Handbook of Turbomachinery Second Edition Revised - Ventech!

Table 1 Variables of Interest in Turbomachines
with Their Dimensions
Flow rate Q L 3 t 1
Specific energy E L 2 t 2
Power P ML 2 t 3
Rotational speed N t 1
Size D L
Density r ML 3
Viscosity m ML 1 t 1
Using Buckingham’s pi theorem (see Streeter and Wylie [4]), these
variables can be combined into the following dimensionless groups:
p1 ¼ Q
ND3 p2 ¼ E
N2D2 p3 ¼ P
rN3D5 p4 ¼ m
rND2 The groups p1 and p3 are called the capacity (or flow) coefficient and power
coefficient, respectively. The group p4 has the form of reciprocal of
Reynolds number and therefore represents the importance of viscous effects
of the fluid. If it is recognized that the product ND represents the peripheral
velocity of the rotor u, then p4 indeed is the reciprocal of Reynolds number.
Finally, p2 is called the head coefficient. If E, the specific energy of the fluid,
is replaced by its dimensional equivalent gH, then the equation for p2 can be
replaced by
p2 ¼ gH
N 2 D 2
When dealing with hydraulic machines, whether they are power-producing
or power-absorbing, it a is very common practice to refer to the head H on
the machine. Centrifugal pumps often are used to pump fluids in reservoirs
located H units above the location of the pump. Similarly, all hydraulic
turbines utilize the stored potential energy of the fluid to convert into
mechanical shaft power. Such potential energy is available either in the form
of natural reservoirs or artificially created on rivers through dams. Hence
the total specific energy available to the fluid is equivalent to gH (less the
losses). Thus it is quite appropriate to replace E by gH while dealing with
hydraulic machines.
The head and power coefficients can be combined by eliminating D
from them. The resulting variable is called the specific speed (or sometimes
Copyright © 2003 Marcel Dekker, Inc.
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