Page 433 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

388 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

on physical properties of the interacting materials other particles that would strike a collector at the
1 and 2. This is known as the Hamaker constant end of a unit cell. Particles outside the limiting
(Gregory, 1975, p. 78). trajectory would not strike collectors within a given
Happel collector: Refers to a particular geometry that repre- collector pore volume. The proportion of particles
sents a single collector of a granular media filter bed that would strike the collector, that is, h, can then be
used in mathematical modeling. The geometry calculated.
selected by Happel in 1958 and used by other mod- log Removal
elers, for example, Tien, is a spherical granular
media particle enveloped by a spherical volume of
log R ¼ log C o log C
water that has the same volume as the pore volume
for that particle. C o
¼ log
Headloss: The difference in head across the filter bed is C
the headloss. The gravel support and the under-
drain system may be included. Note: The term is
where log R is the common log of the removal ratio.
found in the literature frequently as two words,
The relationship between the %R and log R is
i.e., ‘‘headloss’’, and less-frequently as ‘‘headloss’’;
the latter is used here, however, since its used
throughout the text. Its combination represents the %R ¼ 100 10 log R
well-known concept regarding loss of energy head
due to pipe friction, pipe bends, porous media Manometer: A tube that penetrates the wall with a fluid on
flow, etc. the other side that has a U-shape for reading the
Heterodisperse suspension: Suspended particles are hetero- difference in pressure between the tap point and
geneous in size (Darby et al., 1992). some other point, that is, a ‘‘differential manometer.’’
In-line filtration: The ‘‘in-line’’ mode of filtration is com- If the other end is open to the atmosphere, the man-
prised of rapid-mix=coagulation followed by filtra- ometer is a special type, called a piezometer. The
tion. This mode is used most often with low turbidity manometer fluid may be any fluid that is different
waters. from the fluid whose pressure is being measured so
Inertia: Streamlines approaching a filter pore converge that an interface is visible. The U-tube is fitted with a
as the flow passes through. If the particles have scale so that the vertical elevations of each interface
sufficient inertia they maintain a trajectory that can be read, which must also be related to the eleva-
may cause the particle to impinge against a col- tions of each pressure tap.
lector. In water filtration, inertia is not a significant Mass flow diagram: A plot of the total volume of flow
transport mechanism, but in air filtration it has a versus time is a mass flow diagram. The two condi-
major effect. tions are (1) raw water flow and filter plant flow
Interception: When a particle is transported by a streamline versus time and (2) demand flow and filter plant
that passes within a distance d=2 from a collector flow versus time.
(d being the diameter of the particle), the particle 1. Raw water storage: If the diagram is used to esti-
will brush the collector; the contact is called mate raw water storage for a water treatment plant
interception. The probability of an interception that has a steady flow, the latter is a straight line.
contact is proportional to d(particle)=d(pore). The maximum difference between the line repre-
When d(particle)=d(pore) ) 1, straining becomes senting the total water supply volume and the
dominant. In filtration of water and wastewater, straight line representing the plant flow is the raw
1
2 10 4 < d(particle)=d(pore) <1 10 , with higher water storage required. The time scale on the raw
values causing straining (from Ives, 1975b, p. 188). water side usually is in years so that years of
Iwasaki equations: Three equations proposed by Iwasaki in drought conditions can be incorporated; the more
his 1937 paper described, in part, the filtration pro- years included, the better the estimate of storage
cess and were (1) a kinetic equation, describing the required. The time scale could also be for a year, to
rate of change of concentration with distance, (2) a reflect seasonal variation, or daily to reflect daily
materials balance equation that accounts for the loss variation.
of particles from the fluid suspension as the gain to 2. Treated water storage: Similarly, on the demand
an attached phase, and (3) a statement that postulates side, the maximum difference between the total
that the filter coefficient, l, changes over time as the demand volume, over a 24 h period (which is a
filter pores clog. varying line with some sharp increases), and the
Limiting trajectory: A trajectory that separates the trajector- total water produced by the plant at a constant rate
ies that intercept the collector from those that do not. (which is a straight line) is the volume of treated
To amplify, the limiting trajectory approach calcu- water storage required. On the treated water side,
lates the trajectory of the particle that includes all the time scale usually is 24 h and reflects the