3.1 Fluid Statics
Stanley A. Berger
Equilibrium of a Fluid Element
If the sum of the external forces acting on a ?uid element is zero, the ?uid will be either at rest or
moving as a solid body ? in either case, we say the ?uid element is in equilibrium. In this section we
consider ?uids in such an equilibrium state. For ?uids in equilibrium the only internal stresses acting
will be normal forces, since the shear stresses depend on velocity gradients, and all such gradients, by
the de?nition of equilibrium, are zero. If one then carries out a balance between the normal surface
stresses and the body forces, assumed proportional to volume or mass, such as gravity, acting on an
elementary prismatic ?uid volume, the resulting equilibrium equations, after shrinking the volume to
zero, show that the normal stresses at a point are the same in all directions, and since they are known
to be negative, this common value is denoted by ?p, p being the pressure.
Hydrostatic Pressure
If we carry out an equilibrium of forces on an elementary volume element dxdydz, the forces being
pressures acting on the faces of the element and gravity acting in the ?z direction, we obtain
(3.1.1)
The ?rst two of these imply that the pressure is the same in all directions at the same vertical height in
a gravitational ?eld. The third, where g is the speci?c weight, shows that the pressure increases with
depth in a gravitational ?eld, the variation depending on r(z). For homogeneous ?uids, for which r =
constant, this last equation can be integrated immediately, yielding
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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