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22 Fluid Mechanics, Thermodynamics of Turbomachinery
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Problems

3
1. A fan operating at 1750 rev/min at a volume flow rate of 4.25 m /s develops a head
of 153 mm measured on a water-filled U-tube manometer. It is required to build a larger,
geometrically similar fan which will deliver the same head at the same efficiency as the
existing fan, but at a speed of 1440 rev/min. Calculate the volume flow rate of the larger fan.
2. An axial flow fan 1.83 m diameter is designed to run at a speed of 1400 rev/min with an
average axial air velocity of 12.2 m/s. A quarter scale model has been built to obtain a check
on the design and the rotational speed of the model fan is 4200 rev/min. Determine the axial
air velocity of the model so that dynamical similarity with the full-scale fan is preserved.
The effects of Reynolds number change may be neglected.
A sufficiently large pressure vessel becomes available in which the complete model can
be placed and tested under conditions of complete similarity. The viscosity of the air is
independent of pressure and the temperature is maintained constant. At what pressure must
the model be tested?
3. A water turbine is to be designed to produce 27 MW when running at 93.7 rev/min
under a head of 16.5 m. A model turbine with an output of 37.5 kW is to be tested under
dynamically similar conditions with a head of 4.9 m. Calculate the model speed and scale
ratio. Assuming a model efficiency of 88%, estimate the volume flow rate through the model.
It is estimated that the force on the thrust bearing of the full-size machine will be 7.0 GN.
For what thrust must the model bearing be designed?
4. Derive the non-dimensional groups that are normally used in the testing of gas turbines
and compressors.
A compressor has been designed for normal atmospheric conditions (101.3 kPa and 15 ° C).
In order to economise on the power required it is being tested with a throttle in the entry
duct to reduce the entry pressure. The characteristic curve for its normal design speed of
4000 rev/min is being obtained on a day when the ambient temperature is 20 ° C. At what
speed should the compressor be run? At the point on the characteristic curve at which the
mass flow would normally be 58 kg/s the entry pressure is 55 kPa. Calculate the actual rate
of mass flow during the test.
Describe, with the aid of sketches, the relationship between geometry and specific speed
for pumps.