Drag
Any object immersed in a viscous ?uid ?ow experiences a net force from the shear stresses and pressure
differences caused by the ?uid motion. Drag is the force component parallel to, and lift is the force
component perpendicular to, the ?ow direction. Streamlining is the art of shaping a body to reduce ?uid
dynamic drag. Airfoils (hydrofoils) are designed to produce lift in air (water); they are streamlined to
reduce drag and thus to attain high lift?drag ratios.
In general, lift and drag cannot be predicted analytically for ?ows with separation, but progress
continues on computational ?uid dynamics methods. For many engineering purposes, drag and lift forces
are calculated from experimentally derived coef?cients, discussed below.
Effect of Pressure Gradient
Boundary layer ?ow with favorable, zero, and adverse pressure gradients is depicted schematically in
Figure 3.6.3. (Assume a thin boundary layer, so ?ow on the lower surface behaves as external ?ow on
a surface, with the pressure gradient impressed on the boundary layer.) The pressure gradient is favorable
when ¶p/¶x < 0, zero when ¶p/¶x = 0, and adverse when ¶p/¶x > 0, as indicated for Regions 1, 2, and 3.
Viscous shear always causes a net retarding force on any ?uid particle within the boundary layer. For
zero pressure gradient, shear forces alone can never bring the particle to rest. (Recall that for laminar
and turbulent boundary layers the shear stress varied as 1/x1/2 and 1/x1/5, respectively; shear stress never
becomes zero for ?nite x.) Since shear stress is given by tw = m ¶u/¶y)y=0, the velocity gradient cannot
be zero. Therefore, ?ow cannot separate in a zero pressure gradient; shear stresses alone can never cause
?ow separation.
In the favorable pressure gradient of Region 1, pressure forces tend to maintain the motion of the
particle, so ?ow cannot separate. In the adverse pressure gradient of Region 3, pressure forces oppose
the motion of a ?uid particle. An adverse pressure gradient is a necessary condition for ?ow separation.
Velocity pro?les for laminar and turbulent boundary layers are shown in Figure 3.6.2. It is easy to
see that the turbulent velocity pro?le has much more momentum than the laminar pro?le. Therefore,
the turbulent velocity pro?le can resist separation in an adverse pressure gradient better than the laminar
pro?le.
The freestream velocity distribution must be known before the MIE can be applied. We obtain a ?rst
approximation by applying potential ?ow theory to calculate the ?ow ?eld around the object. Much
effort has been devoted to calculation of velocity distributions over objects of known shape (the ?direct?
problem) and to determination of shapes to produce a desired pressure distribution (the ?inverse?
problem). Detailed discussion of such calculation schemes is beyond the scope of this section; the state
of the art continues to progress rapidly.
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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