ESDU TM 148:2004

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.