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(3.7.5)

**Variation of C _{D} (Drag-coefficient) **

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 non-spherical 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

- Particles settle as individual entities
- No interaction between particles

**(ii) Flocculation settling: **Applicable for dilute suspension of particles that coalesce or flocculate

- By flocculation, particle size increases and terminal velocity increases.
- Settling can be increased by addition of some ballasting agent such as polymers.

**(iii) Hindered settling**

- For suspension of intermediate settling.
- In this case, particles are such close together that the inter-particle force due to one hinders the settling of other particle.
- The particles remain in fixed position with respect to each other and particles settles as a whole

**(iv) Compression settling**

- Case in which particles are in such high concentration that a whole structure is formed.
- Compression takes place due to weight of whole mass which continuously increases.
- A clear water is formed above compression zone

**CLASSIFICATION OF SEDIMENTATION TANKS **

**Grit chamber:**For removal of sand, grits, etc.**Plain sedimentation tank:**For removal of settleable solids.**Chemical precipitation tank:**for removal of very fine suspended particles by adding coagulants, etc**Septic tanks:**For doing sedimentation and sludge digestion together in households**Secondary settling tanks:**After activated sludge or trickling filter treatment systems.

**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 (unit-less) and its value varies in the range 0.02- 0.03; k is cohesion constant that depends upon the type of material being scoured (unit-less). 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, Cross-sectional 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 re-suspend 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: **

- The terminal velocity should be ≥ surface loading of the tank.
- Surface area is more important than the height of the settling tank.
- Higher the surface area, higher will be the removal efficiency and more will be the removal of finer particles.
- All particles having settling velocity u
_{t}≥ v_{o}will be completed removed. - For particles having u
_{t}< v_{o}, only u_{t}/v_{o}only fraction will be removed.

**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 at-least four times the settling velocity and horizontal velocity at-most one-third 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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