We have that the power of the compressor is
[tex]H_p=24.242hp[/tex]
From the question we are told that:
Flow rate [tex]W=1kg/s[/tex]
inlet Pressure [tex]P_1=1 bar[/tex]
inlet Temperature [tex]T_1= 288k[/tex]
Outlet Temperature [tex]T_2= 370k[/tex]
Outlet Pressure [tex]P_2=200 kN/m^2=2bars[/tex]
[tex]Cp = 1.103 kJ[/tex]
[tex]R = 287 kJ (kg.k)[/tex]
Generally, the equation for Adiabatic head is mathematically given by
[tex]H=\frac{ZRT_1}{Cp-1/K}[\frac{P_2}{P_1}^{(Cp-1)/Cp}-1][/tex]
Where
[tex]Z=Compressibility\ factor[/tex]
[tex]Z=0.99[/tex]
Therefore
[tex]H=\frac{(0.99)(287)(288)}{(1.103)-1/(1.103)}[\frac{(200)}{(1)}^{((1.103)-1)/(1.103)}-1][/tex]
[tex]H=560925.5958 J/kg[/tex]
[tex]H=5.6*10^5J/kg[/tex]
Generally, the equation for centrifugal compressor power is mathematically given by
[tex]H_p=\frac{WH}{E*33000}[/tex]
Where
E is efficiency (adiabatic)
[tex]E=70\%=0.7[/tex]
Therefore
[tex]H_p=\frac{(1)(5.6*10^5)}{0.7*33000}[/tex]
[tex]H_p=24.242hp[/tex]
In conclusion
The power of the compressor is
[tex]H_p=24.242hp[/tex]
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