Nh. March et Bv. Paranjape, A MICROSCOPIC GENERALIZATION OF BERNOULLIS EQUATION TO INCLUDE LOW-ORDER DENSITY GRADIENTS, Physics and chemistry of liquids, 28(3), 1994, pp. 201-206
A microscopic generalization of Bernoulli's equation is established by
appealing to low-order density gradient theory of an inhomogeneous li
quid. This theory, used earlier to relate surface energy, bulk compres
sibility and the thickness of the liquid surface, is here generalized
to embrace the case in which the inhomogeneous fluid is subjected to a
velocity gradient to simulate the case of steady flow. Finally the th
eory is extended to include non-steady flow and contact is again estab
lished with Bernoulli's equation.