The method is shown to produce accurate results for laboratory experiments and is computationally cheap, however it makes a number of assumptions that may limit its application to field based analysis. These assumptions include: that corrosion of the pipe wall only occurs internally and does not affect Young’s modulus of the material; that corrosion is uniform in both radial and longitudinal directions; that no corroded material remains attached to the pipe wall and that the time of the induced head perturbation is less than the time it takes for the wave front to travel two lengths of the deteriorated section. Accuracy of the method is also subject to the operator’s selection of reference data points.To improve upon the versatility of these detection methods it is necessary to reduce the number of simplifying assumptions.

This paper describes an ITA method which can account for variations in the wavespeed, diameter and length of a deteriorated section independently, thus reducing the number of assumptions to be made.2.?Modelling TheoryThis investigation uses the Method of Characteristics (MOC) to solving the governing mass and linear momentum conservation equations for one dimensional unsteady pipe flow [8]:gAa2?H?t+?Q?x=0(1)1gA?Q?t+?H?x+hf=0(2)where H is the head in the pipe, Q is the pipe discharge, A is the cross-sectional area of the pipe, a is the wavespeed, g is acceleration due to gravity, x is the distance along the pipeline, t is time and hf is the sum of steady and unsteady frictional head losses. The derivation of these two equations assumes that both the fluid and the pipe behave in a linear elastic fashion.

The equations can be solved using the MOC through confining the solution to a grid in the time and space domains by applying the following relationship:dxdt=��a(3)where dx is the grid spacing in the along the length of the pipe and dt is the time step for the numerical solution.Solving Equations (1) and (2) subject to the condition in Equation (3) gives two simultaneous equations which can be used to solve for the head (HP) and flow (QP) at a grid point where the head (HA, HB) and flow (QA, QB) are known values at adjacent nodes in the previous time step:HP=HA?B(QP?QA)?RQP|QA|(4)HP=HB+B(QP?QA)+RQP|QB|(5)where B is the characteristic impedance of the pipeline given by:B=agA(6)and R is the pipeline resistance coefficient, which can be calculated by:R=fdx2gDA2(7)where D is the nominal diameter of the pipe section and f is the Darcy-Weisbach friction factor.

The additional effects of unsteady friction can be accounted for using the efficient approximation Brefeldin_A of Vardy and Brown [9] for smooth turbulent pipe flow presented in Vitkovsky et al. [10].The MOC model described is coded in Fortran using a constant time step discretisation such that numerical dissipation and dispersion errors that arise with the use of interpolation methods are avoided.