Abstract
A general simple continua can be enhanced by constitutive equations which depend on the acceleration and velocity gradients to model the effects of a material characteristic length. This paper shows that for irrotational flows of a class of incompressible materials this model yields a Bernoulli equation. Consequently, for this class of materials and flows, it is possible to satisfy the balance of linear momentum exactly, including the effect of a material characteristic length which introduces size dependence of solutions. An example of a rigid circular cylinder moving through an inviscid fluid is considered to demonstrate dependence of the motion on the size of the cylinder.
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