Handbook of Turbomachinery Second Edition Revised - Ventech!

the turbine specific speed). The resulting equation can be written as
n 0 pffiffiffi
N P
s ¼ pffiffi 5=4
RðgHÞ
ð3aÞ
An alternate but perhaps more useful form of Eq. (3) can be obtained by
combining the head and flow coefficients and eliminating D from them. The
result is then
pffiffiffiffi
N Q
ns ¼ ð3bÞ
ðgHÞ 3=4
The variable ns is sometimes called the pump specific speed. A close look at
Eqs. (3) and (3a) would immediately reveal that they are both equivalent,
since P, Q, andH are related by the expression
P ¼ rgQH ð4Þ
In writing Eq. (4), care must be exercised to distinguish whether H
represents the gross or net head. Here it is assumed that H is the net head.
Otherwise the hydraulic efficiency Z needs to be introduced, which for most
hydraulic turbines operating at the design point is close to 90%.
The variable specific speed defined in Eq. (3a) or (3b) is one of the
most useful practical factors in sizing hydraulic machines. For turbines or
pumps handling large discharges at low heads, a high specific speed is
indicated; for high heads and low discharges the specific speed is low. It is
interesting to observe that the type (axial, radial, or mixed) of the machine
in question is strongly influenced by the specific speed. For high specific
speeds, which are due to high discharges (and/or low heads), a large flow
area is required to accommodate these high flow rates. An axial-flow
machine would best accomplish this since for such machines the flow area is
proportional to D 2 (in fact, *pD 2 less the area occupied by the hub).
Kaplan turbines and axial-flow fans fall into this category. These are
designed for best efficiency when operating at low heads and high
discharges. On the other hand, for low specific speed machines, which
require low discharges and correspondingly high heads, centrifugal or
radial-flow type machines are best suited. In such machines, since the flow is
radial the flow area is proportional to the circumference, and therefore D,
thus producing relatively low discharges. Also, since the flow moves radially,
the change in centrifugal head produces high pressure changes. Examples of
such machines are the centrifugal pump and Francis turbine. Thus as the
specific speed increases, the shape of the impeller changes from purely
centrifugal, to mixed, to purely axial. These are shown pictorially in Fig. 1.
Copyright © 2003 Marcel Dekker, Inc.