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Application of the Newton Method in Valve Discharge Coefficient Relationships

by Jorge A. Garcia, (M.ASCE),
Antonia M. Romero,



Document Type: Proceeding Paper

Part of: North American Water and Environment Congress & Destructive Water

Abstract:

This paper presents a methodology that utilizes the Newton Method to compute the dimensionless valve discharge coefficient Cd from a manufacturers valve discharge coefficient Cv. The implicit relationship between Cd and Cv requires a trial- and-error approach to finding Cd or a mathematical approach such as the Newton method. A simple program in QBASIC is used to mathematically solve for the dimensionless discharge coefficient from a known valve diameter and manufacturers Cv coefficient. Two options are presented; the traditional Newton-Raphson method which uses the function derivative, and the Newton-Secant method which utilizes a numerical approximation to the function derivative.

Subject Headings: Valves | Numerical methods | Approximation methods | Water discharge | Mathematics | Computing in civil engineering | Ratings

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