  This paper introduces the Bayesian mass average and details its computation.
Owing to the complexity of flow in an engine and the limited instrumentation
and the precision of the sensor apparatus used, it is difficult to rigorously
calculate mass averages. Building upon related work, this paper views any
thermodynamic quantity's spatial variation at an axial plane in an engine (or a
rig) as a Gaussian random field. In cases where the mass flow rate is constant
in the circumferential direction but can be expressed via a polynomial or
spline radially, this paper presents an analytical calculation of the Bayesian
mass average. In cases where the mass flow rate itself can be expressed as a
Gaussian random field, a sampling procedure is presented to calculate the
Bayesian mass average. Examples of the calculation of the Bayesian mass average
for temperature are presented, including with a real engine case study where
velocity profiles are inferred from stagnation pressure measurements.
