Answer:
The mass flow rate is m = 12.0 kg/s
Explanation:
From the question we are given the following parameters
inlet temperature , [tex]T_1 = 20[/tex]°C = 293 K
inlet pressure , [tex]P_1 = 95KPa[/tex]
Outlet pressure [tex]P_2[/tex] [tex]= 1.25*10^3 kPa[/tex]
Outlet temperature , [tex]T_2 = 430[/tex]°C
[tex]=703K[/tex]
Final velocity , [tex]V_2 = 90m/s[/tex]
Power Input , [tex]W_c =5000kW[/tex]
Considering the energy equation we have
[tex]h_1 +\frac{V_1^2}{2} +q = h_2 +\frac{V_2^2}{2} +w[/tex]
q is the net heat transferred
w is the net workdone
Lets assume that q = 0 and [tex]V_1 = 0[/tex] Hence in this question the specific heat capacity is constant
= > [tex]-w =h_2 - h_1 +\frac{V_2^2}{2}[/tex]
[tex]=(C_P)_0 (T_2 -T_1) + \frac{V_2^2}{2}[/tex]
[tex]= (1.004)(703-293) + \frac{90^2}{2(1000)}[/tex]
The division by 1000 is to convert the kinetic energy to KJ
Note the specific heat of air is 1.004 kJ/kg⋅K
[tex]= 415.5 KJ/kg[/tex]
The mass flow rate is given as [tex]m = \frac{Z}{-w}[/tex]
Where Z is The power input to the compressor which is given as 5000 kW
[tex]m = \frac{5000}{415.5}[/tex]
[tex]12kg/s[/tex]
