Affinity laws
Encyclopedia
The affinity laws are used in hydraulics
and HVAC
to express the relationship between variables involved in pump or fan performance (such as head, volumetric flow rate
, shaft speed) and power
. They apply to pump
s, fans
, and hydraulic turbines. In these rotary implements, the affinity laws apply both to centrifugal and axial flows.
The affinity laws are useful as they allow prediction of the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter. The only requirement is that the two pumps or fans are dynamically similar, that is the ratios of the fluid forced are the same.
Law 1. With impeller diameter (D) held constant:
Law 1a. Flow is proportional to shaft speed: ,
Law 1b. Pressure or Head is proportional to the square of shaft speed:
Law 1c. Power is proportional to the cube of shaft speed:
Law 2. With shaft speed (N) held constant:
Law 2a. Flow is proportional to impeller diameter:
Law 2b. Pressure or Head is proportional to the square of impeller diameter:
Law 2c. Power is proportional to the 3rd power of impeller diameter:
where
These laws assume that the pump/fan efficiency remains constant i.e.
. When applied to pumps the laws work well for constant diameter variable speed case (Law 1) but are less accurate for constant speed variable impeller diameter case (Law 2).
Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
and HVAC
HVAC
HVAC refers to technology of indoor or automotive environmental comfort. HVAC system design is a major subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics, and heat transfer...
to express the relationship between variables involved in pump or fan performance (such as head, volumetric flow rate
Volumetric flow rate
The volumetric flow rate in fluid dynamics and hydrometry, is the volume of fluid which passes through a given surface per unit time...
, shaft speed) and power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
. They apply to pump
Pump
A pump is a device used to move fluids, such as liquids, gases or slurries.A pump displaces a volume by physical or mechanical action. Pumps fall into three major groups: direct lift, displacement, and gravity pumps...
s, fans
Fan (mechanical)
A mechanical fan is a machine used to create flow within a fluid, typically a gas such as air.A fan consists of a rotating arrangement of vanes or blades which act on the air. Usually, it is contained within some form of housing or case. This may direct the airflow or increase safety by preventing...
, and hydraulic turbines. In these rotary implements, the affinity laws apply both to centrifugal and axial flows.
The affinity laws are useful as they allow prediction of the head discharge characteristic of a pump or fan from a known characteristic measured at a different speed or impeller diameter. The only requirement is that the two pumps or fans are dynamically similar, that is the ratios of the fluid forced are the same.
Law 1. With impeller diameter (D) held constant:
Law 1a. Flow is proportional to shaft speed: ,
Law 1b. Pressure or Head is proportional to the square of shaft speed:
Law 1c. Power is proportional to the cube of shaft speed:
Law 2. With shaft speed (N) held constant:
Law 2a. Flow is proportional to impeller diameter:
Law 2b. Pressure or Head is proportional to the square of impeller diameter:
Law 2c. Power is proportional to the 3rd power of impeller diameter:
where
-
is the volumetric flow rate (e.g. CFMCFMCFM is an abbreviation for cubic feet per minute which is a measure of flow for liquids and gases, like air or water. CFM may also refer to:*Calea Ferată din Moldova, the Moldovan State Railway...
, GPM or L/s), -
is the impeller diameter (e.g. in or mm), -
is the shaft rotational speed (e.g. rpm), -
is the pressure or head developed by the fan/pump (e.g. ft or m), and -
is the shaft power (e.g. W).
These laws assume that the pump/fan efficiency remains constant i.e.
. When applied to pumps the laws work well for constant diameter variable speed case (Law 1) but are less accurate for constant speed variable impeller diameter case (Law 2).