Page 252 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 233
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Problems

NOTE. In problems 2 to 6 assume
and R are 1.4 and 287 J/(kg ° C) respectively. In
problems 1 to 4 assume the stagnation pressure and stagnation temperature at compressor
entry are 101.3 kPa and 288 K respectively.)
1. A cheap radial-vaned centrifugal fan is required to provide a supply of pressurised air
to a furnace. The specification requires that the fan produce a total pressure rise equivalent
3
to 7.5 cm of water at a volume flow rate of 0.2 m /s. The fan impeller is fabricated from 30
thin sheet metal vanes, the ratio of the passage width to circumferential pitch at impeller exit
being specified as 0.5 and the ratio of the radial velocity to blade tip speed as 0.1.
Assuming that the overall isentropic efficiency of the fan is 0.75 and that the slip can be
estimated from Stanitz’s expression, eqn. (7.18a), determine
(1) the vane tip speed;
(2) the rotational speed and diameter of the impeller;
(3) the power required to drive the fan if the mechanical efficiency is 0.95;
(4) the specific speed.
3
For air assume the density is 1.2 kg/m .
2. The air entering the impeller of a centrifugal compressor has an absolute axial velocity
0
of 100 m/s. At rotor exit the relative air angle measured from the radial direction is 26 ° 36 ,
the radial component of velocity is 120 m/s and the tip speed of the radial vanes is 500 m/s.
Determine the power required to drive the compressor when the air flow rate is 2.5 kg/s and