## Speed – Affinity Laws

The following applies: 1. Model law 2. Model law 3. Model law Q – flow rate H – delivery head P – power consumption n – speed The indices relate to the respective speed. The affinity laws apply exactly to frictionless, incompressible flows. For technical applications, they are to be regarded as an approximate solution. In general, these affinity laws are independent of how the speed change is technically implemented. Traditionally, multi-speed functions of small and medium size pumps are realized by changing the motor windings configurations to achieve stepped speed variations. Meanwhile, these have been largely replaced by frequency converters. Slow-running electric drives are very expensive for larger centrifugal pumps, so that reduction gears are used for these cases. Combustion engines are used for some mobile applications. They are also variable in speed within a specified range.

## Performance curve conversion for impeller trimming

The following applies approximately: Q = flow rate H = delivery head D = impeller diameter r = index for the reduced impeller diameter t = index for the reference wheel diameter The throttle curve H (Q) can be roughly determined from this relationship. A more precise calculation, however, requires the consideration of performance charts in which an impeller diameter is assigned to each performance curve. The new performance curve is determined by interpolating the conversion from the neighboring curves. In order to fully utilize the efficiency of the method, it is recommended to record an duty chart with at least three performance curves. If there is a large difference between the smallest and largest impeller diameter, some (2..4) intermediate curves are required. An alternative calculation method is described in ISO 9906. Knowledge of the mean impeller diameter at the leading edge D 1 is required here. According to the standard, this procedure is valid for
• Diameter reduction up to max. 5%
• Type number K ≤ 1.5
• Unchanged blade geometry (outlet angle, tapering, etc.) after cutting
D 1 = Mean diameter at the impeller leading edge For pumps with a type number K ≤ 1.0 and a maximum impeller diameter reduction of 3%, the efficiency can be considered as unaltered.

## Shaft Power

The required shaft power of the pump is given as a performance curve depending on the flow rate. The performance curve changes when the speed of the pump changes in accordance with the affinity laws. The shaft power of the pump is directly proportional to the density of the pumped medium. In the case of highly viscous media, the shaft power also depends on the viscosity. Depending on the application and size of the pump, the drive is designed so that the motor power is either greater than or equal to the viscosity of the pumped medium.
•  the shaft power at the operating point or
•  the maximum power of the characteristic curve,
in each case plus a security surcharge of at least 5%. The required safety margin depends on the required engine power. While the safety margin is reduced to up to 5% for larger motors, surcharges of over 20% are applied for smaller power values. In addition, the nominal motor power for standard motors must be converted to the ambient conditions. P2 is used as the symbol for the shaft power.