Impellers Affinity laws

It rhc vclociry should remain fixed, rhe flow, head and BHP will change when rhe impeller diameter changes. With a change in rhe impeller diameter (this is called an impeller trim ), rhe affinity laws indicate ... 

Manipulating flow and controlling prcs.surc by varying the impeller diameter conserve.s kilowatts of energy, and this is the third affinity law in this group. A pump consuming 10 BHP with a 10 inch impeller, would only consume 7.3 horses with a 9 inch impeller. 

Small impellers with high motor speeds may produce the necessary pump pressure. This ty pe of combination produces high fluid velocities that will wear pump parts much faster than desirable. This is in the Affinity Laws. In addition the impeller suffers rapid wear due to high tip velocities. When a pump is disassembled and excessive wear is found, 95% of the time high velocity fluid is to blame. 

For geometrically similar impellers operating at the same specific speed, the affinity laws are [25,11] ... 

Recognizing the flexibility of the affinity laws, it is better to select an original pump impeller diameter that is somewhat larger than required for the range of anticipated performance, and then cut this diameter dowm after in-service tests to a slightly smaller diameter. This new performance can be predicted in advance. Once the impeller diameter is too small, it cannot be enlarged. The only solution is to order the required large impeller from the manufacturer. 

The affinity laws express the relationship between the head, capacity, speed, and size of centrifugal blowers and compressors. In general these relations can be applied to inlet volume conditions for good preliminary designs, but all final designs apply these laws to the actual discharge volumes from the impeller. ... 

At any constant or steady speed of operation of a compressor, the head-capacity and efficiency curves are characteristic of the impeller and casing design only. These curves that are determined by test can be translated to other reasonable speeds and conditions of operation of the wheel-casing combination of the affinity laws. The operation of the compressor must meet or establish the desired point on the head-capacity-system curve, which requires a combination of controls. 

Two different size pumps are said to be geometrically similar when the ratios of corresponding dimensions in one pump are equal to those of the other pump [Holland and Chapman (1966)]. Geometrically similar pumps are said to be homologous. A set of equations known as the affinity laws govern the performance of homologous centrifugal pumps at various impeller speeds. 

Compute the pump performance at the new speed. The similarity or affinity laws can be stated in general terms, with subscripts p and m for prototype and model, respectively, as Qp = K KnQm-,Hp = K2dK2Hm- NPSH = K2K2NPSHm Pp = K3K3Pm, where Kd = size factor = prototype dimension/model dimension. The usual dimension used for the size factor is the impeller diameter. Both dimensions should be in the same units of measure. Also, Kn = prototype speed, r/min/model speed, r/min. Other symbols are the same as in the previous example. 

The affinity laws are valid only for compressors where the Mach number (defined in terms of the exit velocity from the stage) is less than 0.8, or, under vacuum conditions, the mean free path does not approach the impeller dimensions. Outside these limits, no simple correlations with speed exist, and the full characteristics must be stored rather than a single curve for each section. Fortunately, most industrial compressors will stay within these limits. 

When a characteristic curve for just one rotation rate and/or impeller diameter is available and an approximate characteristic curve is desired for another rotation rate and/or impeller diameter, the affinity laws for a centrifugal pump can be applied ... 

Affinity laws are used to predict the effects of changing the speed of a pump, trimming an impeller, and extrapolating the performance of a pump from case (A) to case (B). They state that ... 

Pump affinity law is used to estimate pump performance, when its speed or impeller diameter is chmiged. It is derived based on pump specific speed doesn t change. The first set of pump affinity law is based on fixed impeller diameter and varied pump speed. It is used to estimate pump performance at different pump speed. The new pumping rale (Q2), pump head (H2), and required power (BHP2) are estimated from the known pumping rate (Ql), pump head (HI), and power (BHPl) by the following equations ... 

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