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| The '''affinity laws''' are used in [[hydraulics]] and [[HVAC]] to express the relationship between variables involved in pump or fan performance (such as [[head (hydraulic)|head]], [[volumetric flow rate]], shaft speed) and [[Power (physics)|power]]. They apply to [[pump]]s, [[fan (mechanical)|fans]], and [[hydraulic turbine]]s. In these rotary implements, the affinity laws apply both to centrifugal and axial flows.
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| 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.
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| '''Law 1. With impeller diameter (D) held constant:'''
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| Law 1a. Flow is proportional to shaft speed:,<ref name=pumpfun>{{cite web|url=http://www.pumpfundamentals.com/yahoo/affinity_laws.pdf|title=Affinity Laws|work=www.pumpfundamentals.com}}</ref><ref>{{cite web|url=http://www.airturbine.com/fanlaws.html|title=Basic Fan Laws - Axial Fan Blades|work=airturbine propeller company}}</ref>
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| : <math> { Q_1 \over \ Q_2} = { \left ( {N_1 \over N_2} \right )} </math>
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| Law 1b. Pressure or Head is proportional to the square of shaft speed:
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| : <math> {H_1 \over H_2} = { \left ( {N_1 \over N_2} \right )^2 }</math>
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| Law 1c. Power is proportional to the cube of shaft speed:
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| : <math> {P_1 \over P_2} = { \left ( {N_1 \over N_2} \right )^3 }</math>
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| '''Law 2. With shaft speed (N) held constant:''' <ref name=pumpfun />
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| Law 2a. Flow is proportional to the impeller diameter to the 3rd power:
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| : <math> { Q_1 \over \ Q_2} = { \left ( {D_1 \over D_2} \right )^3 } </math>
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| Law 2b. Pressure or Head is proportional to the square of impeller diameter:
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| : <math> {H_1 \over H_2} = { \left ( {D_1 \over D_2} \right )^2 }</math>
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| Law 2c. Power is proportional to the fifth power of impeller diameter:
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| : <math> {P_1 \over P_2} = { \left ( {D_1 \over D_2} \right )^5 }</math>
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| http://www.engineeringtoolbox.com/affinity-laws-d_408.html | |
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| where
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| * <math> Q </math> is the volumetric flow rate (e.g. [[Cubic feet per minute|CFM]], GPM or L/s),
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| * <math> D </math> is the impeller diameter (e.g. in or mm),
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| * <math> N </math> is the shaft rotational speed (e.g. [[rpm]]),
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| * <math> H </math> is the pressure or head developed by the fan/pump (e.g. psi or Pascal), and
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| * <math> P </math> is the shaft power (e.g. W).
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| These laws assume that the pump/fan efficiency remains constant i.e. <math> \eta_1 = \eta_2 </math> . 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).
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| ==References==
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| <references />
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| {{DEFAULTSORT:Affinity Laws}}
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| [[Category:Hydraulics]]
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| [[Category:Pumps]]
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| [[Category:Fans]]
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| [[Category:Turbines]]
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| {{Mech-engineering-stub}}
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