Handbook of Turbomachinery Second Edition Revised - Ventech!

above becomes a factor. This statement is sort of a ‘‘hybrid’’ of the
above two observations but serves as an alternate way to picture the
same process.
An interested reader who researches the marketplace of positive displacement
pump products will find variations on the simplified picture of Fig.
15(a) which allow variations in pump flow rate. However, it should be
understood that these are modifications of a machine whose basic tendencies
are as described in the above paragraphs.
Variable Displacement Pumping Elements
Dominating the specific speed spectrum from a ‘‘low’’ value on the order of
200 (rpm-gpm-ft units) to values in excess of 10,000 is the class of pumping
elements broadly known as variable displacement pumps. These machines are
also referred to as ‘‘dynamic’’ or ‘‘rotodynamic pumps.’’ Centrifugal pumps
and axial-flow pumps both fall into this general class, as well as a broad
range of ‘‘in-between’’ pumps that are neither purely centrifugal or axial.
These ‘‘in-between’’ pumps are often referred to as ‘‘mixed-flow’’ or
‘‘Francis’’ pumps.
Shown in Fig. 15(b) is ageneralized rotor of ahypothetical variable
displacement pump. This rotor has a radius r1 at its inlet, and a radius r2 at
its outlet. These radii may be equal, or the outlet radius r2 may be somewhat
greater than r1. The rotor is being turned about the axis of rotation as
shown, at an angular velocity o, requiring a torque T to maintain this
velocity. For this example, our rotor is assumed to consist of a single row of
moving blades. In the case of multiple moving rows, most real machines
intersperse stationary rows between the moving ones. In these cases, the
accounting procedure is slightly more involved than that presented here, but
not different in generality.
Fluid is flowing steadily through this rotor at a mass rate _m. Fluid
enters the rotor in the plane of the radius r1, with a ‘‘bulk’’ or ‘‘throughflow’’
velocity Cm1. This velocity is also referred to as a ‘‘meridonal’’
velocity. In addition to Cm1, a component exists in the tangential direction,
Cu1. The velocity component Cu1 is often equal to zero. If not equal to zero,
Cu1 is normally in the same direction as rotor rotation and is known as
‘‘prewhirl.’’ In cases where prewhirl exists, it is normally generated by the
designer for some particular reason. This topic will be discussed in more
detail in a subsequent section.
Fluid leaves the rotor in the plane of radius r2, with a ‘‘meridonal’’
velocity Cm2 (note that Cm2 may have a radial component, depending on
whether or not the inlet and exit radii are unequal). In addition, a tangential
Copyright © 2003 Marcel Dekker, Inc.