Answer :
Answer:
The outlet velocity is 159.9m/s
The outlet temperature = 290.6K
Explanation:
At initial condition
P=2 MPa
T=30°C
V=25 m/s
At final condition
P=0.3 MPa
Now from first law for open system
[tex]h_1+\dfrac{V_1^2}{2000}=h_2+\dfrac{V_2^2}{2000}[/tex]
We know that for air
h= 1.010 x T KJ/kg
[tex]1.01\times 303+\dfrac{25^2}{2000}=1.01\times T+\dfrac{V_2^2}{2000} -----1[/tex]
Now from mass balance
[tex]\rho=\dfrac{P}{RT}\dfrac{P_1}{RT_1}V_1=\dfrac{P_2}{RT_2}V_2\dfrac{2}{R\times 303}\times 25=\dfrac{0.3}{RT_2}V_2T_2=1.81V_2 ----------2[/tex]
Now from equation 1 and 2
[tex]V_2^2+3673.749V-612916.49=0[/tex]
So we can say that
[tex]V_2=159.9\ m/s[/tex]
The outlet velocity is 159.9m/s
Now by putting the values in equation 2
[tex]T_2=1.81\times 159.9 \\T_2=290.6K[/tex]
The outlet temperature = 290.6K