Page 254 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 235
(i) the volume flow rate;
(ii) the slip factor using Busemann’s method;
(iii) the impeller vane inlet angle required for zero incidence angle;
(iv) the power required to drive the pump.
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8. A centrifugal pump delivers 50 dm /s of water at an impeller speed of 1450 rev/min.
The impeller has eight vanes inclined backwards to the direction of rotation with an angle at
0
the tip of ˇ D 60 ° . The diameter of the impeller is twice the diameter of the shroud at inlet
2
and the magnitude of the radial component of velocity at impeller exit is equal to that of
the axial component of velocity at the inlet. The impeller entry is designed for the optimum
flow condition to resist cavitation (see eqn. (7.8)), has a radius ratio of 0.35 and the blade
shape corresponds to a well tested design giving a cavitation coefficient b D 0.3.
Assuming that the hydraulic efficiency is 70 per cent and the mechanical efficiency is
90 per cent, determine:
(1) the diameter of the inlet;
(2) the net positive suction head;
(3) the impeller slip factor using Wiesner’s formula;
(4) the head developed by the pump;
(5) the power input.
Also calculate values for slip factor using the equations of Stodola and Busemann,
comparing the answers obtained with the result found from Wiesner’s equation.
9. (a) Write down the advantages and disadvantages of using free-vortex guide vanes
upstream of the impeller of a high pressure ratio centrifugal compressor. What other sorts of
guide vanes can be used and how do they compare with free-vortex vanes?
(b) The inlet of a centrifugal air compressor has a shroud diameter of 0.2 m and a hub
diameter of 0.105 m. Free-vortex guide vanes are fitted in the duct upstream of the impeller
so that the flow on the shroud at the impeller inlet has a relative Mach number, M r1 D 1.0,
an absolute flow angle of ˛ 1 D 20 ° and a relative flow angle ˇ 1 D 55 ° . At inlet the stagnation
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conditions are 288 K and 10 Pa.
Assuming frictionless flow into the inlet, determine:
(1) the rotational speed of the impeller;
(2) the air mass flow.
(c) At exit from the radially vaned impeller, the vanes have a radius of 0.16 m and a design
point slip factor of 0.9. Assuming an impeller efficiency of 0.9, determine:
(1) the shaft power input;
(2) the impeller pressure ratio.