- Affinity laws
The

**affinity laws**are used inhydraulics andHVAC 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 topump s, fans, andhydraulic turbine s. 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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