A MATHEMATICAL MODEL FOR CONVEYING WATER THROUGH A LONG PIPE LINE

Abstract

ABSTRACT Transportation by pipeline is the means most frequently used to transport water for their safe and economical properties and also for their ability to maintain a high quality of life. A pipelines flow condition where the velocity and pressure change rapidly with time is called hydraulic transient. It can collapse a water pipeline system if that system is not equipped with adequate transient protection device(s). A hydraulic transient normally occurs when a flow control component changes situation (for example, a pump stopping or valve closing), and this flow changes through the system as a pressure wave is called water hammer phenomenon. The water hammer transient is a non-uniform flow which is a change in the pressure resulting from a sudden change in the flow. The mathematical model has been verified with several published data namely (Elbashir and Amoah (2007), Gubashi and Kubba (2010) and Mansuri et al. (2014)). It is found that the developed mathematical model agree very well with these previous studies and can rely on it for simulation a transient water flow in pipes. The developed model was used to simulate the water transport from region called Five Bridges to Wadi abi-Naft (within the villages of Clans Neda) in the outskirts of Mandali city, Diyala governorate, Iraq. The total length of pipeline path is 54km. The simulation results showed that the pipeline path need three pumping stations II in order to transport water to Mandali City. The pipeline used with diameter is equal to 1200mm. Each pumping station was simulated separately under transient flow condition. The required remediation to overcome the water hammer phenomenon is suggested. A surge tanks with different capacities namely 1700m3, 1530m3 and 1475m3 for first, second and third stage respectively are suggested. Sensitivity analysis has been performed using several variables such as p the diameter of the pipe has a significant effect on the results of water hammer compared to the effect of both velocity wave and frication factor. Also, it has been found that the ending section of pipe is the critical zone for the water hammer effect. In the present study, it has been found that pumps failure has relatively smaller effect in increasing the negative pressure compared with the valve closure effect.