• Created by user-3cacb, last updated on May 12, 2008 2 minute read

You are viewing an old version of this page. View the current version.

Compare with Current View Page History

« Previous Version 5 Next »

Equation 1

Unknown macro: {latex}

$$
1 - {N \over {N_0 }} = {{\left( {{N \mathord{\left/
{\vphantom {N

Unknown macro: {N_0 } }} \right.
\kern-\nulldelimiterspace}

}} \right)_

Unknown macro: {max }

t} \over {K_S + t}}
$$

or it also can be represented as:

Unknown macro: {latex}

$$
{N \over {N_0 }} = {{K_S + t - \left( {{N \mathord{\left/
{\vphantom {N

Unknown macro: {N_0 } }} \right.
\kern-\nulldelimiterspace}

}} \right)_

Unknown macro: {max }

t} \over {K_S + t}}
$$

where
N is the effluent turbidity [-]
No is the maximum/initial effluent turbidity during settling state [-]
(N/N0)max is the maximum value that the hyperbolic function will asymptomatically approach to.
t is the time [T]
KS is the rate of settling flocs [T].

Terminal velocity is the velocity of the flocs settling in the column.

Unknown macro: {latex}

$$
v =

Unknown macro: {L over t}

$$

where
v is the terminal velocity [L/T2]
L is the distance of the column above turbidimeter [L]

t can be redefined as:

Equation 2

Unknown macro: {latex}

$$
t =

Unknown macro: {d over v}

$$

substitution of Equation (2) in Equation (1) yields:

Equation 3

Unknown macro: {latex}

$$
1 - {N \over {N_0 }} = {{\left( {{N \mathord{\left/
{\vphantom {N

Unknown macro: {N_0 } }} \right.
\kern-\nulldelimiterspace}

}} \right)_

Unknown macro: {max }

L} \over {K_S v + L}}
$$

Reciprocating both axes in Equation 3 gives:

Equation 4

Unknown macro: {latex}

$$
{1 \mathord{\left/
{\vphantom {1 {\left( {1 - {N \over

Unknown macro: {N_0 } }} \right)}}} \right.
\kern-\nulldelimiterspace} {\left( {1 - {N \over

}} \right)}} = {{K_S v} \over {\left( {{N \mathord{\left/
{\vphantom {N

Unknown macro: {N_0 } }} \right.
\kern-\nulldelimiterspace}

}} \right)_

Unknown macro: {max }

L}} + {1 \over {\left( {{N \mathord{\left/
{\vphantom {N

Unknown macro: {N_0 } }} \right.
\kern-\nulldelimiterspace}

}} \right)_

}}
$$

For the experimental data that is less than number of window specify (at lower end), Equation 5a is used and Equation 5b is used at the upper end.

Equation 5a

Unknown macro: {latex}

$$
{{\sum\limits_

Unknown macro: {j = 0}

^

Unknown macro: {2i}

Unknown macro: {Y_j }

} \over {2i + 1}}
$$

Equation 5b

Unknown macro: {latex}

$$
{{\sum\limits_

Unknown macro: {j = 2i - n + 1}

^

Unknown macro: {n - 1}

Unknown macro: {Y_j }

} \over {2n - 2i - 1}}
$$

For any other experimental data in between these two condition, Equation 6 is used.
Equation 6

Unknown macro: {latex}

$$
{{\sum\limits_

Unknown macro: {j = i - m}

^

Unknown macro: {i + m}

Unknown macro: {Y_j }

} \over w}
$$

where
w is the number of window (odd number)
Y is the data
n is the length of experimental data
m is (w-1)/2

  • No labels