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

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

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

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

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

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, $eta_1 = eta_2$ .

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Affinity — Affinity, in etymology affinity is the opposite of infinity . These two words have the same root coming from the Latin: finis = end . “Affinity” meaning is near to the “finis” e.g. close to the “zero point” in a before assumed space. On the other …   Wikipedia

• Laws of attraction — In the history of science, the laws of attraction are a set of assumed laws or, in a sense, a general catch phrase used when discussing the nature of bodies that attract. Historically, the concept of there being a known set of the laws of… …   Wikipedia

• Affinity (in the Bible) —     Affinity (in the Bible)     † Catholic Encyclopedia ► Affinity (in the Bible)     Scripture recognizes affinity as an impediment to wedlock. This is evident from the legislation contained in Lev., xviii, 8, 14 16, 18; xx, 11, 12, 14, 20, 21.… …   Catholic encyclopedia

• Conflict of marriage laws — Conflict of laws Preliminiari …   Wikipedia

• Conflict of nullity laws — Conflict of laws Preliminiari …   Wikipedia

• Centrifugal compressor — Centrifugal compressors, sometimes termed radial compressors, are a sub class of dynamic axisymmetric work absorbing turbomachinery.[1] Centrifugal impeller with a highly polished surface likely to improve performance …   Wikipedia

• Water turbine — A water turbine is a rotary engine that takes energy from moving water.Water turbines were developed in the nineteenth century and were widely used for industrial power prior to electrical grids. Now they are mostly used for electric power… …   Wikipedia

• Ventilatorkennlinie — Ein Ventilator, der in einem Gerät oder in einer Anlage eingebaut ist, muss gegen einen Strömungswiderstand arbeiten. Der Ventilator erzeugt dazu einen Überdruck (Druckerhöhung) und sein Volumenstrom nimmt ab. Die Ventilatorkennlinie (auch… …   Deutsch Wikipedia

• Mechanical fan — Household electric box fan with a propeller style blade 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… …   Wikipedia

• Pump — For information on Wikipedia project related discussions, see . A pump is a device used to move gases, liquids or slurries. A pump moves liquids or gases from lower pressure to higher pressure, and overcomes this difference in pressure by adding… …   Wikipedia