For the adiabatic expansion of a perfect gas through a turbine, show that the overall efficiency ηt and small stage efficiency ηp are related by
where , and r is the expansion pressure ratio, γ is the ratio of specific heats. An axial flow turbine has a small stage efficiency of 86%, an overall pressure ratio of 4.5 to 1 and a mean value of γ equal to 1.333. Calculate the overall turbine efficiency.