# Demand Law of Fabric Weight on the Airflow Velocity of a Gas-Assisted Model
## 4 Discussion of the Demand Law
### Simulation Adjustment of the conveyed Fabric under Different Gram Weights  
According to Section 2.4, having determined the boundary layer thickness of each row of the pipeline output airflow on the lower surface of the conveyed fabric and set up monitoring points, the value changes in the monitoring points are observed, and the flow velocity is adjusted at the outlet of the pipeline, so that the flow velocity at the monitoring point is close to the theoretical value. The thickness of the boundary layer after the air outlet of each row of pipes under conveyed fabrics with different gram weights is shown in Table 6.  
Figure 13: Cloud map of the final pressure distribution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Conveyed Fabric Weight (g/m\({}^{2}\))** & **30** & **40** & **50** & **60** & **70** & **80** \\ \hline Theoretical air velocity in the \(x\)-direction (m/s) & 1.04 & 1.20 & 1.34 & 1.43 & 1.60 & 1.43 \\ Theoretical air velocity in \(y\)-direction (m/s) & 1.24 & 1.43 & 1.60 & 1.70 & 1.90 & 2.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Theoretical flow rate of the air outlet when the conveyed fabric has different gram weights. The flow rate of each row of pipelines for different grammage fabric requirements is summarized in Table 7.  
The fitting of the linear equation to the data in Table 7 is shown in Figure 14.  
The airflow formula is  
\[Q=\left(\frac{d}{2}\right)^{2}v\pi \tag{20}\]  
The total flow of the air compressor is calculated, and data fitting is conducted, as shown in Figure 15. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Conveyed Fabric Weight (g/m2)** & **30** & **40** & **50** & **60** & **70** & **80** \\ \hline Boundary layer thickness of the first row & 3.78 & 3.52 & 3.33 & 3.22 & 3.05 & 2.91 \\ Boundary layer thickness of the second & 5.00 & 4.66 & 4.41 & 4.27 & 4.04 & 3.85 \\ Boundary layer thickness of the third row of pipes (mm) & 5.76 & 5.36 & 5.07 & 4.91 & 4.64 & 4.43 \\ Boundary layer thickness of the fifth row of pipes (mm) & 6.35 & 5.91 & 5.60 & 5.41 & 5.12 & 4.88 \\ Boundary layer thickness of the fifth row & 6.10 & 5.67 & 5.37 & 5.20 & 4.91 & 4.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Boundary layer thickness of the gas flowing through the lower surfaces of different fabrics. Figure 14: The relationship between the airflow rate of each row of ducts and the weight of the fabric. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Conveyed Fabric Weight (g/m2)** & **30** & **40** & **50** & **60** & **70** & **80** \\ \hline The flow velocity of the first row & 3.08 & 3.47 & 3.86 & 4.12 & 4.49 & 4.60 \\ \begin{tabular}{c} of pipes \(V_{11}\) (m/s) \\ \end{tabular} & 3.97 & 4.50 & 5.04 & 5.52 & 6.15 & 6.78 \\ The flow velocity of the third row & 5.63 & 6.00 & 6.60 & 7.19 & 8.01 & 8.84 \\ \
\begin{tabular}{c} The flow velocity of the fourth \\ row of pipes \(V_{14}\) (m/s) \\ \end{tabular} & 6.65 & 7.59 & 7.94 & 8.45 & 9.46 & 10.36 \\
\begin{tabular}{c} The flow velocity of the fifth row \\ of pipes \(V_{15}\) (m/s) \\ \end{tabular} & 8.09 & 9.12 & 10.06 & 10.97 & 12.32 & 13.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The flow velocity of each row of pipe outlet under different fabric weights. The simulation results of this study are roughly the same as the expected results, and the pressure on the lower surface of the fabric is evenly distributed. The simulation results are roughly the same for different fabric weights. At the same time, it was found that the pressure at the boundary of the lower surface of the fabric is relatively small. It is speculated that the reason for this may be that the air velocity at the boundary increases significantly, resulting in a decrease in the peripheral pressure. The shortcoming of this study is that the fabric deformation, and the effect of this deformation on the airflow, are not considered. In future studies, the degree of fabric deformation and the coupling of the fabric to the airflow will be considered.