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Forces on Surfaces Immersed in Fluids

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 16:44:36

INTRODUCTION
In the previous chapter the pressure distribution in fluids in static and dynamic condition was discussed. When a fluid is in contact with a surface is exerts a normal force on the surface. The walls of reservoirs, sluice gates, flood gates, oil and water tanks and the hulls of ships are exposed to the forces exerted by fluids in contact with them. The fluids are generally under static condition. For the design of such structures it is necessary to determine the total force on them. It is also necessary to determine the point of action of this force. The point of action of the total force is known as center of pressure or pressure center. From the basic hydrodynamic equation it is known that the force depends on the pressure at the depth considered.
i.e.,
P = ?h. Force on an elemental area dA as a depth, h, will be
dF = ?hdA
The total force is obtained by integrating the basic equation over the area

F=??_A?hdA

From the definition of center of gravity or centroid
?_A?hdA=h^- A
where h^- is the depth of the Centre of gravity of the area.
To determine the point of action of the total force, moment is taken of the elemental forces with reference to an axis and equated to the product of the total force and the distance of the Centre of pressure from the axis namely hcp
F. hcp = ?_A?hdF = ? ?_A?h^2 ^dA
The integral over the area is nothing but the second moment or the moment of inertia of the area about the axis considered. Thus there is a need to know the Centre of gravity and the moment of inertia of areas.



FORCE ON AN ARBITRARILY SHAPED PLATE IMMERSED IN A LIQUID

Case 1 : Surface exposed to gas pressure : For plane surface, force = area × pressure The contribution due to the weight of the gas column is negligible. The resultant acts at the centroid of the area as the pressure at all depths are the same.
Case 2 : Horizontal surface at a depth y.
P = – y × ? and as y is – ve, force = Ay? in which y may also be expressed as head of the fluid. The resultant force acts vertically through the centroid of the area, Here also the pressure at all locations are the same.
Case : Plane inclined at angle ? with horizontal.

Centre of Pressure for Immersed Vertical Planes
Case 1: A rectangle of width b and depth d, the side of length b being horizontal.
Case 2: A circle of diameter d.
Case 3: A triangle of height h with base b, horizontal and nearer the free surface.


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 .