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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. |
