• Mohamed M. M. Amin Professor of Hydraulics, Civil Engineering Department, Faculty of Engineering, Port Said University, Port Said, Egypt
  • Medhat M. H. ElZahar Associate Professor of Sanitary and Environmental Engineering, Department of Civil Engineering, Faculty of Engineering, Port Said University, Port Said, Egypt



Discharge Lines, Economic Considerations, Pipe-Nozzle Diameter Ratio, Free Jets, Pipe Cost Function


The present study focuses on finding an economic design of nozzles used in water discharge lines. An analytical solution is reached for computing the economic pipe-nozzle diameter ratio achieving the minimum pipe cost using the derivative method. The derived equation shows that at a particular pipe-nozzle diameter ratio, the pipe cost CP is minimum. However, this is evident from the worked illustrative example. On a comparison basis between this equation and the conventional one, the derived equation shows a satisfactory reduction in the pipe cost, which may reach 56.7%. It is of great interest to recognize that, by increasing the relative distance to 400, a reduction in pipe cost of 231 % associated with an increase in the power of the jet by 41.5 %, are verified. Also, the derived equation achieves a reduction in pipe cost ranging from 34 to 39.7 % depending on the frictional effects in the approach pipe. The study reflects the reliability of the derived equation in computing the economic pipe-nozzle diameter ratio used in discharge lines delivering free jets. However, there are many engineering applications of water jet nozzles used in; water filters, flotation tanks, sedimentation tanks, water storage tanks, trickling filters, and other units of water and wastewater systems.


Download data is not yet available.


BETE for Nozzle Performance Engineering (2022). Spray Nozzles For The Waste Management Industry.

De Cock, N. (2017). Design of a Hydraulic Nozzle with a Narrow Droplet Size Distribution. Phd Dissertation, Université De Liège, Liège, Belgium.

Featherstone, R. E., and El-Jumaily, K. K. (1983). Optimal Diameter Selection for Pipe Networks. Journal of Hydraulic Engineering, 109(2), 221-234, Computer-Aided Design, 15(5), 300. DOI:

Joseph B. Franzini, E., and Finnemore, J. (2010). Fluid Mechanics with Engineering Applications. Mcgraw-Hill College, MA, USA, 10th International Edition.

Koirala, R., Ve, Q. L., Zhu, B., Inthavong, K., and Date, A. (2021). A Review on Process and Practices in Operation and Design Modification of Ejectors. Fluids, 6(11), 409. DOI:

Mazzoleni, A. P. (1994). Design of High-Pressure Waterjet Nozzles. Alabama Univ., Research Reports : 1994 NASA (ASEE Summer Faculty Fellowship Program).

Medan, N., Banica, M., and Ravai-Nagy, S. (2017). Full Factorial DOE to Determine and Optimize the Equation of Impact Forces Produced by Water Jet Used in Sewer Cleaning. MATEC Web of Conferences, 137, 07003. DOI:

Poeck, E. C. (2008). Performance Evaluation of Various Nozzle Designs for Waterjet Scaling in Underground Excavations, Phd Dissertation, Colorado School of Mines.

Radkevich, M., Abdukodirova, M., Shipilova, K., and Abdullaev, B. (2021). Determination of the Optimal Parameters of the Jet Aeration. IOP Conference Series: Earth and Environmental Science, 939(1), 012029. DOI:

Renjie, L., Xiaochen, L., Jin-Shi, L., and Zhang, X. (2020). Design and Simulation of Curved Nozzle for Removing the Fish Scale by the Water Jet. U.P.B. Science Bulletin, Series D, 82(1).

Schwartzentruber, J., Narayanan, C., Papini, M., and Liu, H. T. (2016). Optimized Abrasive Waterjet Nozzle Design Using Genetic Algorithms. The 23rd International Conference on Water Jetting, Seattle, USA.

Sharp, B. B. (1985). Economics of Pumping and the Utilization Factor. Journal of Hydraulic Engineering, 111(11), 1386–1395. DOI:

Simon, A.L.SS. (1987). Hydraulics. John Wiley and Sons Ltd, 3rd Edition.

Somaida M., El-Zahar M., and 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, M. M. (1994). Optimal Design of Pipe-Nozzle Lines Discharging Free Jets. Port Said Engineering Research Journal, 6(1).

Somaida, M. M., El-Zahar, M. M., Hamed, Y. A., and Sharaan, M. S. (2013). Optimizing Pumping Rate in Pipe Networks Supplied by Groundwater Sources. KSCE Journal of Civil Engineering, 17(5), 1179-1187. DOI:

Somaida, M., Elzahar, M., and Sharaan, M. (2011). A Suggestion of Optimization Process for Water Pipe Networks Design. International Conference on Environment and Bio-Science IPCBEE, 21, 68-73.

Streeter, V. L., Wylie, E. B. (1985). Fluid Mechanics. Mcgraw-Hill Education, 8th Edition.

Swaffield, J., Jack, L., Douglas, J. F. and John Gasiorek. (2011). Fluid Mechanics, Pearson Canada, 6th Edition.

Wright, D., Wolgamott, J., and Zink, G. (2003). Water Jet Nozzle Material Types. WJTA American Waterjet Conference, 17-19.




How to Cite

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.