Water Treatment Processes - Mathematics and Statistics for the Environment - page 645

Solution: The mudball volume is the volume that the water rose:

565 mL - 500 mL = 65 mL

Because 5 samples of media were taken, the total sample volume is 5 times the sample volume:

5 × 680 mL = 3400 mL

Mudball volume(mL)
Totals

65 mL
3400 mL

%Mudball volume = ×= ×= 100 100 1.%

ample volume(mL)

23.6.11 F filter b ed e xpansion
In addition to backwash rate, it is also important to expand the filter media during the wash to
maximize the removal of particles held in the filter or by the media; that is, the efficiency of the
filter wash operation depends on the expansion of the sand bed. Bed expansion is determined by
measuring the distance from the top of the unexpanded media to a reference point (e.g., top of the
filter wall) and from the top of the expanded media to the same reference. A proper backwash rate
should expand the filter 20 to 25%. Percent bed expansion is given by dividing the bed expansion by
the total depth of expandable media (i.e., media depth less support gravels) and multiplied by 100,
as follows:

Expanded measurement = Depth to top of media during backwash (in.)

Unexpanded measurement = Depth to top of media before backwash (in.)

Bed expansion = Unexpanded measurement (in.) - expanded measurement (in.)

(in.)
Totaldepth of expandablemedia (in.)

Bedexpansionmeasurement

Bedexpansion (%) = ×100 (23.78)

■ EXAMPLE 23.95
Problem: The backwashing practices for a filter with 30 in. of anthracite and sand are being evalu-
ated. While at rest, the distance from the top of the media to the concrete floor surrounding the top
of filter is measured to be 41 in. After the backwash has begun and the maximum backwash rate
is achieved, a probe containing a white disk is slowly lowered into the filter bed until anthracite is
observed on the disk. The distance from the expanded media to the concrete floor is measured to be
34.5 in. What is the percent bed expansion?

Solution:

Given:
Unexpanded measurement = 41 in.
Expanded measurement = 34.5 in.

Bed expansion = 41 in. - 34.5 in. = 6.5

.. )
Totaldepth of expandablemedia (in.)

Bedexpansionmeasurement(in 6.5 in.

30 in.

Bedexpansion = ×100 = × 100 = 22 %