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Problems

1. Show, for an axial flow turbine stage, that the relative stagnation enthalpy across the
rotor row does not change. Draw an enthalpy entropy diagram for the stage labelling all
salient points.
Stage reaction for a turbine is defined as the ratio of the static enthalpy drop in the rotor
to that in the stage. Derive expressions for the reaction in terms of the flow angles and draw
velocity triangles for reactions of zero, 0.5 and 1.0.
2. (a) An axial flow turbine operating with an overall stagnation pressure of 8 to 1 has a
polytropic efficiency of 0.85. Determine the total-to-total efficiency of the turbine.
(b) If the exhaust Mach number of the turbine is 0.3, determine the total-to-static efficiency.
(c) If, in addition, the exhaust velocity of the turbine is 160 m/s, determine the inlet total
temperature.
Assume for the gas that C P D 1.175 kJ/(kg K) and R D 0.287 kJ/(kg K).
3. The mean blade radii of the rotor of a mixed flow turbine are 0.3 m at inlet and 0.1 m
at outlet. The rotor rotates at 20,000 rev/min and the turbine is required to produce 430 kW.
The flow velocity at nozzle exit is 700 m/s and the flow direction is at 70 ° to the meridional
plane.
Determine the absolute and relative flow angles and the absolute exit velocity if the gas
flow is 1 kg/s and the velocity of the through-flow is constant through the rotor.