Derive the radial equilibrium equation for an incompressible fluid flowing with axisymmetric swirl through an annular duct. Air leaves the inlet guide vanes of an axial-flow compressor in radial equilibrium and with a free-vortex tan genital 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 in viscid and incompressible. Take R 5 0.287 kJ/(kg °C) for air.