قارن الطرق

	منهج هاردي كروس	Terzaghi Consolidation	نموذج التدفق المروري (نموذج LWR)
المجال	الهندسة المدنية	الهندسة المدنية	الهندسة المدنية
العائلة	Process / pipeline	Process / pipeline	Process / pipeline
سنة النشأة	1936	1943	1955
صاحب الطريقة	Hardy Cross	Karl Terzaghi	M. J. Lighthill and G. B. Whitham
النوع	Iterative method for pipe network flow distribution	Diffusion equation for pore pressure dissipation and soil settlement	Macroscopic traffic flow modeling using conservation laws
المصدر التأسيسي	Cross, H. (1936). Analysis of flow in networks of conduits or conductors. University of Illinois Bulletin, 34(17), 3-29.	Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley & Sons. ISBN: 0-471-85305-1	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.
الأسماء البديلة	Cross method, Moment distribution method, Iterative balancing	Primary consolidation, Soil settlement, Effective stress	LWR model, Traffic wave, Kinematic wave theory
ذات صلة	3	3	3
الملخص	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.	Terzaghi consolidation theory describes how water-saturated clay soils compress over time as excess pore water pressure dissipates and effective stress increases. Formulated by Karl Terzaghi in 1943, this foundational theory enables prediction of settlement rates for foundations on compressible soils, a critical design concern in geotechnical engineering.	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.