<![CDATA[This study explores the mathematical analysis of external factors affecting the operating modes of pump installations in industrial processes. External influences, such as fluctuations in fluid properties, hydraulic resistance, cavitation risks, and environmental conditions, were systematically investigated using a combination of mathematical modeling and experimental validation. The developed model accurately predicts the impact of these factors on pump performance metrics, including flow rate, pressure head, power consumption, and efficiency. Results demonstrate that a 10°C increase in fluid temperature leads to a 4% efficiency reduction due to viscosity changes, while optimizing pipe diameter reduces hydraulic resistance by 15%. The study further highlights the critical role of maintaining adequate Net Positive Suction Head (NPSH) to prevent cavitation, as efficiency drops by 12% when NPSHavailable is below NPSHrequired. The validated model provides actionable insights for optimizing pump operations, reducing energy consumption by up to 20%, and enhancing reliability in industrial settings. These findings contribute to the development of sustainable and energy-efficient pumping systems. Highlights: Mathematical Analysis of External Factors on Pump Operations Impact on Performance, Efficiency, and Energy Consumption Optimizing Pump Systems for Sustainability and Reliability Keywords - Pump installations, mathematical modeling, external factors, hydraulic resistance, cavitation, Net Positive Suction Head (NPSH), energy efficiency, industrial processes, fluid dynamics, variable frequency drives (VFDs)]]>
