, in g; t is the time of water collection, in sec.  
The apparatus is able to measure the actual amount of liquid flow through the building composite; the principle is similar to the device presented above. In order to verify the accuracy of the results obtained on the prototype, a simulation model was created based on the calculation of the time outflow of liquid Q [g] from a system of three circular cross-section containers, where their diameter (\(\emptyset\) D1, \(\emptyset\) D2, \(\emptyset\) D3), height (h1, h2, h3) and cross-sectional area (S1, S2, S3) are defined. The total height H1 defines the initial hydrostatic pressure in the system, see Figure 2B. The size of the flow openings \(\emptyset\) d and their number n are defined in the drain container.  
It is considered that the case when the entire assembly (Figure 2B) is filled with liquid up to the upper container, i.e., up to the height H1; after filling, the assembly is without any further inflow (q0 = 0) of the liquid.  
For the i-area of the circular cross-section Si = 0,25.\(\pi\).Di2; I = 1,2,3; s = 0,25.\(\pi\).d2, the height limits, see Figure 2B, are H1 = h1 + h2 + h3, H2 = h2 + h3, H3 = h3.  
Depending on the level of z, during the discharge of liquid from the system of three containers, the area of their cross-section S (z) changes according to:  
\[\begin{array}{l}S(z)=S_{1}\text{ pro H2}\leq z\leq H1,\\ S(z)=S_{2}\text{ pro H3}\leq z\leq H2,\\ S(z)=S_{3}\text{ pro \ \ \ 0}\leq z\leq H3.\end{array} \tag{2}\]  
The time change of the water level is based on the differential equation  
\[\dot{z}(t)=\frac{q_{0}}{\rho.S(z)}-\frac{s.n}{S(z)}\sqrt{2.g.z}\,\ \ \ \ \ \ z(0)=H1. \tag{3}\]  
The time course of the weight of the leaked liquid is similarly based on the differential equation  
\[\dot{Q}(t,z)=\rho.s.n\sqrt{2.g.z},\ \ \ \ \ \ \ \ \ \ \ Q(0)=0. \tag{4}\]  
In the case where a constant mass inflow q0 > 0 flows into the upper container, Equation (2) for z (t) = 0 can express the steady level of water  
\[\overline{z}=\frac{1}{2.g}\bigg{(}\frac{q_{0}}{\rho.s.n}\bigg{)}^{2}. \tag{5}\]  
The functionality of the measuring apparatus through an above-mentioned simulation (computation) model was further verified. This simplified porosity model was used for the planned experiment to exclude various measurement effects, such as swelling of material or seals around the circumference of the test sample. That is why the test containers with defined holes diameters (1 and 5 mm) and a specified number of holes (1 to 9) were created. The results of the experiment and simulation model are show in Figure 3.  
As is shown in Figure 3, the experimental results obtained were compared to the calculation model. Sealing effectiveness is one of the critical factors in the permeability measurement. On this computation simulation, it was able to test various seals used to fix the test sample in the container.