Page 159 - Chemical Process Equipment - Selection and Design

7.2. PUMP THEORY 131
electrical motor control. Double-ported valve (d) gives better high velocity initially and high pressure head ultimately to the
control at large flow rates; the pressures on the upper and Power liquid. Elements of their theory will be discussed here. A glossary
plugs are balanced SO that less force is needed to move the stem. of pump terms and terms relating primarily to centrifugal pumps are
The single port (e) is less expensive but gives a tighter shutoff and is defined in the Glossary at the end of this chapter. The chief
generally satisfactory for noncritical service. The reverse acting variables involved in pump theory are listed here with typical units:
valve (f] closes on air failure and is desirable for reasons of safety in
some circumstances. D, diameter of impeller (ft or m),
H, output head (ft or m),
7.2. PUMP ~~~E~~~ n, rotational speed (llsec),
k, output power (HP or kW),
Pumps are of (TWO main classes: centrifugal and the others. These
others mostly have positive displacement action in which the Q, volumetric discharge rate (cfs or m’/sec),
discharge rate is largely independent of the pressure against which p, viscosity (lb/ft sec or N sec/m’),
they work. Centrifugal pumps have rotating elements that impart p3 density (Ib/cuft or kg/m3),
E, surface roughness (ft or m).

BASIC RELATIONS
A dimensional analysis with these variables reveals that the
functional relations of Eqs. (7.1) and (7.2) must exist:

The group DZnp/p is the Reynolds number and €ID is the
roughness ratio. Three new groups also have arisen which are
named

capacity coefficient, C, = Q/nD3, (7.3)
head coefficient, CH = gH/n2D2, (7.4)
power coefficient, Ck = P/pn3D5. (7.5)

The hydraulic efficiency is expressed by these coefficients as
q = gHpQ/P = CHCQ/Cp. (7.6)
Although this equation states that the efficiency is independent of
the diameter, in practice this is not quite true. An empirical relation
is due to Moody [ASCE Trans. 89, 628 (192611:
qz= 1 - (1 - ~1)(D1/Dz)o~z5. (7.7)
D’
4s) Geometrically similar pumps are those that have all the
dimensionless groups numerically the same. In such cases, two
1 .0 different sets of operations are related as follows:

0.8 (7.8)
(7.9)
(7.10)
0.6
The performances of geometrically similar pumps also can be
8.4 represented in terms of the coefficients C,, C,, Cp, and q. For
instance, the data of the pump of Figure 7.2(a) are transformed into
the plots of Figure 7.2(b). An application of such generalized curves
0.2 is made in Example 7.1.
Another dimensionless parameter that is independent of
diameter is obtained by eliminating D between C, and CH with the
‘b 0.2 0.4 0.6 0.8 1.0 result,

(h) N, = ~ZQ’.~/(~H)O.~~. (7.11)
Figure 7.1-(continued) This concept is called the specific speed. It is commonly used in the