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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.
10th Edition
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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