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• Notes

$\begin{array}{l}{\text { Air enters a nozzle steadily at } 2.21 \mathrm{kg} / \mathrm{m} 3 \text { and } 40 \mathrm{m} / \mathrm{s} \text { and leaves at } 0.762 \mathrm{kg} / \mathrm{m} 3 \text { and } 180 \mathrm{m} / \mathrm{s} \text { , If the inlet }} \\ {\text { area of the nozzle is } 90 \mathrm{cm} 2, \text { determine (a) the mass flow rate through the nozzle, and (b) the exit area of }} \\ {\text { the nozzle }}\end{array}$

$\rho_{1}=2.21 \mathrm{kg} / \mathrm{m}^{3}$

$\rho_{2}=0.762 \mathrm{kg} / \mathrm{m}^{3}$

$\dot{m}_{1}=\rho_{1} A_{1} V_{1}$

$=2 \cdot 21(0.009)(40)=0.796 \mathrm{kg} / \mathrm{s}$

$\dot m_{1}=\dot m_{2}=\dot{m}=0.796$

$\dot{m}=\rho_{2} A_{2} V_{2} \rightarrow A_{2}=\frac{\dot{m}}{\rho_{2} v_{2}}=\frac{0.796}{0.762*180}$

$=58 \mathrm{cm}^{2}=0.0058 \mathrm{m}^{2}$

$\text { A I-m } 3 \text { rigid tank initially contains air whose density is } 1.18 \mathrm{kg} / \mathrm{m} 3 . \text { The tank is } \mathrm{c}$

$\text { high-pressure supply line through a valve. The valve is opened, and air is allowe }$

$\begin{array}{l}{\text { the tank until the density in the tank rises to } 7.20 \mathrm{kg} / \mathrm{m} 3 \text { . Determine the mass of }} \\ {\text { entered the tank. }}\end{array}$

$\Delta m_\text { msystem }=m_{\text {in }}-m_{\text {out }}$

$m_{i n}=m_{2}-m_{1}$

$=\rho_{2} v-\rho_{1} v$

$m_{i n}=v\left(\rho_{2}-\rho_{1}\right)=1(72-1.18)={6.02 \mathrm{kg}}$

$\dot{V}_{\text {air }}=\dot{V}_{\text {air/pressure }} * \# person$

$=30 * 15=450 \mathrm{L} / \mathrm{s}$

$=0.45 \mathrm{m}^3/ \mathrm{s}$

$\dot{V}=V A=V (\frac{\pi D^2}{4})$

$D=\sqrt{\frac{4 \dot V}{\pi V}}=\sqrt{\frac{4*0.45}{\pi(8)}}=0.268 \mathrm{m}$

$=26.8 \mathrm{cm}$