Extended irreversible thermodynamics (EIT) provides a framework for derivin
g extensions to phenomenological equations (e.g., Newton's law of viscosity
, Fick's law of mass transport, and Darcy's law for porous media flow) for
problems involving high frequencies (i.e., rapid transients). In this paper
, a phenomenological equation is derived for energy loss in 1D unsteady pip
e flow using an EIT formalism. The resulting wall shear stress is equal to
the sum of (1) the steady-state shear stress; (2) a term that is proportion
al to the local (i.e., temporal) acceleration; and (3) a term that is propo
rtional to the product of the velocity and the convective (i.e., spatial) a
cceleration. The form of this FIT-based wall shear stress formula shows tha
t EIT provides a physical basis for instantaneous acceleration based unstea
dy friction formulas. It also illustrates the limitations and underlying as
sumptions of these models. For example, instantaneous acceleration based un
steady friction formulas are limited to fast transients (i.e., transients i
n which the water hammer timescale is significantly smaller than the diffus
ion timescale). A characteristics solution for unsteady pipe flow is propos
ed in which the phenomenological equation is used to model energy dissipati
on. Comparison of numerical test results with measured data from upstream a
nd downstream valve closure laboratory experiments shows excellent agreemen
t.