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# المحاضرة 4-1

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 4
أستاذ المادة محمد عبد مسلم عبد الله الطفيلي       04/07/2018 08:44:55
The frictional drag force depends on the particle velocity, fluid density, fluid viscosity, particle diameter, and the drag coefficient Cd (dimensionless), and is given by:

F_d=(C_(d ) A_(p ) ?_(w ) ?v^2?_(p ))/2
Where:
Fd = frictional drag force, (kg. m/s2 )
Cd = drag coefficient, (unit less)
Ap = cross sectional or projected area of particles in direction of flow, (m2)
vp = particle settling velocity, (m/s)

Equating the resultant gravitational force to the frictional drag force for spherical particles yields Newton law:
v_(p(t))=?((4 g)/(3 C_(d ) ) (??_(p )- ??_(w )/?_w ) d_p ) = ?((4 g)/(3 C_(d ) ) (Sg_p-1) d_p )
Where:
v p(t) = terminal velocity of particle, (m/s)
dp = diameter of particle, (m)
SgP = specific gravity of the particle
The coefficient of drag Cd takes on different values depending on whether the flow regime surrounding the particle is laminar or turbulent. There are three distinct regions, depending on the Reynolds number NR:
laminar (NR < 1),
transition< (NR = 1 to 2000), and
turbulent (NR > 2000). Although

Although particle shape affects the value of the drag coefficient, for particles that are approximately spherical, the coefficient of drag Cd is approximated by the following equation:
C_d=24/N_R + 3/?(N_R )+0.34
The Reynolds number NR (or Re) for settling particles is defined as:

N_R=(v_(p ) d_(p ) ?_w)/?= (v_(p ) d_(p ))/?
where :
?? = dynamic viscosity, (N.s/m2)
? = kinematic viscosity, (m2/s)
Newton s Equation must be modified for non-spherical particles. An application that has been proposed is to rewrite the equation as follows :
v_(p(t))=?((4 g)/(3 C_(d ) ?) (??_(p )- ??_(w )/?_w ) d_p ) = ?((4 g)/(3 C_(d ) ?) (S g_p-1) d_p )
where ? is a shape factor. The value of the shape factor is 1.0 for spheres, 2.0 for sand grains, and up to and greater than 20 for fractal floc. The shape factor ? especially important in wastewater treatment where few, if any, particles are spherical.

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 .