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Problems

1. Derive the radial equilibrium equation for an incompressible fluid flowing with axisym-
metric swirl through an annular duct.
Air leaves the inlet guide vanes of an axial flow compressor in radial equilibrium and
with a free-vortex tangenital velocity distribution. The absolute static pressure and static
temperature at the hub, radius 0.3 m, are 94.5 kPa and 293 K respectively. At the casing,
radius 0.4 m, the absolute static pressure is 96.5 kPa. Calculate the flow angles at exit from
the vanes at the hub and casing when the inlet absolute stagnation pressure is 101.3 kPa.
Assume the fluid to be inviscid and incompressible. (Take R D 0.287 kJ/(kg ° C) for air.).
2. A gas turbine stage has an initial absolute pressure of 350 kPa and a temperature
of 565 ° C with negligible initial velocity. At the mean radius, 0.36 m, conditions are as
follows:
Nozzle exit flow angle 68 deg
Nozzle exit absolute static pressure 207 kPa
Stage reaction 0.2
Determine the flow coefficient and stage loading factor at the mean radius and the reaction
at the hub, radius 0.31 m, at the design speed of 8000 rev/min, given that stage is to have a