To cool a summer home without using a vapor compression refrigeration cycle, air is routed through a plastic pipe (k=0.15 W/m*K,
D_inner=0.15m, D_outer=0.17m) that is submerged in an adjoining body of water. the water temperature is nominally at T_infinity=17 degrees Celsius and has a convection coefficient of h=1500W/m^2*K is maintained at the outer surface of the pipe. If air from the home enters at T_m,i=29 degrees Celsius and a volumetric flow rate of V_i=0.025 m^3/s, what pipe length, L, is needed to provide a discharge temperature of T_m,o=21 degrees Celsius?
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Answer:
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To cool a summer home without using a vapor compression refrigeration cycle, air is routed through a plastic pipe (k=0.15 W/m*K, D_inner=0.15m, D_outer=0.17m) that is submerged in an adjoining body of water. the water temperature is nominally at T_infinity=17 degrees Celsius and has a convection coefficient of h=1500W/m^2*K is maintained at the outer surface of the pipe. If air from the home enters at T_m,i=29 degrees Celsius and a volumetric flow rate of V_i=0.025 m^3/s, what pipe length, L, is needed to provide a discharge temperature of T_m,o=21 degrees Celsius
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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, = 32.2 lbm.ft/lbf.s², 1Btu/lbm=25037ft²/s²
Air standard assumptions:
= 0.0240Btu/lbm.°R, R = 53.34ft.lbf/lbm.°R = 1717.5ft²/s².°R 0.0686Btu/lbm.°R
k= 1.4
Energy balance:
As enthalpy exerts more influence than the kinetic energy inside the engine, kinetic energy of the fluid inside the engine is negligible
hence
= 20+460 = 480°R
= 533.25°R
Pressure at the inlet of compressor at isentropic condition
=
= 14.45 psia