Linganisha mbinu

	Traffic Flow (LWR Model)	Njia ya Hardy Cross	Njia ya Muskingum
Nyanja	Uhandisi wa Ujenzi	Uhandisi wa Ujenzi	Uhandisi wa Ujenzi
Familia	Process / pipeline	Process / pipeline	Process / pipeline
Mwaka wa asili	1955	1936	1938
Mwanzilishi	M. J. Lighthill and G. B. Whitham	Hardy Cross	George McCarthy
Aina	Macroscopic traffic flow modeling using conservation laws	Iterative method for pipe network flow distribution	Hydrologic method for flood attenuation in rivers
Chanzo asilia	Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves I. Flow movement in long rivers. Proceedings of the Royal Society A, 229(1178), 281-316.	Cross, H. (1936). Analysis of flow in networks of conduits or conductors. University of Illinois Bulletin, 34(17), 3-29.	McCarthy, G. T. (1938). The Unit Hydrograph and Flood Routing. US Army Corps of Engineers Document 608.
Majina mbadala	LWR model, Traffic wave, Kinematic wave theory	Cross method, Moment distribution method, Iterative balancing	Flood routing, Stream flow attenuation, Hydrologic routing
Zinazohusiana	3	3	3
Muhtasari	The Lighthill-Whitham-Richards (LWR) model is a macroscopic traffic flow model that treats traffic as a compressible fluid, applying conservation of vehicles and a flow-density relationship. Introduced independently by Lighthill and Whitham (1955) and Richards (1956), the model predicts traffic wave propagation, congestion formation, and bottleneck behavior on highways.	The Hardy Cross method is an iterative technique for solving steady-state flow distribution in pipe networks, originally developed for water distribution systems. Introduced by Hardy Cross in 1936, this method balances flow continuity and pressure head constraints through successive iterations, making it ideal for hand calculations and gaining physical insight into network behavior.	The Muskingum method is a hydrologic flood routing technique that predicts how a flood wave attenuates (reduces in peak) and spreads as it travels down a river reach. Developed by McCarthy in 1938 for the US Army Corps of Engineers, the method is simple enough for hand calculations while capturing the essential physics of flood propagation.