# Blockage Effects in Wind Tunnel Tests for Tall Buildings with Surrounding Buildings
## 2 Wind Tunnel Tests
### Data Processing of Wind Tunnel Tests  
The wind pressures of the upper four layers were analyzed in this study, and only one lateral surface was considered because of the symmetry of the square model. The mean pressure coefficient of the \(i\)-th pressure point can be calculated as follows:  
\[\mu_{i}=\overline{w}_{i}/(\frac{1}{2}\rho V^{2}) \tag{2}\]  
where \(\overline{w}_{i}\) is the mean pressure of the \(i\)-th pressure point, \(\rho\) is the air density, and \(V\) is the test velocity. In turn, the layer pressure coefficient is defined as:  
\[\mu_{layer,j}=\sum_{n=1}^{6}\mu_{j,n}/6 \tag{3}\]  
where \(n\) represents the \(n\)-th pressure point of the \(j\)-th layer.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Condition** & **Small Model (I/600)** & **Medium Model (I/300)** & **Large Model (I/200)** & **Surrounding Model Height** \\ \hline
1a & 1.19\% & 4.76\% & 10.71\% & 0.5H \\
2a & 1.19\% & 4.76\% & 10.71\% & 0.5H \\
3a & 1.19\% & 4.76\% & 10.71\% & 0.5H \\
4a & 1.19\% & 4.76\% & 10.71\% & 0.5H \\
5a & 1.79\% & 7.14\% & 16.07\% & 0.5H \\
6a & 1.79\% & 7.14\% & 16.07\% & 0.5H \\
7a & 1.79\% & 7.14\% & 16.07\% & 0.5H \\
8a & 1.79\% & 7.14\% & 16.07\% & 0.5H \\
1b & 1.79\% & 7.14\% & 16.07\% & H \\
2b & 1.79\% & 7.14\% & 16.07\% & H \\
3b & 1.79\% & 7.14\% & 16.07\% & H \\
4b & 1.79\% & 7.14\% & 16.07\% & H \\
5b & 2.98\% & 11.90\% & \(-----\) & H \\
6b & 2.98\% & 11.90\% & \(-----\) & H \\
7b & 2.98\% & 11.90\% & \(-----\) & H \\
8b & 2.98\% & 11.90\% & \(-----\) & H \\ \hline \end{tabular}
\end{table}
Table 2: The blockage ratio of each test condition.  
Figure 5: Photos of the wind tunnel test. (**a**) Small single model; (**b**) Test condition 5a of the medium model; (**c**) Test condition 7a of the medium model.  
The blockage ratio of the small model is relatively small, generally less than 2%, so the wind pressure of the small model is less affected by the blockage effect. Therefore, the wind pressure results of the small model were used as a benchmark in this paper, and the relative error of the mean pressure coefficient of each layer is defined as:  
\[\Delta\mu_{layer,j,l}=\frac{(\mu_{layer,j,l}-\mu_{layer,j,s})}{\mu_{layer,j,s}} \tag{4}\]  
\[\Delta\mu_{layer,j,m}=\frac{(\mu_{layer,j,m}-\mu_{layer,j,s})}{\mu_{layer,j,s}} \tag{5}\]  
where the subscripts \(l\), \(m\), and \(s\) are the initials for large, medium, and small, respectively, representing the large, medium, and small models.  
The equation of drag coefficient is as follows:  
\[C_{D}=\frac{F_{D}}{0.5\rho V^{2}A} \tag{6}\]  
where \(F_{D}\) is the mean along-wind force and \(A\) is the windward area of the target pressure model.  
Based on the wind pressure data of the small model, the relative error of the drag coefficient can be obtained as follows:  
\[\Delta C_{D,l}=\frac{(C_{D,l}-C_{D,s})}{C_{D,s}} \tag{7}\]  
\[\Delta C_{D,m}=\frac{(C_{D,m}-C_{D,s})}{C_{D,s}} \tag{8}\]  
where \(C_{D,l}\), \(C_{D,m}\), and \(C_{D,s}\) represent the drag coefficients of the large model, medium model, and small model, respectively; \(\Delta C_{D,l}\) and \(\Delta C_{D,m}\) represent the relative error of the drag coefficients of the large model and medium model, respectively.