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An inward flow radial gas turbine operates with a total-to-total efficiency (from nozzle inlet to diffuser outlet) of 0.92. At entry to the nozzles, the stagnation pressure and temperature of the gas are 300 kPa and 870 °C respectively. At outlet from the diffuser the pressure is 100 kPa and the velocity of flow is negligible at that point. The Mach number at exit from the nozzle (M₁) is 0.9. If the gas enters the impeller radially and there is no whirl at the impeller exit, find; i. ii. iii. density of the gas at entry to the nozzles the impeller tip speed (U₁) the flow angle at the nozzle outlet (₁) For gas: Specific heat ratio, y = 1.333, gas constant, R=287 J/kg.K and specific heat at constant pressure, Cp = 1147 J/kg.K (CO1- 12 marks, CO2-6 marks)