Fixed and Variable Area Discharges

Pressure influences some leakage paths more than others

Japanese and UK research data in 1980 on pressure/leak flow rate relationships were reconciled with other test data worldwide using the Fixed and Variable Area Discharges (FAVAD) concept, proposed by John May in 1994. The velocity of flow of a leak varies with a Coefficient of Discharge (Cd) and the square root of pressure; but May recognised that the area of some leakage paths may also vary with pressure, and influence these relationships.

The FAVAD equation, with fixed and variable area components of leak flow rates

Leak Flow Rate L (volume/unit time) = (Af + B x AZP) x Cd x √(2g x AZP)

was used by specialist consultants, but a simpler version known as the N1 Power Law Equation

Leakage Rate L (volume/unit time) varies with Pressure P to the power NI

was more widely used by leakage practitioners, assuming constant N1 values, independent of pressure changes; and for analysis of laboratory tests of pressure:leak flow relationships on cracked pipes. Despite the approximations inherent in the Power Law equation, it proved successful in introducing, to practitioners, calculations relating leak flow rates to average zone pressure in most distribution systems. However, the wide variation in N1 values from field tests over the next decade was only partially explained by component analysis of different types of leaks (background, rigid pipes, flexible pipes).

Source: A. Lambert

By 2014, improved understanding of pressure:burst frequency relationships, and advances in valve control technology and data transfer, had resulted in increasingly complex forms of advanced pressure management, with generally lower and more varied pressures at times of low consumption, particularly at night. Because variable leakage area reduces with pressure, the N1 value must also reduce, to a greater or lesser extent.

Research by Professor Kobus van Zyl and colleagues at University of Cape Town from 2012 to 2017 on cracks in different pipe materials confirmed the assumptions in the FAVAD equation to be valid. With that confirmation, Allan Lambert of WLR&A Ltd was able to analyse N1 test results in greater detail, and develop fast track FAVAD and N1 equations in simplified format suitable for leakage practitioners, for:

• Quickly identifying fixed and variable components of flow directly from an N1 value
• Calculating the equation relating N1 to AZP for any Zone at any particular time
• Creating an overview graph of N1 vs AZP relationships
• Defining the equation relating leak flow rates (fixed, variable and total) to AZP
• Continuously tracking leak flow rates directly from measured Average Zone Pressure
• Developing the Correction Factor (CF) method for calculating Night-Day Factors

The transition from using constant N1 values to the FAVAD relationships listed above can be found in the FAVAD and N1 Update webpage in the Influences of Pressure Info-Hub. A few of the graphs in that update are shown below.

The original September 2012 version of FAVAD N1 webpage in the Concepts Section is now stored, for reference purposes, in the Archive

The Correction Factor method for calculating Night-Day Factor (known as Hour-Day Factor in the UK) means that the AZP&NDFCalcs free software will not be updated or issued in future. Average Zone Point (AZP) now has a separate webpage.
9th November 2017