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This post was last edited by 3983596_FPPZ on 2018-11-21 09:13. 1.1.8 Similarity Theory and Its Applications. Similarity theory: The pump similarity theory is widely used in pump design and testing. Similarity theory is divided into geometric similarity, kinematic similarity, and dynamic similarity. The premise of pump similarity theory is geometric similarity. In simple terms, geometric similarity refers to a certain proportional relationship between the hydraulic dimensions of the actual pump and those of the model pump ； Kinematic similarity means that the direction of the fluid flow velocity is the same in both the full-scale pump and the model pump, and the magnitudes of the velocities are in a certain proportional relationship ； Dynamic similarity means that the direction of the force acting on the fluid in the full-scale pump and the model pump is the same, and the magnitude of these forces is in proportion to each other. In this way, the similarity laws can be derived under conditions of geometric similarity and identical operating conditions. Application of similarity theory: With similarity theory as a foundation, we can do the following things: 1. Design hydraulic components using model substitution methods. Many hydraulic designs are not created from scratch; otherwise, the design results would be highly inaccurate and the risks would be high. Instead, we first determine the hydraulic dimensions of a model pump (model pumps are those that have been well-designed, tested repeatedly in the market, and enjoy high recognition), and then use the proportional relationships provided by similarity theory to calculate the hydraulic dimensions of the actual pump, making some adjustments as necessary. 2. Changes in pump performance parameters when the speed is changed. For example, when changing the pump speed using an inverter-driven motor, we can calculate the performance parameters of the pump at different speeds through similar theories. 3. Obtain the performance curve (efficiency variation) at the new speed. From point to line, the performance curve at the new speed can be deduced accordingly. 4. Impeller cutting law. We can derive the cutting law based on similarity theory to calculate the performance parameters of the impeller after its outer diameter has been cut, thereby determining the required amount of cutting. According to similarity theory, the ratio of the squares of the outer diameters of similar pump impellers before and after cutting is equal to the ratio of their head values before and after cutting. 5. Modify the blade shapes at the inlet and outlet of the impeller to achieve a minimal change in performance parameters. There are many practical examples for reference, but all of them are based on similar theories. 6. Generating pattern diagrams. By using impeller cutting and variable speed, the pump can have a wide range of performance characteristics, thereby enabling the creation of performance maps – diagrams that show the effective performance ranges of various pump models with different performance curves. The specific speed can be determined based on geometric similarity; from this, certain comprehensive parameters related to performance can be derived. If these comprehensive parameters are equal, it can be assumed that there is both geometric similarity and kinematic similarity, allowing the use of similarity laws for performing calculations related to performance. This comprehensive parameter is known as the specific speed, denoted by the symbol ns. ns = 3.65 * n * Q1/2 / (H)3/4; where n is the rotational speed in r/min, Q is the flow rate in m3/s, and H is the head in meters. Pumps with a lower specific speed generally have lower efficiency; they feature a low flow rate, a relatively high head, and narrow impeller channels. Pumps with a higher specific speed have higher efficiency; they are characterized by large flow rates, low head, and wide impeller channels. The specific speed is not frequently used in the actual operation of products, but it serves as the basis for hydraulic design and an important reference. Many aspects of pumps’ hydraulic characteristics, such as their hydraulic geometry and performance parameters, are determined based on the specific speed. The theoretical aspects of similarity theory are too complex; I have only provided an introduction to it. Those who are interested can consult relevant materials and study them in detail – they will surely gain something from it. I managed to summarize all this content in just a few words, without any diagrams, tables, or formulas – I’m actually amused by that. After-class questions (multiple choice): There is one ZA pump with a rotational speed of 2950 RPM. The test bench shows a head of 82 m, while the actual head required is 75 m. The diameter of the impeller used in the tests is 259 mm. According to the similarity theory, what should be the outer diameter of the impeller? A. 250.5mm B. 259mm C. 247.7mm C. 248.8mm C