(Solved): A three-stages air compressor with similar pressure ratio, swept and clearance volume, operating a ...

A three-stages air compressor with similar pressure ratio, swept and clearance volume, operating at \( 1400 \mathrm{rpm} \). The compressor delivery pressure is set at 12 bar with free air delivery conditions of \( 1.013 \) bar and \( 27^{\circ} \mathrm{C} \). To minimize the work input, an intercooler is fitted in between stages and the air temperature flowing into the intermediate-pressure (IP) and high-pressure (HP) are \( 40^{\circ} \mathrm{C} \) and \( 45^{\circ} \mathrm{C} \) respectively. The swept volume and clearance volumes of each cylinder are \( 1000 \mathrm{~cm}^{3} \) and \( 50 \mathrm{~cm}^{3} \) respectively. The compression and expansion process of the air is done polytropically following, \( P V^{l .3}= \) constant i) Sketch the indicator \( P-V \) diagram of the compressors. ii) Sketch the processes on a T-s diagram. iii) Calculate the pressure ratio of each cylinder. iv) Determine the indicated power for each compressor stage, \( \mathrm{kW} \). v) Calculate the free air delivery, \( \mathrm{m}^{3} / \mathrm{min} \). vi) Calculate the volumetric efficiency of the low-pressure (LP) compressor, \( \% \). vii) Determine the indicated power if the compression process is done in a single-stage compressor, \( k W \). Take for air, \( \mathrm{R}=0.287 \mathrm{~kJ} / \mathrm{kg} . \mathrm{K} \).