Answer:
[tex]A_{out} = 134.64\,cm^{2}[/tex]
Explanation:
The area of the outlet can be found by means of the Principle of Mass Conservation. A diffuser works usually as a steady state system:
[tex]\dot m_{in} - \dot m_{out} = 0[/tex]
[tex]\rho_{in}\cdot A_{in}\cdot v_{in}- \rho_{out}\cdot A_{out}\cdot v_{out} = 0[/tex]
The area of the outlet is:
[tex]A_{out} =\frac{\rho_{in}\cdot A_{in}\cdot v_{in}}{\rho_{out}\cdot v_{out}}[/tex]
[tex]A_{out} = \frac{(0.748\,\frac{kg}{m^{3}} )\cdot (60\,cm^{2})\cdot (150\,\frac{m}{s})}{(2\,\frac{kg}{m^{3}} )\cdot (25\,\frac{m}{s} )}[/tex]
[tex]A_{out} = 134.64\,cm^{2}[/tex]
