This paper presents a method to calibrate pipe roughness coefficient (i.e., Manning n-factor) with genetic algorithm (GA) under multiple loading conditions. Due to the old pipe age as well as deleting valves and blend...This paper presents a method to calibrate pipe roughness coefficient (i.e., Manning n-factor) with genetic algorithm (GA) under multiple loading conditions. Due to the old pipe age as well as deleting valves and blends in the skeleton of distribution network, most of the pipes in hydraulic model of practical water distribution system (WDS) are rough. The commonly used Hazen-Williams C-factor is therefore replaced by Manning n-factor in calibrating WDS hydraulic model. Adjustment to GA is designed, and the program efficiency is improved. A case study shows that the adjustment can save 60% of the total runtime. About 90% of the relative differences between simulated and observed pressures at monitoring locations are lower than 3%, which suggests that the proposed adjustment to the calibration is efficient and effective.展开更多
The Moody Diagram is widely used to determine the friction factor for fluid flow in pipes. The diagram combines the effects of Reynolds number and relative roughness to determine the friction factor. The relationship ...The Moody Diagram is widely used to determine the friction factor for fluid flow in pipes. The diagram combines the effects of Reynolds number and relative roughness to determine the friction factor. The relationship is highly non-linear and appears to have a complex interaction between viscous and boundary roughness effects. The Moody Diagram is based on predictions from an equation developed by Colebrook in 1939. The relationship requires an iteration process to make predictions. While empirical relationships have been developed that provide good predictions without an iteration process, no one has fully explained the cause for the observed results. The objective of this paper is to present a logical development for prediction of the friction factor. An equation has been developed that models the summed effect of both the laminar sublayer and the boundary roughness on the fluid profile and the resulting friction factor for pipes. The new equation does not require an iteration procedure to obtain values for the friction factor. Predicted results match well with values generated from Colebrook’s work that is expressed in the Moody Diagram. Predictions are within one percent of Colebrook values and generally less than 0.3 percent error from his values. The development provides insight to how processes operating at the boundary cause the friction factor to change.展开更多
基金Supported by National Natural Science Foundation of China (No 50778121)Science and Technology Innovation Special Foundation of Tianjin (NO 06FZZDSH00900)
文摘This paper presents a method to calibrate pipe roughness coefficient (i.e., Manning n-factor) with genetic algorithm (GA) under multiple loading conditions. Due to the old pipe age as well as deleting valves and blends in the skeleton of distribution network, most of the pipes in hydraulic model of practical water distribution system (WDS) are rough. The commonly used Hazen-Williams C-factor is therefore replaced by Manning n-factor in calibrating WDS hydraulic model. Adjustment to GA is designed, and the program efficiency is improved. A case study shows that the adjustment can save 60% of the total runtime. About 90% of the relative differences between simulated and observed pressures at monitoring locations are lower than 3%, which suggests that the proposed adjustment to the calibration is efficient and effective.
文摘The Moody Diagram is widely used to determine the friction factor for fluid flow in pipes. The diagram combines the effects of Reynolds number and relative roughness to determine the friction factor. The relationship is highly non-linear and appears to have a complex interaction between viscous and boundary roughness effects. The Moody Diagram is based on predictions from an equation developed by Colebrook in 1939. The relationship requires an iteration process to make predictions. While empirical relationships have been developed that provide good predictions without an iteration process, no one has fully explained the cause for the observed results. The objective of this paper is to present a logical development for prediction of the friction factor. An equation has been developed that models the summed effect of both the laminar sublayer and the boundary roughness on the fluid profile and the resulting friction factor for pipes. The new equation does not require an iteration procedure to obtain values for the friction factor. Predicted results match well with values generated from Colebrook’s work that is expressed in the Moody Diagram. Predictions are within one percent of Colebrook values and generally less than 0.3 percent error from his values. The development provides insight to how processes operating at the boundary cause the friction factor to change.
