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المحاضرة 4-7

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 4
أستاذ المادة محمد عبد مسلم عبد الله الطفيلي       04/07/2018 08:51:54
































EXAMPLE:
A settling basin is designed to have a surface overflow rate of 0.37 mm / s. Determine the overall removal obtained for a suspension with the size distribution given. The specific gravity of particles is 1.2 and the water temperature is 20 0C .


Particle size d_p
mm Weight fraction
greater than size %
0.1 10
0.08 15
0.07 40
0.06 70
0.04 93
0.02 99
0.01 100

Solution:

At 20 0C: (From Table) , ?=1.003 x ?10?^(-6) m2/s,
The settling velocities may be calculated from stokes law as follow:

v_p=( g (S g_p-1) ?d^2?_p)/18?= ( 9.81m/s^2 (1.2-1) ?d^2?_p)/(18(1.003 x ?10?^(-6)))
v_p=108674.?? d?^2?_p ,?(v?_p in m/s and d_p in m )
Calculate v_p for each particle size
For d_p = 0.1 mm = 0.0001 m
v_p=108674?? d?^2?_p=108674 (0.0001)^2
= 0.001 m/s=1.08 mm/s
Particle size d_p
mm Weight fraction
greater than size % Settling velocity v_p
mm/s NR
0.1 10 1.08 0.1
0.08 15 0.69 0.05
0.07 40 0.53 0.04
0.06 70 0.39 0.02
0.04 93 0.17 0.01
0.02 99 0.04 0.001
0.01 100 0.01 0.0001

Since the calculated Reynolds numbers are all less than 1.0. Stokes law is applicable and the calculation of velocity is valid. From the calculated settling velocities the cumulative distribution curve is drawn. All particles with settling velocities greater than v_c= 0.37 mm/s will be removed. Thus, from the graph, the fraction (1-X_c )=0.73



















Cumulative distribution of particle settling velocity






The graphical determination of ???? v?_(p ) ?X? is tabulated below:
?X 0.04 0.04 0.04 0.04 0.04 0.04 0.027
? v?_(p ) 0.06 0.16 0.22 0.26 0.3 0.34 0.37
? v?_(p ) ?X 0.0024 0.0064 0.0088 0.0104 0.012 0.0136 0.0099
???? v?_(p ) ?X? 0.0635

fraction removed= (1-X_c )+1/? v?_(c ) ???? v?_(p ) ?X=0.73+(1/0.37)(0.0635)=0.9016=90.16%?
Flocculent Particle Settling (Type 2 Settling)

In practice, the actual settling performance cannot be adequately predicted because of unrealistic assumptions on ideal discrete particle settling. Under quiescent conditions, suspended particles in water or wastewater exhibit a natural tendency to agglomerate. Also, suspended solids in wastewater are not discrete particles and vary more than light and small particles, as they contact and agglomerate and grow in size.
Flocculent settling occurs when the particles agglomerate during the settling period with a resulting change in size and settling rate. This phenomenon is called flocculant or type 2 sedimentation. The flocculation process increases removal efficiency but it cannot be adequately expressed by equations.
Settling-column analysis is usually used to determine the settling characteristics of flocculated particles. The settling column may be of any diameter but its length should be equal to the depth of the settling tank to be designed. The settling column usually used in laboratories is 6 in. (15 cm) diameter and about (3 m) deep. It contains sampling ports at (45 – 60 cm) intervals.


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 .