Page 238 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 219
Solution. Equation (7.16) is used for estimating the slip factor. Since
0
exp.2 cos ˇ /Z/ D exp.2 ð 0.643/7/ D 1.78, is less than r 2 /r 1 D 2, then B D 1
2
and A ' 0.77, obtained by replotting the values of A given in Figure 7.11 for
0
ˇ D 50 deg and interpolating.
2
The vane tip speed,U 2 D ND 2 /60 D ð 1200 ð 0.4/60 D 25.13 m/s.
The radial velocity,c r2 D Q/. D 2 b 2 / D 0.1/. ð 0.4 ð 0.0317/
D 2.51 m/s.
Hence the Busemann slip factor is

B D .0.77 0.1 ð 1.192//.1 0.1 ð 1.192/ D 0.739.

Hydraulic losses occur in the impeller and in the diffuser. The kinetic energy leaving
the diffuser is not normally recovered and must contribute to the total loss, H L . From
2
inspection of eqn. (2.45b), the loss in head in the diffuser is .1 D /.c 2 c //.2g/.
2 3
2
The head loss in the impeller is 0.1 ð U 2 c 2 /g and the exit head loss is c /.2g/.
3
Summing the losses,
2
2
H L D 0.485.c 2 c //.2g/ C 0.1 ð U 2 c 2 /g C c /.2g/.
2 3 3
Determining the velocities and heads needed,
0
c 2 D B U 2 .1 2 tan ˇ / D 0.739 ð 25.13 ð 0.881 D 16.35 m/s.
2
H i D U 2 c 2 /g D 25.13 ð 16.35/9.81 D 41.8m.
2
2
2
c /.2g/ D .16.35 C 2.51 //19.62 D 13.96 m.
2
2
2
c 3 D 4Q/. d / D 0.4/. ð 0.15 / D 5.65 m/s.
2
Therefore c /.2g/ D 1.63 m.
3
Therefore H L D 4.18 C 0.485.13.96 1.63/ C 1.63 D 11.8m.
The manometric head is
H L D 41.8 11.8 D 30.0m
H D H i
and the hydraulic efficiency

h D H/H i D 71.7%.

Performance of centrifugal compressors

Determining the pressure ratio
Consider a centrifugal compressor having zero inlet swirl, compressing a perfect
gas. With the usual notation the energy transfer is

h 01 D U 2 c 2 .
W D P W c / Pm D h 02