  In this paper, we discover the fundamental quantity that Nature minimizes in
almost all flows encountered in everyday life: river, rain, flow in a pipe,
blood flow, airflow over an airplane, etc. We show that the norm of the
pressure gradient over the field is minimum at every instant of time! We call
it the principle of minimum pressure gradient (PMPG). The principle is deeply
rooted in classical mechanics via Gauss' principle of least constraint.
Therefore, while we prove mathematically that Navier-Stokes' equation
represents the necessary condition for minimization of the pressure gradient,
the PMPG stands on its own philosophy independent of Navier-Stokes'. It turns
any fluid mechanics problem into a minimization one. We demonstrate this
intriguing property by solving three of the classical problems in fluid
mechanics using the PMPG without resorting to Navier-Stokes' equation. In fact,
the inviscid version of the PMPG allowed solving the long-standing problem of
the aerohydrodynamic lift over smooth cylindrical shapes where Euler's equation
fails to provide a unique answer. Moreover, the result challenges the accepted
wisdom about lift generation on an airfoil, which has prevailed over a century.
The PMPG is expected to be transformative for theoretical modeling of fluid
mechanics as it encodes a complicated nonlinear partial differential equation
into a simple minimization problem. The principle even transcends
Navier-Stokes' equations in its applicability to non-Newtonian fluids with
arbitrary constitutive relations and fluids subject to arbitrary forcing (e.g.
electric or magnetic).
