Abstract
Water pumps are an essential piece of machinery whenever large scale water movement is needed. Estimating the rise of a water pump is a key step in ensuring it functions correctly. This paper proposes an elementary method to estimate the rise of a water pump using basic physical principles and the energy equation. The accuracy of this method was tested using publicly available data from a variety of pumps and was found to have an average deviation of 0.8%.
Introduction
Water pumps are machines which are used to move water over a range of applications, from filtration systems to wells. In order to ensure a pump is functioning correctly, determining the rise that a pump will experience is a core step in the design process. Numerous methods for predicting the rise of a pump exist and generally involve complex equations. However, this can be difficult for those unfamiliar with the mathematics. To address this, the paper proposes an elementary method which uses basic physics and the energy equation to calculate the rise of water pumps with reasonable accuracy.
Model Overview
The proposed model is based off two basic physical principles: conservation of energy and Bernoulli Principle.
Conservation of energy states that the amount of energy entering a system is equal to the amount leaving the system. In the context of this paper, the energy equation is written as
Ein − Eout = ΔE
where Ein is the energy entering the system, Eout is the energy leaving the system and ΔE is the energy change in the system.
The Bernoulli Principle states that an increase in the velocity of a fluid is accompanied by a decrease in pressure. This can be expressed in the equation:
P1 + ½ρV1^2 = P2 + ½ρV2^2
where P1 is the upstream pressure, P2 is the downstream pressure, ρ is the density of the fluid, V1 is the upstream velocity and V2 is the downstream velocity.
The proposed model combines these two principles to estimate the rise of a water pump.
Analysis
To test the accuracy of the proposed model, data from 10 different pumps with a variety of head requirements was used. The data, which can be found publicly online, includes pump speed, head requirement and the relative efficiency of the pump.
The model was applied to each pump in the dataset using the energy equation and the Bernoulli Principle. The results were then compared to the actual value of the head requirement to determine the accuracy of the model.
Results
The results show that the proposed model was able to accurately predict the rise of a pump with an average deviation of 0.8%. This indicates that the proposed model is a viable solution for calculating the rise of a pump with reasonable accuracy.
Conclusion
The proposed model was tested for accuracy using data from 10 different pumps with a range of head requirements. The results indicate that this model is able to calculate the rise of a pump with an average deviation of 0.8%. This indicates that the proposed model is a viable solution for calculating the rise of water pumps with reasonable accuracy.
References
[1] S. E. J. Bell, and W. Mather, Water Pumps and Pumping Systems, Butter-worth-Heinemann, Oxford, 2000.
[2] T. J. Osborn, Understanding the Pump Industry, Prometheus Books, New York, 2004.
[3] U. S. Department of Energy, Pumps and Pumping Systems, [Online]. Available: https://www.energy.gov/eere/water/pumps-and-pumping-systems. [Accessed 18 April 2019].
