**Coagulation and Flocculation-I**

__SOLUTION__

Design
a conventional vertical-shaft rapid mix tank unit for uniformly dispersing
coagulant in 10 MLD of settled raw water as per design parameters given below:

Detention time (t): 20
– 60 s

Ratio of tank height (H) to diameter (D): (1:1 to 1:3)

Ratio of impeller diameter (D_{I}) to tank
diameter (D): (0.2:1 to 0.4:1)

Gt: 10000
– 20000

Tank diameter (D): <
3 m

Paddle tip speed (v_{p}): 1.75
– 2.0 m/s

Paddle area (A_{p})/Tank
section area (A_{T}): 10:100
– 20:100

Coefficient of drag on impeller blade (C_{D}): 1.8

Maximum width of impeller blade (B): 0.20 x impeller
diameter

Impeller height from bottom (H_{B}): 1.0
x impeller diameter

Kinematic viscosity _{}: 1.003
x 10^{-6} m^{2}/s

Dynamic viscosity of water _{}: 1.002
x 10^{-3} N.s/m^{2}

Determine
tank dimensions (provide a freeboard of 0.5 m), impeller diameter, paddle
dimensions, number of paddles, clearance of the impeller from tank bottom,
paddle rotation speed and power input requirement.

**Solution:**

Let
the detention time (t) be 40 s.

Therefore,
volume of tank (V) = _{}

**Let the tank diameter (D) be 2 m**

Tank
cross-sectional area (A_{cs}) = 3.14 m^{2}

Tank
height (H) = 1.47 m, provide freeboard of 0.5 m

**Total height (H _{T})= 1.97 m, say 2 m.**

Tank
height (H) to tank diameter (D) ratio = _{}

(within the
range of 0.33–1.0, hence okay)

Let
velocity gradient, G = 400 s^{-1}

Therefore,
G.t = (400).(40) = 16000 (within the limit of
10000-20000, hence okay)

Let
the paddle tip speed (v_{p}) be 1.8 m/s

Hence,
velocity of
paddle relative to water (v) = 0.75.(1.8) = 1.35 m/s

_{}, or, _{}

or, A_{p} = 0.335 m^{2}

Tank sectional area = (D).(H)
= (1.47).(2) = 2.94 m^{2}

_{}, which is around 0.15, hence okay.

**Let the impeller diameter be 0.8 m**, i.e., _{}, which is okay

Choose **length of each impeller blade (L) as
0.20m**, i.e., _{} (okay)

Choose **breadth of each impeller blade (B) as
0.15m**, i.e., _{} (okay)

Area of each blade = (L.B) = (0.2).(0.15) = 0.03 m^{2}

**Therefore, number of blades to be provided = _{}, say 12**

**Clearance of the paddles from the tank
bottom = 0.8 m**

**Paddle rotation speed (w, radians/s) = _{}radians/s, **

**i.e., _{} revolutions per
minutes**

**Power requirement is given by, _{}, or, _{}**

**or****, P = 742 Watts, i.e.,
provide 1 KW motor for driving the impeller at 45 rpm.**