Air at a stagnation temperature of $300 K$ (ratio of specific heats, $\gamma=1.4$ and specific gas constant $\mathrm{R}$ $=287 \mathrm{~J} / \mathrm{kgK}$ ) enters the impeller of a centrifugal compressor in axial direction. The stagnation pressure ratio between the diffuser outlet and impeller inlet is $4.0 .$ The impeller blade radius is 0.3 $\mathrm{m}$ and it is rotating at $15000 \mathrm{rev} / \mathrm{min} .$ If the slip factor $\sigma_{s}$ (Ratio of tangential component of air velocity at the blade tip to the blade tip speed) is $0.88,$ the overall efficiency (total-to-total) of the compressor (in \%) is__________

Air at a stagnation temperature of $300 K$ (ratio of specific heats, $\gamma=1.4$ and specific gas constant $\mathrm{R}$ $=287 \mathrm{~J} / \mathrm{kgK}$ ) enters the impeller of a centrifugal compressor in axial direction. The stagnation pressure ratio between the diffuser outlet and impeller inlet is $4.0 .$ The impeller blade radius is 0.3 $\mathrm{m}$ and it is rotating at $15000 \mathrm{rev} / \mathrm{min} .$ If the slip factor $\sigma_{s}$ (Ratio of tangential component of air velocity at the blade tip to the blade tip speed) is $0.88,$ the overall efficiency (total-to-total) of the compressor (in \%) is__________

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