## 6 Application in Hot Wire Calibration
### Influence of Temperature and Humidity Discrepancies  
In Figure 18 we assume that the hot-wire anemometer outputs a series of values of hot wire voltage \(E\) = 1.33, 1.35, \(\ldots\), 1.50, and 1.52 when used in measuring flow velocity in a flow that has a temperature of \(T\) = 30 \({}^{\circ}\)C and a humidity of \(H\) = 20%RH, 60%RH, and 80%RH, respectively, then the points where the horizontal lines of \(E\) = 1.33, 1.35, \(\ldots\), 1.50, and 1.52 intersect the fitting curves of \(H\) = 20%RH, 60%RH, and 80%RH will give the measured velocity values (as presented in Table 16) under the corresponding flow temperature and humidity conditions. Further, if the hot wire had only been calibrated at humidity of \(H\) = 20%RH under \(T\) = 30 \({}^{\circ}\)C but not done at any other humidity values, and it was then used to measure flow velocity in a flow which had a different humidity of \(H\) = 60%RH or 80%RH and the same temperature \(T\) = 30 \({}^{\circ}\)C, then the measured velocity could only be extracted from the fitting curve of \(H\) = 20%RH via the output voltage values, which would lead to false measured velocity values. The velocity deviation errors \(\Delta U\) between the false and true values resulting from the humidity discrepancies (between 20%RH and 60%RH, or between 20%RH and 80%RH) will be equal to the velocity derived from the fitting curve of 20%RH minus the velocity derived from that of 60%RH (or 80%RH) in Figure 18, which are calculated in Table 16. From Table 16 it can be seen that if the fitting curve of 20%RH (at \(T\) = 30 \({}^{\circ}\)C) is used to provide measured velocity value of a flow with a humidity of 60%RH (or 80%RH) at the same \(T\) = 30 \({}^{\circ}\)C, the error in measured velocity will be in a range from 0.893% to 3.768% at a humidity of 60%RH (or from 0.726% to 20.225% at a humidity of 80%RH). The maximum error within the velocity range from 0.1 m/s to 1.0 m/s (corresponding to \(E\) = 1.35 to 1.50) is 3.245% over a humidity discrepancy of 40%RH (at 60%RH) and 10.811% over a humidity discrepancy of 60%RH (at 80%RH), contributing an error of 0.0811% and 0.18% per percentage point of relative humidity discrepancy, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**\(E\) (V)**} & \multirow{2}{*}{**\(H\)**} & \multirow{2}{*}{**20\%RH**} & \multicolumn{3}{c}{**60\%RH**} & \multicolumn{3}{c}{**80\%RH**} \\ \cline{3-8}  & & \(U\) **(m/s)** & \(U\) **(m/s)** & \(\Delta U\) **(m/s)** & \(\Delta U\) **(m/s)** & \(\Delta U\) **(m/s)** & \(\Delta U\) **(m/s)** & \(\Delta U\) **(\%)** \\ \hline  
Similarly, as can be seen in Figure 19 when the fitting curve of \(H=20\%\)RH (under \(T=40\)\({}^{\circ}\)C) is used in measuring flow velocity in a flow with a humidity of 60%RH or 80%RH under \(T=40\)\({}^{\circ}\)C, the errors in measured velocity (\(\Delta U\)) are the difference between the velocity extracted from the fitting curve of \(H=20\%\)RH and that of \(H=60\%\)RH or \(H=80\%\)RH at hotwire voltage \(E=1.30\), \(1.33\), \(\ldots\), \(1.45\), and \(1.47\), respectively. The velocity values and corresponding errors are shown in Table 17. The relative errors are in a range from 5.436% to 19.048% over a humidity discrepancy from 40%RH (at 60%RH) and 10.262% to 76.056% over a humidity discrepancy of 60%RH (at 80%RH), providing a maximum error of 19.048% and 76.056%, respectively. The error per percentage point of relative humidity discrepancy is 0.4762% and 1.2676%, respectively. In fact, the velocity values in Table 16 (\(T=30\)\({}^{\circ}\)C) minus those in Table 17 (\(T=40\)\({}^{\circ}\)C) at corresponding positions (meaning the same output voltage values \(E=1.33\), \(\ldots\), \(1.47\) and the same humidity (\(H\)) values) will yield the error in measured velocity if the fitting curves of \(T=30\)\({}^{\circ}\)C are used to predict the velocity values when the hot wire is applied to measure the flow velocity at a different temperature \(T=40\)\({}^{\circ}\)C (under the same humidity value \(H=20\%\)RH, 60%RH, and 80%RH, respectively).