Question 9.3: Figure 9.2 shows the data of a wind tunnel test for a new ve......
Figure 9.2 shows the data of a wind tunnel test for a new vehicle on a model scale of 1 : 15. The variation in the model coefficient of drag C_D with Reynolds number is shown.
It is necessary to estimate the aerodynamic drag force and the power required in the prototype when it moves at a steady speed of 100 km/h. The prototype vehicle is 2.3 m wide and has a frontal area is 7.5 m².
Assume that standard air is used in the wind tunnel test.
Therefore, ρ_{air} = 1.23 kg/m³, μ_{air} = 1.8 × 10^{-5} Pa-s, v_{air} = 1.45 × 10^{-5} m²/s
The test results of the plot show that the coefficient of drag is independent of the Reynolds number exceeding a value of 5 × 10^{5}. The vehicle moves at 100 km/h, i.e.,
v_{p}=100\times{\frac{10^{3}}{3600}}=27.78\,{\mathrm{m/s}}Therefore (R_{e})_{p}=\frac{27.78\times2.3}{1.45\times10^{-5}}=4.4\times10^{6}\gt 5\times10^{5}
Since the prototype Reynolds number exceeds the threshold value, dynamic similarity has been attained. Hence, the coefficient of drag of the prototype C_{Dp} = 0.40 (C_D by definition is a modified version of the Euler number E)
(F)_{p}=C_{D p}\times{\frac{1}{2}}\rho_{p}v_{p}^{2}A_{p}=0.4\times{\frac{1}{2}}\times1.23\times27.78^{2}\times7.5=1424~\mathrm{N}=1.424~\mathrm{kN} \\ (\text{Power})_{p}=F_{p}\times v_{p}=1424\times27.78=39554\ \mathrm{W}=39.55\ \mathrm{kW}