(3.7.5)
Variation of C_{D} (Dragcoefficient)
In laminar zone, Stoke’s law is applicable
(3.7.6)
(3.7.7)
For transition zone,
(3.7.8)
For turbulent zone, C_{D} is independent of Re and C_{D}=0.4
For nonspherical particles, formula for Reynold number and settling velocity calculation are modified using the shape factor ( φ ) [1]:
(3.7.9)
(3.7.10)
Problem 3.7.1: A sand particle has an average diameter of 1 mm and a shape factor of 0.90 and a specific gravity of 2.1, determine the terminal velocity of the particle settling in water at 20 ^{o}C (kinematic viscosity of water=1.003×10^{6} m^{2}/s and specific gravity=1). Drag coefficient can be computed using the following equation:
Solution: kinematic viscosity(V) =
Settling velocity using stokes law is:
Since Re>1, therefore, Newton’s law should be used for finding terminal velocity in transition zone. For initial assumption of settling velocity, stoke’s law is used. This initially assumed velocity is used to determine the Reynold number which is further used to find settling velocity. This iterative procedure is repeated till initial assumed velocity is approximately equal to settling velocity calculated from Newton’s equation.
Initial drag coefficient is calculated as:
Now, iterative procedure is continued:
Final settling velocity=0.1419 m/s.
TYPES OF GRAVITATIONAL SETTLING PHENOMENON
(i) Discrete particle settling: Applicable for very low concentration solids
(ii) Flocculation settling: Applicable for dilute suspension of particles that coalesce or flocculate
(iii) Hindered settling
(iv) Compression settling
CLASSIFICATION OF SEDIMENTATION TANKS
SCOUR VELOCITY
Maximum horizontal velocity though the tank which does not allows resuspension (scouring) of settled particles. It is given as [1]:
(3.8.1)
Where, f is the Darcy–Weisbach friction factor (unitless) and its value varies in the range 0.02 0.03; k is cohesion constant that depends upon the type of material being scoured (unitless). Its value varies in the range of 0.04 0.06. For sticky interlocking matter k=0.6 whereas for ungrounded sand k=0.4.
Important point in design of sedimentation tank Assume t is the detention time for which a suspension is detained in the settling tank having height H, length L and width W. Also assume, VH is the horizontal velocity and ut is the terminal settling velocity of the target particle. Now, Crosssectional area of tank (AC)=H×W Surface area of tank (A)=L×W If Q is the flow rate of wastewater into the tank,
(3.8.2)
Since the target particle should not resuspend during its flow along the length of the tank, therefore, detention time
(3.8.3)
Also, the target particle should settle down before it reaches the outlet, therefore,
(3.8.4)
Combining,
(3.8.5)
This expression gives following important points:
Problem 3.8.1: A municipal wastewater plant is to be designed to treat maximum flow rate of 60000 m^{3}/d. Target particle for settling has the following characteristics: D_{P}=200×10^{6} m, k=0.05, f=0.025, ρ_{P}=1.25×10^{3} kg/m^{3}. For a rectangular classifier having ratio of length to width>6, overflow rate is atleast four times the settling velocity and horizontal velocity atmost onethird of the scour velocity. (a) Find the dimensions of the rectangular tank (b) Determine detention time
Solution:
Actual horizontal velocity=V_{H}/3=0.02951 m/s.
Overflow rate=3×u_{t }= 21 .7 6 x 10 ^{3} m / s
If W is the width, L is the length and H is the height of the rectangular settling basin,
Also given:
W=2.305 m,
L=6×2.305=13.83 m
H=23.54/2.305=10.21 m
Volume of tank, V=LWH=325.47 m^{3}
Detention time,
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