INTRODUCTION

where ^p is the change in static or total pressure between two reference sections and q_ref is a reference kinetic pressure or dynamic pressure. This definition implicitly assumes that the flow at the reference sections is uniform or one-dimensional.

In contrast to the fundamental definition, the interpretation of measurements from experiment or computation uses measurements made in flow that will usually not be uniform at either the measurement sections or the reference section.

This Note explores the implications of this dichotomy which leads to the need to make choices in the derivation of a pressure-loss coefficient when deriving one from experiment or computation or a requirement to know what choices were made in the derivation when applying given loss coefficients. The essential requirement is to define appropriate mean values to represent the profiled flow in a onedimensional manner.

Given a profile of a property across a section in a flow, mean values of that property can be defined in various ways^3,4,6. The magnitude of the differences between the different mean values depends on the severity of the profile (and for some definitions, on the severity of other profiles). It is not possible to define a set of mean property values that, on their own, fully represent the profiled flow, a minimum number of mean-set factors relating sectional properties to their mean-set values is always required as well.

In the present context the profiles are defined to be for fully-developed axial flow. For fully-developed laminar flow, differences between different definitions can be large but for full-developed turbulent flow smaller differences result. However, even in turbulent flow these differences can contribute significantly to the apparent spread between experimental results from different sources and to the uncertainty of predicted pressure losses.

For flow of an incompressible fluid, the value taken for q_ref is the kinetic pressure ½_PV². The kinetic 2 pressure is conventionally assumed to be equal to the dynamic pressure (p_t - p) but this is only universally true in one-dimensional flow, for other cases equality will depend on compatible definition of mean pt and mean V² .

This note focuses primarily on derivation or application of "standard" pressure loss coefficients for which the flow at the measurement sections is a fully-developed axial flow. The derivation applies for flow of incompressible fluids, the case of compressible fluids is more complex and will be considered elsewhere.