Page 253 - Fluid Mechanics and Thermodynamics of Turbomachinery

234 Fluid Mechanics, Thermodynamics of Turbomachinery
the mechanical efficiency is 95%. If the radius ratio of the impeller eye is 0.3, calculate
a suitable inlet diameter assuming the inlet flow is incompressible. Determine the overall
total pressure ratio of the compressor when the total-to-total efficiency is 80%, assuming the
velocity at exit from the diffuser is negligible.
3. A centrifugal compressor has an impeller tip speed of 366 m/s. Determine the absolute
Mach number of the flow leaving the radial vanes of the impeller when the radial component
of velocity at impeller exit is 30.5 m/s and the slip factor is 0.90. Given that the flow area at
2
impeller exit is 0.1 m and the total-to-total efficiency of the impeller is 90%, determine the
mass flow rate.
4. The eye of a centrifugal compressor has a hub/tip radius ratio of 0.4, a maximum
relative flow Mach number of 0.9 and an absolute flow which is uniform and completely
axial. Determine the optimum speed of rotation for the condition of maximum mass flow
given that the mass flow rate is 4.536 kg/s. Also, determine the outside diameter of the eye
and the ratio of axial velocity/blade speed at the eye tip. Figure 7.4 may be used to assist
the calculations.
5. An experimental centrifugal compressor is fitted with free-vortex guide vanes in order
to reduce the relative air speed at inlet to the impeller. At the outer radius of the eye, air
leaving the guide-vanes has a velocity of 91.5 m/s at 20 deg to the axial direction. Determine
the inlet relative Mach number, assuming frictionless flow through the guide vanes, and the
impeller total-to-total efficiency.
Other details of the compressor and its operating conditions are:

Impeller entry tip diameter, 0.457 m
Impeller exit tip diameter, 0.762 m
Slip factor 0.9
Radial component of velocity at impeller exit, 53.4 m/s
Rotational speed of impeller, 11 000 rev/min
Static pressure at impeller exit, 223 kPa (abs.)
6. A centrifugal compressor has an impeller with 21 vanes, which are radial at exit, a
vaneless diffuser and no inlet guide vanes. At inlet the stagnation pressure is 100 kPa abs.
and the stagnation temperature is 300 K.
(i) Given that the mass flow rate is 2.3 kg/s, the impeller tip speed is 500 m/s and the
mechanical efficiency is 96%, determine the driving power on the shaft. Use eqn. (7.18a)
for the slip factor.
(ii) Determine the total and static pressures at diffuser exit when the velocity at that position
is 100 m/s. The total to total efficiency is 82%.
(iii) The reaction, which may be defined as for an axial flow compressor by eqn. (5.10b),
is 0.5, the absolute flow speed at impeller entry is 150 m/s and the diffuser efficiency
is 84%. Determine the total and static pressures, absolute Mach number and radial
component of velocity at the impeller exit.
(iv) Determine the total-to-total efficiency for the impeller.
(v) Estimate the inlet/outlet radius ratio for the diffuser assuming the conservation of angular
momentum.
(vi) Find a suitable rotational speed for the impeller given an impeller tip width of 6 mm.
7. A centrifugal pump is used to raise water against a static head of 18.0 m. The suction
and delivery pipes, both 0.15 m diameter, have respectively, friction head losses amounting to
2.25 and 7.5 times the dynamic head. The impeller, which rotates at 1450 rev/min, is 0.25 m
0
diameter with 8 vanes, radius ratio 0.45, inclined backwards at ˇ D 60 deg. The axial width
2
of the impeller is designed so as to give constant radial velocity at all radii and is 20 mm
at impeller exit. Assuming an hydraulic efficiency of 0.82 and an overall efficiency of 0.72,
determine