$07-$Mec$-$B$6$; Dec. $2014$

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Question $5$: You are working for a company which manufactures air compressors. A

client would like to be able to handle air at $P_{01}=101\mathrm{.}3$kPa and $T_{01}=250K$ at a rate of $200$

$\frac{m^3}{s}.$ The available company model has a rotor tip$-$to$-$tip diameter of $0\mathrm{.}5$ m and handles

atmospheric air at $P_{01}=101\mathrm{.}3$kPa and $T_{01}=293K$ at a rate of when rotating at $5000$

rpm $.$ The totai$-$to$-$total pressure ratio is $1\mathrm{.}05.$ For a single stage you are given that the

total$-$to$-$total efficiency is $0\mathrm{.}93.$ The properties of air are: $y-1\mathrm{.}4$;$R=287\mathrm{.}0\frac{J}{k}g-K$ and

$Cp=1004\mathrm{.}5\frac{J}{k}g-K.$ Assuming that the stage efficiency does not change, determine: the

required size of the geometrically similar compressor stage, its operating speed; the outiet

total pressure and total temperature.