Water-Lifting Devices – Pumps - Practices of Irrigation and On-farm Water Management - page 448

Law 1 (for discharge): Q 1

D 1
D 2 Q 2 =

D 1
D 2

2

Law 2 (for head): H 1

H 2 =

(12.6)

D 1
D 2

3

Law 3 (for impeller diameter): BHP 1

BHP 2 =

where

D 1 = initial diameter of the impeller

D 2 = diameter of the impeller after changes

This second set of affinity laws strictly applies only to radial-flow pumps. They are
only approximate for mixed-flow impellers. In addition, these equations only hold
for small changes in impeller diameter. Calculations for a trim of more than 10% of
the original diameter can be significantly in error.

12.4.6 Priming of Centrifugal Pumps

All centrifugal pumps must be primed by filling them with water before they can
operate. The objective of priming is to remove a sufficient amount of air from the
pump and suction line to permit atmospheric pressure and submergence pressure
to cause water to flow into the pump, when pressure at the eye of the impeller is
reduced below atmospheric as the impeller rotates.
When axial-flow and mixed-flow pumps are mounted with the propellers sub-
merged, there is normally no problem with re-priming of these pumps because the
submergence pressure causes water to refill the pumps as long as air can readily be
displaced. On the other hand, radial-flow pumps are often located above the water
source, and they can lose prime. Often, loss of prime occurs due to an air leak on
the suction side of the pump. Volute or diffuser pumps may lose prime when water
contains even small amounts of air or vapor. Prime will not be lost in a radial-flow
pump if the water source is above the eye of the impeller and flow of water into the
pump is unrestricted.
In some cases pumps are primed by manually displacing the air in them with
water every time the pump is restarted. Often, by using a foot valve or a check valve
at the entrance to the suction pipe, pumps can be kept full of water and primed when
not operating. If prime is lost, the water must be replaced manually, or a vacuum
pump can be used to remove air and draw water into the pump.
A self-priming pump is one that will clear its passages of air and resume delivery
of liquid without outside attention. Centrifugal pumps are not truly self-priming. So
called self-priming centrifugal pumps are provided with an air separator in the form
of a large chamber or reservoir on the discharge side of the pump. This separator
allows the air to escape from the pump discharge and entraps the residual liquid