Models of Quasi-Steady and Unsteady Discharge from Plumbing Fixtures

Modeling methods are developed to predict the discharge characteristics of simulated simplified configurations for plumbing fixtures connected to horizontal drain branch piping. Computations are carried out to illustrate several methods of determining the effect of various loss coefficients of the drain connection, pipe length, pipe diameter, and friction factor. Solutions are obtained for the case of a fixture with a constant head (continuous refill) and a falling head (emptying of a sink). Numerical solution of the non-linear differential equation for the falling head case was obtained by the Runge-Kutta method. Discharge characteristics are presented for a range of flows and pipe diameter-to-length ratios representative of plumbing installations. The feasibility of developing predictive models for hydraulic characteristics of interconnected plumbing fixture and drainage piping systems is shown. The variations of efflux rate with the drain pipe diameter, length, and slope obtained from the assumed models are similar in trend to the available experimental data.