A note on the application of the extended Bernoulli equation

A general form of the momentum equation is presented. Because the solution is presented as an integral along a flow line, it is here referred to as an “extended’’ Bernoulli equation. The equation, as presented, is valid for unsteady, compressible, rotational, elasto-viscoplastic flows measured relative to a noninertial (translationally and/or rotationally accelerating) coordinate system, whose motion is known. Though all of these concepts have long been separately addressed in the educational literature of fluid and solid mechanics and dynamics, they are usually not available from a single source, as the literature prefers to reduce the problem to special-case solutions for instructional purposes. Two examples that make use of the extended Bernoulli equation in noninertial reference frames are solved. The consequences of failing to properly account for noninertial effects are discussed.