# Affinity Laws for Pumps and Fans

Affinity laws are used to relate the performance of a pump or fan from a known operating condition to a new, unknown condition.  The affinity laws can be calculated at a single point or charts of flow rate, head, and power can be plotted against changes in impeller speed or diameter.  Changes to a pump’s configuration, such as impeller diameter or pump size in general can be analyzed for these conditions:

• Constant impeller diameter with changing speed.
• Constant speed, with two pumps of different size as measured by impeller diameter.
• Constant speed, with a trimmed impeller. Trimmed impeller means that diameter is changed, but the pump casing has not.

The first two conditions are also applicable for fans.  For the purposes of discussion in this article, we will refer to pumps.

The affinity law calculations assume that each pump operates at the same efficiency and that the pumped fluid does not change (constant density).

### Affinity Law Terminology

Before we cover the laws, we'll define the following terms:

N is shaft rotational speed

D is impeller diameter

Q is flow rate

P is power

### Constant Impeller Diameter

These equations model the effect on flow rate, head, and shaft power from changes to shaft rotational speed.

### Constant Shaft Speed

The constant shaft speed equations are developed from pump similarity and assume two pumps that are geometrically similar (homologous).  They model the effect on flow rate, head, and shaft power from changes to impeller diameter.

### Constant Shaft Speed, Trimmed Impeller

These equations apply to a pump where the impeller diameter is changed, but not the casing, or impeller eye diameter.  This is often the case where the impeller is machined to a smaller diameter.  This is where the term trimmed impeller comes into play.  This could also apply where a smaller impeller is initially installed and replaced with a larger impeller that still fits in the casing.

One of the conditions for pump similarity is that the two configurations are geometrically similar.  When an impeller is trimmed (or enlarged), geometric factors such as casing clearance, vane angles, and eye to outside diameter ratio change.  Therefore, the assumption of geometric similarity is not valid, and different equations must be used.

MEboost can perform affinity law calculations as well as create charts in Excel for varying speed and diameter.

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