Physical Model of Three Reservoir Problem

Abstract

[500] The three-reservoir problem is one of the pivotal phenomena of hydraulics which involves solution of pipe networks. In this, three reservoirs at varying elevations are connected with each other using three pipes and converge at a junction. As a result, liquid flows from the highest to the lowest reservoir. The main question is whether the middle reservoir will experience inflow or outflow. Conventionally, this problem involves calculating the steady flow rates and hydraulic grade lines within the system but often faces problem of understand the dynamics of flow involved in this phenomenon. To illustrate this, it is essential to demonstrate the flow in exactly similar manner as it is in the original phenomenon. This necessitates the development of “physical model” for this problem which can simulate as well as elaborate the phenomenon of “three reservoir problem” with the help of which one can study and give a reliable solution to it. Consequently, in the present work, a physical model of “Three reservoir problem” is fabricated and developed in fluid mechanics laboratory of Department of Civil Engineering, Vishwakarma Institute of Technology (VIT), Pune, Maharashtra, India. Physical experiments were carried out using the developed equipment and observations were recorded. The results were then compared with solution of the three-reservoir problem using EXCEL based solution. This model will be useful for academicians, industrialists, technocrats to visualize and study the phenomenon of three reservoir problem in a better manner and use it in related applications. The innovation of this study is the “physical model” fabricated and developed in VIT Pune Laboratory.

Specification

Description:In a water supply system often a number of reservoirs are required to be interconnected by means of a pipe system consisting of a number of pipes namely main and branches which meet at a junction. Figures 1, 2 and 6 shows three reservoirs A, B and C interconnected by pipes 1, 2 and 3 which meet at a junction D. In the problems of this type, the lengths, diameters, and friction factors of the different pipes are supposed to be known. Further it is assumed that the flow is steady, minor losses are small and hence neglected and the reservoirs are large enough so that their water surface levels are constant. The three basic equations that are used in order to solve these problems are continuity equation, Bernoulli's equation and Darcy-Weisbach equation. At any junction according to the continuity equation the total rate of flow towards the junction is equal to the total rate of flow away from it.
Based on this, in the present study, an equipment is fabricated in which a system is modelled consisting of three pipes of different lengths and same diameter with reservoirs placed at different elevations. Entire equipment is represented in all the six figures serially from Figure 1 to Figure 6. The friction factor is considered constant though in reality it varies somewhat with flow velocity 'V'. Each pipe is at one end connected to a reservoir of given elevation and at the other end to a three-way junction. Each reservoir has different volume. Figures 1 and 2 showcase the drawing of fabricated model (front view and top view of the model respectively). Details of the developed model including pipe material, T junctions etc are presented in the subsections of this same part. Experiments were carried out using different inflow and outflow conditions on the same model and experimental observations were studied to solve the three-reservoir problem.

In the three-reservoir problem, following assumptions are made.
1. All pipes are sufficiently long so that minor losses and velocity heads can be neglected
2. Actual reservoirs are large so that in steady condition levels in the reservoirs are constant
3. Darcy-Weisbach equation is satisfied for pipe system.
4. At the junction continuity equation is satisfied.
, Claims:1. The equipment and/or Physical model for solution of Three reservoir problem is developed successfully.
2. The experimental results are matching with the computational results of the three-reservoir problem.

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