Affinity laws

Affinity laws

The affinity laws are used in hydraulics and HVAC to express the relationship between several variables involved in pump or fan performance (such as head, volumetric flow rate, shaft speed, and power). They apply to pumps, fans, and hydraulic turbines. In these various rotary implements, the Affinity Laws apply both to centrifugal and axial flows.

Law 1. With impeller diameter (D) held constant:

Law 1a. Flow is proportional to shaft speed: { Q_1 over Q_2} = { left ( {N_1 over N_2} ight )} Law 1b. Pressure or Head is proportional to the square of shaft speed: {H_1 over H_2} = { left ( {N_1 over N_2} ight )^2 }

Law 1c. Power is proportional to the cube of shaft speed: {P_1 over P_2} = { left ( {N_1 over N_2} ight )^3 }

Law 2. With shaft speed (N) held constant:

Law 2a. Flow is proportional to impeller diameter: { Q_1 over Q_2} = { left ( {D_1 over D_2} ight )} Law 2b. Pressure or Head is proportional to the square of impeller diameter: {H_1 over H_2} = { left ( {D_1 over D_2} ight )^2 }

Law 2c. Power is proportional to the cube of impeller diameter : {P_1 over P_2} = { left ( {D_1 over D_2} ight )^3 }

where
* Q is the volumetric flow rate (e.g. CFM or GPM),
* D is the impeller diameter (e.g. in),
* N is the shaft rotational speed (e.g. rpm),
* H is the pressure or head developed by the fan/pump, and
* P is the shaft power.

These laws assume that the pump/fan efficiency remains constant. In other words, eta_1 = eta_2 .


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