Page 207 - Centrifugal Pumps Design and Application

High Speed Pumps 181

This is to say that the estimated head coefficient in this breakdown is $
— .74, which falls within the ^ = .70 to .75 range typically occurring in
test experience.
No pretense exists about the theoretical elegance of the actual head ex-
ercise, but it does provide some insight into the workings of the pump. It
2
is clear that roughly /3 of the total head is provided by the forced vortex
l
in the bowl and that the remaining b comes from diffusion recovery. Or,
for example, assume that it would be possible to improve difraser effi-
ciency to 90% as is attainable in the relatively idealized case of a venturi
meter, thus increasing the head coefficient to \j/ — .77. Using this result,
we go to the following expression relating head coefficient to efficiency:

Then, assuming an original pump efficiency of 60%, the improved diffu-
sion recovery would increase the pump efficiency to 62.4%. A dramatic
(and probably unachievable) 10% improvement in diffusion recovery
would dilute to 2.4% improvement in the overall pump efficiency. Simi-
larly, truncation of the diffuser cone from an area ratio of 4 to an area
ratio of 3 would reduce the overall efficiency only from 60% to 59%.
It is useful to express head in convenient terms. Non-homogeneous
units are used in this chapter as is commonly done in everyday practice,
so constants in the main result from unit conversions. Impeller tip speed
is:

Specific Speed

To those familiar with algebra, but unfamiliar with pump technology, it
would appear that specific speed, described in Chapter 2, can be altered
by simply changing the rotational speed. Not so. To illustrate this, we
note from the affinity laws (also described in Chapter 2) that flow is pro-
portional to speed and head is proportional to the square of speed. Start
with a given pump with a specific speed of: