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Introduction to Environmental Engineering

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Chapter 6, Problem 41P

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Continuing the preparation of the proposal for the Eau Gaullie treatment plant (Problem 6-38), design the flocculation tank by providing the following for the first two compartments only: 1. Water power input in kW

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2. Tank dimensions in m 3. Diameter of the impeller in m 4. Rotational speed of impeller in rpm Use the following assumptions:

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2. Tapered G in three compartments: 90, 60, and 30 s–1 3. Gθ = 120,000 4. Compartment length = width = depth

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5. Impeller type: axial-flow impeller, three blades, NP = 0.31 6. Available impeller diameters: 1.0, 1.5, and 2.0 m 7. Assume

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Step 1 of 12 Write the expression to determine the detention time of the treatment plant. …… (1) Here,

is the detention time of the treatment plant and

is the average of the Galileo

numbers. Determine the average of the Galileo numbers.

Comment

Step 2 of 12 Determine the detention time of the treatment plant. Substitute

for

and 120000 for

in the equation (1).

Comment

Step 3 of 12 Write the expression to determine the volume of the flocculation basin.

Here,

is the volume of the basin and

Substitute

for

and

is the flow discharge. for

.

Calculate the volume of the each flocculation basin.

Comment

Step 4 of 12 Each basin is divided into the three compartments, calculate the volume of the each compartment.

Assume the square compartment with the depth equal to the side of the square.

Comment

Step 5 of 12 Calculate the volume of the square compartment. Substitute

for

.

Therefore, the tank dimensions are

.

Comment

Step 6 of 12 Write the expression to determine the input power of each compartment.

Here,

is the input power and

Substitute

for

is the dynamic coefficient of viscosity.

,

Therefore, the water power input is

for

, and

for

.

.

Comment

Step 7 of 12 Determine the area of the compartment.

Determine the equivalent diameter of the tank using the following relation:

Consider the width of the tank.

Comment

Step 8 of 12 Calculate the geometric mean ratio of the radial turbine.

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Substitute 3.3m for



and

for

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Step 9 of 12 Determine the impeller diameter of the turbine as follows: Obtain the allowable tip speed from the table “Radial Turbine Impeller” of the text book for impeller diameter of 1m corresponding to the geometric ratio. Geometric ratio Impeller diameter

Impeller diameter

0.887

Hence, use the

0.89

as the impeller diameter.

Comment

Step 10 of 12 Write the expression to determine the rotational speed of the impeller for the first compartment. …… (2) Here,

is the rotational speed and

Substitute

for

is the density of the water.

,

for

, and

for

in the equitation (2).

Comment

Step 11 of 12 Calculate the rotation speed of the second compartment. Substitute

for

,

for

, and

for

in the equation (2).

Comment

Step 12 of 12 From the above two compartments, observe the tip speeds of the two compartments. The first impeller tip speed is less than the second one. Therefore, the assumption is correct.

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