Answer:
Pressure = 115.6 psia
Explanation:
Given:
v=800ft/s
Air temperature = 10 psia
Air pressure = 20F
Compression pressure ratio = 8
temperature at turbine inlet = 2200F
Conversion:
1 Btu =775.5 ft lbf, [tex]g_{c}[/tex] = 32.2 lbm.ft/lbf.s², 1Btu/lbm=25037ft²/s²
Air standard assumptions:
[tex]c_{p}[/tex]= 0.0240Btu/lbm.°R, R = 53.34ft.lbf/lbm.°R = 1717.5ft²/s².°R 0.0686Btu/lbm.°R
k= 1.4
Energy balance:
[tex]h_{1} + \frac{v_{1} ^{2} }{2} = h_{a} + \frac{v_{a} ^{2} }{2}\\[/tex]
As enthalpy exerts more influence than the kinetic energy inside the engine, kinetic energy of the fluid inside the engine is negligible
hence [tex]v_{a} ^{2} = 0[/tex]
[tex]h_{1} + \frac{v_{1} ^{2} }{2} = h_{a} \\h_{1} -h_{a} = - \frac{v_{1} ^{2} }{2} \\ c_{p} (T_{1} -T_{a})= - \frac{v_{1} ^{2} }{2} \\(T_{1} -T_{a}) = - \frac{v_{1} ^{2} }{2c_{p} }\\ T_{a}=T_{1} + \frac{v_{1} ^{2} }{2c_{p} }[/tex]
[tex]T_{1}[/tex] = 20+460 = 480°R
[tex]T_{a} =480+ \frac{(800)(800}{2(0.240)(25037}[/tex]= 533.25°R
Pressure at the inlet of compressor at isentropic condition
[tex]P_{a } =P_{1}(\frac{T_{a} }{T_{1} }) ^{k/(k-1)}[/tex]
[tex]P_{a}[/tex] = [tex](10)(\frac{533.25}{480}) ^{1.4/(1.4-1)}[/tex]= 14.45 psia
[tex]P_{2}= 8P_{a} = 8(14.45) = 115.6 psia[/tex]
