Analytical Solution for Optimum Design of Nozzle Discharge Lines Based on Hydraulic Considerations
DOI:
https://doi.org/10.54536/ajise.v2i3.1876Keywords:
Analytical Solution, Derivative Method, Discharge line, Pipe-Nozzle Diameter Ratio, OptimizationAbstract
This study focuses on finding the best design of nozzles used in the water discharge pipelines delivering free jets based on hydraulic considerations. An analytical solution is carried out to determine the best design for these nozzles. The solution depends on the derivative method applied to the energy head concerning the nozzle diameter to maximize the power of the jet. The equation derived for computing the best pipe-nozzle diameter ratio D/d in discharge lines applies over practical ranges of relative distance L/D (50-500) and relative roughness e/D (0.01-0.05). An illustrative example is solved and gives D/d = 1.8858 (closely equal to 1.9), the deviation is 0.77%, which is firmly accepted. The equation holds good for D/d from 1.4 to 3.584 and could be applied to compute D/d ratios without the need for a computer program. In the derived equation, D/d is a function of relative distance L/D, and friction factor F with negligible computational errors. The derived equation when compared with the conventional one, shows an increase in the computed power of the jet ranging from 12.5 to 19.23%. The evaluation study reflects the rigidity of the derived equations and their reliability in computing the best pipe-nozzle diameter ratios in discharge lines delivering free jets with reasonable powers, while the conventional formula is approximate. However, many engineering applications of water jet nozzles are used in; impulsive turbines, power-delivering free jets, water filters, flotation tanks, sedimentation tanks, water storage tanks, trickling filters, and other water and wastewater systems.
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Amin, M. M. M., & ElZahar, M. M. H. (2023). Modeling of Hydrodynamic Dispersion in the Sidi Kirayr Locality’s Coastal Unconfined Aquifer West of Alexandria, Egypt. American Journal of Environment and Climate, 2(1), 1–10. https://doi.org/10.54536/ajec.v2i1.1188.
Amin, M. M. M., & ElZahar, M. M. H. (2022). Economic Design Of Pipe-Nozzle Discharge Lines Delivering Free Jets. International Journal of Engineering Technologies and Management Research, 9(10), 10–25. https://doi.org/10.29121/ijetmr.v9.i10.2022.1232.
De Cock, N. (2017). Design of a hydraulic nozzle with a narrow droplet size distribution.
ElZahar, M. M. H., & Amin, M. M. M. (2023). Optimization of Water Pipe Network and Formulation of Pumping Rate. KSCE Journal of Civil Engineering, 27(7), 2882–2890. https://doi.org/10.1007/s12205-023-0872-8.
ElZahar, M., Salih, M., & Fujisaki, K. (2001). Basic study of bubble formation in dissolved CO2 gas flotation of waste activated sludge. In Proceedings of FILTECH EUROPA International Conference and Exhibition, 1, (pp. 413-420).
Emmanuel, U., Olivier, H., Gloria, H., & Olivier, N. M. J. (2023). Experimentally Study on Optimal Control of the Inertia of Water on the Thermal Performance of All-glass Evacuated Tube Solar Collector. American Journal of Energy and Natural Resources, 2(1), 15–19. https://doi.org/10.54536/ajenr.v2i1.1219.
Finnemore, E. John, and Joseph B. Franzini. (2002). Fluid mechanics with engineering applications. McGraw-Hill Education.
Fujisaki, K., & El-Zahar, M. (2002). A mathematical model for the flotation of waste-activated sludge. Water Science and Technology, 46(11–12), 203–208. https://doi.org/10.2166/wst.2002.0739.
John Swaffield, Lynne Jack, J. F. Douglas, John Gasiorek. (2011). Fluid Mechanics, 6th Edition.
Kawser, A. R., Hossain, M. A., & Yeasmin, M. F. (2020). Optimizing the Planting Density of Lettuce (Lactuca Sativa) with Tilapia (Oreochromis niloticus) in a Recirculation Aquaponic System. American Journal of Agricultural Science, Engineering, and Technology, 4(1), 1–11. https://doi.org/10.54536/ajaset.v4i1.41.
Mazzoleni, Andre P. (1994). Design of high-pressure waterjet nozzles. Alabama Univ., Research Reports: NASA (ASEE Summer Faculty Fellowship Program.
Medan, Nicolae. (2016). Evaluation of Nozzle Coefficients for Water Jet Used in Sewer Cleaning. Hidraulica (3), 14.
Poeck, Eric C. (2008). Performance evaluation of various nozzle designs for waterjet scaling in underground excavations. 2000-2009-Mines Theses & Dissertations.
Radkevich, M., Abdukodirova, M., Shipilova, K., & Abdullaev, B. (2021). Determination of the Optimal Parameters of the Jet Aeration. IOP Conference Series: Earth and Environmental Science, 939(1), 012029. https://doi.org/10.1088/1755-1315/939/1/012029.
Renjie L, Xiaochen L, Jin-Shi L, Zhang X. (2020). Design and simulation of curved nozzle for removing the fish scale by the water jet. University Politehnica of Bucharest Scientific Bulletin. Series D., 82(1), 111-20.
Schwartzentruber, Jeff, et al. (2016). Optimized abrasive waterjet nozzle design using genetic algorithms. The 23rd international conference on water jetting, at Seattle, USA.
Somaida M. M. (1994). Optimal design of pipe-nozzle lines discharging free jets. Port Said Engineering Research Journal, 6(1)..
Somaida M, Elzahar M, Sharaan M. (2011). A suggestion of optimization process for water pipe networks design. International Conference on Environment and BioScience IPCBEE, 21 (pp. 68-73).
Somaida M., Elzahar M., Sharaan M. (2012). The Use of Computer Simulation and Analytical Solutions for Optimal Design of Pipe Networks Supplied from a Pumped-Groundwater Source. Port Said Engineering Research Journal, 16(1), 106-117.
Somaida MM, Elzahar MMH, Hamed YA, Sharaan MS. (2013). Optimizing pumping rate in pipe networks supplied by groundwater sources. KSCE Journal of Civil Engineering. Jun 28, 17(5), 1179–87, http://doi.org.10.1007/s12205-013-0116-4.
SS Simon A.L. (1987). Hydraulics, John Wiley and Sons Ltd, 3rd edition.
Streeter, V. L., E. B. Wylie, and K. W. Bedford. (1985). Fluid Mechanics McGraw-Hill., Inc., New York, NY.
Wright, D., J. Wolgamott, and G. Zink. (2003). Waterjet nozzle material types. WJTA American Waterjet Conference.
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Copyright (c) 2023 Mohamed M. M. Amin, Medhat M. H. ElZahar
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