Answer:
The exit area of the nozzle is 0.000861 m².
Explanation:
Given that,
Velocity = 280 m/s
Rate = 2.5 kg/s
Pressure = 2 MPa
Temperature = 400°C
We need to calculate the volume
Using equation of ideal gas
[tex]PV=RT[/tex]
[tex]V=\dfrac{RT}{P}[/tex]
Put the value into the formula
[tex]V=\dfrac{0.287\times673}{2\times10^{3}}[/tex]
[tex]V=0.0965\ m^3/kg[/tex]
We need to calculate the exit area of the nozzle
Using equation of continuity
[tex]\dfrac{dm}{dt}=\dfrac{A_{1}v}{V}[/tex]
[tex]A=\dfrac{V\times\dfrac{dm}{dt}}{v}[/tex]
Put the value into the formula
[tex]A=\dfrac{0.0965\times2.5}{280}[/tex]
[tex]A=0.000861\ m^2[/tex]
Hence, The exit area of the nozzle is 0.000861 m².
