Affinity Law

Dynamic type pumps obey the affinity laws  

Capacity varies directly with impeller diameter and speed. 

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Affinity Laws. Pump performance is affected by the rotating speed. When speed increases, the flow increases linearly, and the head increases as a square of the speed (14). 

If detailed manufacturer-specified performance curves are not available for a different size of the pump or operating condition, a best estimate of the off-design performance of pumps can be obtained through similarity relationship or the affinity laws. These are ... 

When a pump s velocity changes, measured in revolutions per minute (rpm), the operational characteristics aLso change. These changes can be calculated using the Affinity Laws. Before continuing, let s define some-terms we ll be using ... 

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. 

In a perfect and statie world, we could apply the Affinity- Laws to calculate the Hf and Hv, and calculate how the Hf and Hv change by the square of the change in fiow. Well, the world is neither perfect, nor is it static. And, pipe is not uniform in its construction. 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Actually, everything we said about bearings, mechanical seals, piping, TDH, system curves and mating the pump curve to the system curve, the affinity laws, cavitation, horsepower and efficiency arc as applicable to PD pumps as centrifugal pumps. 

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. 

The affinity laws relate the performance of a known pump along its characteristic curve to a new performance curve when the speed is changed. This would represent the same family of pump curves. As an example, see Figures 3-36A, B, and G. 

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. ... 

The affinity laws will define all the calculations of performance for the different conditions. Thus, every point on the 100% speed capacity-head curve can be adjusted to the 105% or the 95% speed curves by these laws. 

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. 

Accounting, plant construction costs, 48 Cost accumulation, 49 Affinity laws, 201, 202, 203 Air Inleakage, vacuum systems, see vacuum systems Air pressure drop, table, 106 Chart, 114 Orifice flow, 107 Air, absolute viscosity, 132... 

Affinity laws, 201-203 Comparison of types, chart, 177 Enclosed, 171 Inducer, 171 Open, 171... 

Pumps, centrifugal system performance, 197 Affinity laws, 201-203 Branch piping, 200 Calculations, 199... 

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