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Analysis of common adjustment methods for centrifugal pumps. Magnetic pumps are widely used in industries such as water management and chemicals, and there is an increasing focus on the selection of their operating conditions as well as the analysis of their energy consumption. The so-called operating point refers to the actual flow rate, head, shaft power, efficiency, and suction vacuum level of the water pump at a given moment; it represents the pumping capacity of the water pump. Typically, the flow rate and head of electric diaphragm pumps may not match those of the piping system; or due to changes in production tasks or process requirements, it is necessary to adjust the pump’s flow rate, which essentially involves changing the operating point of the centrifugal pump. In addition to the correctness of the centrifugal pump selection during the engineering design phase, the choice of operating conditions during the actual use of the centrifugal pump also directly affects the user’s energy consumption and costs. Therefore, it is particularly important to know how to reasonably change the operating point of the centrifugal pump. The working principle of a centrifugal pump is to convert the mechanical energy generated by the high-speed rotation of the electric motor into the kinetic and potential energy of the liquid being pumped, which is a process of energy transfer and conversion. Based on this characteristic, it can be seen that the operating point of a centrifugal pump is determined by the balance between the energy supply and demand in the pump and pipeline system; whenever there is a change in either of these factors, the operating point will shift. Changes in operating conditions are caused by two factors: first, changes in the characteristic curve of the piping system, such as throttling in self-priming pumps ； II. Changes in the characteristic curve of the water pump itself, such as variable-frequency speed control, cutting of the impeller, or connecting pumps in series or parallel. The following methods are used for analysis and comparison: 1. Magnetic pump – The simplest way to change the flow rate of a centrifugal pump is to adjust the opening degree of the pump’s outlet valve, while keeping the pump’s speed constant (usually at the rated speed). Essentially, this involves changing the position of the pipeline characteristic curve in order to alter the pump’s operating point. As shown in Figure 1, the intersection point A of the pump characteristic curve Q-H and the pipeline characteristic curve Q-∑h represents the extreme operating condition of the pump when the valve is fully open. When the valve is closed, the local resistance in the pipeline increases, causing the operating point of the water pump to shift to the left to point B, with a corresponding decrease in flow rate. When the valve is fully closed, the resistance is infinitely large and the flow rate is zero; at this point, the pipeline characteristic curve coincides with the vertical axis. As can be seen from Figure 1, when flow rate is controlled by closing the valve, the water supply capacity of the pump itself remains unchanged, and its head characteristic stays the same; however, the pipe resistance characteristic changes as the valve opening degree changes. This method is easy to operate, provides a continuous flow rate, and can be adjusted arbitrarily between a maximum flow rate and zero, without requiring any additional investment; it is therefore suitable for a wide range of applications. However, throttling regulation relies on consuming the excess energy of the centrifugal pump (the shaded area in the diagram) to maintain a certain supply volume; as a result, the efficiency of the centrifugal pump decreases, which is not economically reasonable. II. Variable frequency speed control: The deviation of the operating point from the high-efficiency zone is the basic condition that requires speed control for water pumps. When the speed of the water pump changes, the valve opening remains constant (usually at its maximum value); the characteristics of the piping system stay unchanged, while the water supply capacity and head performance change accordingly. As shown in Figure 2, A is the equilibrium operating point of the water pump (also known as the operating point), corresponding to the efficiency ηa. To reduce the flow rate, the speed can be lowered; at this point the operating condition is B, corresponding to an efficiency of ηb, and the water pump remains within the high-efficiency range. If valve throttling is used for regulation, the operating point is C, with an efficiency of ηc; the pump’s efficiency decreases as a result. It can be seen that when the required flow rate is less than the rated flow rate, the head generated under variable frequency speed control is lower than that achieved by valve throttling; therefore, the power required for water supply under variable frequency speed control is also lower. The shaded area in Figure 2 represents the power saved through variable frequency speed control. It is evident that, compared to valve throttling, variable frequency speed control offers a significant energy-saving effect, and centrifugal pumps achieve higher efficiency. Furthermore, the use of variable frequency speed control not only helps to reduce the likelihood of cavitation in centrifugal pumps, but it also allows the start-up and shutdown processes to be extended by presetting the time required for acceleration/deceleration. This results in a significant reduction in dynamic torque, thereby substantially eliminating the highly destructive water hammer effect and **extending the lifespan of the pump and piping systems**. In fact, variable-frequency speed control also has its limitations. Aside from the high initial investment and maintenance costs, excessive changes in the pump’s speed can lead to a decrease in efficiency; once beyond the range dictated by the pump’s proportional law, it is not possible to adjust the speed indefinitely. III. Cutting the impeller: When the rotational speed is constant, both the head and flow rate of the pump are related to the diameter of the impeller. For pumps of the same model, the cutting method can be used to modify their characteristic curves. Let the original impeller diameter of the centrifugal pump be D, its flow rate be Q, its head be H, and its power be P; the diameter of the impeller after cutting be D’, its flow rate be Q’, its head be H’, and its power be P’. Then the relationships between these values are as follows: The above three equations are collectively referred to as the cutting laws for centrifugal pumps. The cutting law is based on a large amount of empirical experimental data; it states that if the amount of cutting on the impeller is kept within certain limits (with this limit being related to the specific speed of the water pump), then the efficiency of the water pump before and after cutting can be considered constant. Cutting the impeller is a simple and effective way to modify the performance of water pumps, namely the so-called diameter adjustment method. It addresses to some extent the contradiction between the limited range of pump types and specifications and the diverse requirements of water supply applications, thereby expanding the application scope of water pumps. Of course, cutting the impeller is an irreversible process, and users must conduct precise calculations and assess the economic viability before proceeding. IV. Series and Parallel Connection of Water Pumps: In a series connection of screw pumps, the outlet of one pump feeds fluid into the inlet of another pump. Taking the simplest case of two centrifugal pumps of the same model and with identical performance connected in series as an example: as shown in Figure 3, the performance curve for the series connection is equivalent to the sum of the head values from the individual pump’s performance curves at the same flow rate. The flow rate and head at point A in the series configuration are both higher than those at point B for a single pump, but they do not reach twice the values of a single pump. This is because, when pumps are connected in series, the increase in head is greater than the increase in pipeline resistance; this excess head leads to an increase in flow rate. On the other hand, the increased flow rate results in a higher resistance, which limits further increases in the total head. When water pumps are operated in series, it is necessary to ensure that the subsequent pump can withstand the increased pressure. Before starting, the outlet valves of each pump must be closed, after which the pumps and valves are turned on in sequence to supply water outward. Parallel operation of chemical pumps refers to the use of two or more pumps to deliver fluid into the same pressure pipeline, with the aim of increasing flow rate while maintaining the same head pressure. Still taking the simplest case of two centrifugal pumps of the same model and with the same performance connected in parallel as an example: as shown in Figure 4, the performance curve for the parallel operation is equivalent to the sum of the flow rates corresponding to the single-pump performance curve, at the same head value. The flow rate and head at the parallel operating point A are both greater than those at the single-pump operating point B, but due to the influence of pipe resistance, they still do not reach twice the values of the single pump. If the goal is purely to increase flow rate, then whether to use a parallel or series configuration should depend on the flatness of the pipeline characteristic curve. The flatter the curve, the closer the flow rate in a parallel setup will be to twice that of a single pump in operation; thus, it yields a higher flow rate than a series setup, which is more advantageous for operation. V. Conclusion Although valve throttling results in energy loss and waste, it remains a fast and straightforward method for flow regulation in some simple applications ； Variable frequency speed control is increasingly favored by users due to its excellent energy-saving effects and high level of automation ； Cutting impellers are generally used in clean water pumps; due to the change in the pump’s structure, their versatility is limited ； Series and parallel connection of water pumps are only applicable when a single pump is not sufficient to meet the pumping requirements, and having too many pumps in series or parallel is actually uneconomical. In practical applications, multiple factors should be taken into consideration, and the best solution should be determined by combining various flow regulation methods to ensure the efficient operation of the centrifugal pump.