CH-24-C120 - The Equal Area, Log-Linear and Log-Tchebycheff Rules: Derivations and Assumptions

The volumetric flow rate in a duct is commonly calculated as the arithmetic average of an array of point velocity measurements across the flow. Various traverse patterns, such as the Equal Area, Log-Linear and Log-Tchebycheff rules, are defined for round and rectangular ducts in ASHRAE and ISO standards. While many studies on the accuracy of these rules have been published, there is little discussion on the reasons for this accuracy, i.e., the assumptions (if any) about the underlying velocity profile. Such knowledge would be useful to engineers involved in ventilation system testing and commissioning, particularly where some compromise is necessary, e.g., for non-ideal traverse locations or duct cross-sections. This paper explains how the three rules are derived, reveals their underlying assumptions, and suggests some ideas for further research.