Development of a convective diffusion model for lead pipe rigs operating in laminar flow

As part of achieving lower lead standards water undertakers are utilising lead pipe rigs to quantify the benefit of treatment measures. A convective diffusion model is developed for lead pipe rigs operating in laminar flow, and applied to the three operating steps of flushing, sampling and stagnation. The model is used to determine the appropriate time-scales for each stage, and the sensitivity of the measure to variations in flow-rate. In contrast to rigs operating in turbulent flow the average lead observed leaving the pipe and that in the pipe, after a period of stagnation, are substantially different. Equations are derived for both, and take into account the residual distribution of lead left in the pipe after flushing. It is shown that the lead concentration observed leaving the pipe is well approximated by a single exponential term in contrast to the concentration within the pipe. Predictions are made on the residual lead concentration that can be achieved through flushing, and its dependence on flow-rate. The relevance of the laminar flow model to that in domestic lead pipes is discussed.