A low speed wind tunnel has a contraction ratio of 14:1 and the cross-sectional area of the test section is 1m^2. The static pressure difference between the settling chamber and the test section is 40 cm of water column. Assume g=9.81m/s2,ρ_air=1.2kg/m3 and ρ_water=1000kg/m3. What is the speed of air in the test section?
A low speed wind tunnel has a contraction ratio of \(14:1\) and the cross-sectional area of the test section is \(1 m^{2}\). The static pressure difference between the settling chamber and the test section is \(40 \;cm\) of water column. Assume \(g=9.81 \;m/s^2,\rho_{air}=1.2\;kg/m^{3}\) and \(\rho_{water}=1000\;kg/m^{3}\). What is the speed of air in the test section?
Using continuity equation we get \[A_{1}V_{1}=A_{2}V_{2}\\\Rightarrow \frac{V_{1}}{V_{2}}=\frac{A_{2}}{A_{1}}=\frac{1}{14}\]
Pressure difference between the settling chamber and the test section will be \[40\times 10^{-2} \times 1000\times 9.81\\=3924\;Pa\]
On using Bernoulli’s equation we will find that velocity of air in the test section will be \[V_{2}=\sqrt{\frac{2\times\left ( P_{1}-P_{2} \right )}{\rho _{air}\left ( 1-\frac{V_{1}^{2}}{V_{2}^{2}} \right )}}
\\\Rightarrow V_{2}=\sqrt{\frac{2\times\left ( 3924 \right )}{1.2\left ( 1-\frac{1}{14\times 14} \right )}}
\\=21.08\;m/s\]
