Standard Methods for Examination of Water & Wastewater_4 potx

Figure 5.7a and 5.7b shows the schematic of a settling zone and the schematic of an effluent weir, tively.. the end of the zone, these solids will have already been deposited at the bott

Screening, Settling, and Flotation

Screening is a unit operation that separates materials into different sizes The unitinvolved is called a screen As far as water and wastewater treatment is concerned,only two “sizes” of objects are involved in screening: the water or wastewater andthe objects to be separated out Settling is a unit operation in which solids aredrawn toward a source of attraction In gravitational settling, solids are drawntoward gravity; in centrifugal settling, solids are drawn toward the sides of cyclones

as a result of the centrifugal field; and in electric-field settling, as in electrostaticprecipitators, solids are drawn to charge plates Flotation is a unit operation inwhich solids are made to float to the surface on account of their adhering to minutebubbles of gases (air) that rises to the surface On account of the solids adhering

to the rising bubbles, they are separated out from the water This chapter discussesthese three types of unit operations as applied to the physical treatment of waterand wastewater

5.1 SCREENING

Figure 5.1 shows a bar rack and a traveling screen Bar racks (also called barscreens) are composed of larger bars spaced at 25 to 80 mm apart The arrangementshown in the figure is normally used for shoreline intakes of water by a treatmentplant The rack is used to exclude large objects; the traveling screen following it is used

to remove smaller objects such as leaves, twigs, small fish, and other materials thatpass through the rack The arrangement then protects the pumping station that liftsthis water to the treatment plant Figure 5.2 shows a bar screen installed in a detritustank Detritus tanks are used to remove grits and organic materials in the treatment

of raw sewage Bar screens are either hand cleaned or mechanically cleaned Thebar rack of Figure 5.1 is mechanically cleaned, as shown by the cable system hoistingthe scraper; the one in Figure 5.2 is manually cleaned Note that this screen isremovable Table 5.1 shows some design parameters and criteria for mechanicallyand hand-cleaned screens

Figure 5.3 shows a microstrainer As shown, this type of microstrainer consists

of a straining material made of a very fine fabric or screen wound around a drum.The drum is about 75% submerged as it is rotated; speeds of rotation are normallyabout from 5 to 45 rpm The influent is introduced from the underside of the woundfabric and exits into the outside The materials thus strained is retained in the interior

of the drum These materials are then removed by water jets that directs the loosenedstrainings into a screening trough located inside the drum In some designs, the flow

is from outside to the inside

5

Microstrainers have been used to remove suspended solids from raw watercontaining high concentrations of algae In the treatment of wastewater using oxi-dation ponds, a large concentration of algae normally results Microstrainers can beused for this purpose in order to reduce the suspended solids content of the effluent

FIGURE 5.1 Bar rack and traveling screen (Courtesy of Envirex, Inc.)

FIGURE 5.2 Bar screen in a detritus tank.

Traveling screen

Bar rack

Rake can reach

to bottom of tank

Detritus tank

Outlet Inlet Heavy solids

pit

Section A-A Penstocks

that may cause violations of the discharge permits of the plant Microstrainers havealso been used to reduce the suspended solids content of wastewaters treated bybiological treatment Openings of microstrainers are very small They vary from 20

to 60 µm and the cloth is available in stainless steel or polyester construction

5.1.1 H EAD L OSSES IN S CREENS AND B AR R ACKS

Referring to b of Figure 5.2, apply the Bernoulli equation, reproduced below, betweenpoints 1 and 2

(5.1)

where P, V, and h are the pressure, velocity, and elevation head at indicated points;

g is the acceleration due to gravity V1 is called the approach velocity; the channel

in which this velocity is occurring is called the approach channel To avoid mentation in the approach channel, the velocity of flow at this point should bemaintained at the self-cleansing velocity Self-cleansing velocities are in the neigh-borhood of 0.76 m/s

sedi-TABLE 5.1 Design Parameters and Criteria for Bar Screens

Parameter Mechanically Cleaned Manually Cleaned

Bar size Width, mm 5–20 5–20 Thickness, mm 20–80 20–80 Bars clear spacing, mm 20–50 15–80 Slope from vertical, degrees 30–45 0–30 Approach velocity, m/s 0.3–0.6 0.6–1.0

FIGURE 5.3 A Microstrainer (Courtesy of Envirex, Inc.)

Influent

Screening

Screening trough Backwash spray

P1

γ - V1 2

2g

- h1

γ - V2 2

2g

- h2

=

Remember from fluid mechanics that the Bernoulli equation is an equation for

frictionless flow along a streamline The flow through the screen is similar to the

flow through an orifice, and it is standard in the derivation of the flow through an

orifice to assume that the flow is frictionless by applying the Bernoulli equation To

consider the friction that obviously is present, an orifice coefficient is simply prefix

to the derived equation

Both points 1 and 2 are at atmospheric, so the two pressure terms can be canceled

out Considering this information and rearranging the equation produces

(5.2)

From the equation of continuity, V1 may be solved in terms V2, cross-sectional area

of clear opening at point 2 (A2), and cross-sectional area at point 1 (A1) V1 is then

V1=A2V2/A1 This expression may be substituted for V1 in the previous equation,

whereupon, V2 can be solved The value of V2 thus solved, along with A2, permit the

discharge Q through the screen openings to be solved This is

(5.3)

Recognizing that the Bernoulli equation was the one applied, a coefficient of

discharge must now be prefixed into Equation (5.3) Calling this coefficient C d,

(5.4)

Solving for the head loss across the screen ∆h,

(5.5)

As shown in Equation (5.5), the value of the coefficient can be easily determined

experimentally from an existing screen In the absence of experimentally determined

data, however, a value of 0.84 may be assumed for C d As the screen is clogging, the

value of A2 will progressively decrease As gleaned from the equation, the head loss

∆h will theoretically rise to infinity At this point, the screen is, of course, no longer

functioning

The previous equations apply when an approach velocity exists In some

situa-tions, however, this velocity does not exist In these situasitua-tions, the previous equations

do not apply and another method must be developed This method is derived in the

next section on microstrainers

- A2 2g ∆h

A1

– -

5.1.2 H EAD L OSS IN M ICROSTRAINERS

Referring to Figure 5.3, the flow turns a right angle as it enters the openings of the

microstrainer cloth Thus, the velocity at point 1, V1, (refer to Figure 5.2) would

be approximately zero Therefore, for microstrainers: applying the Bernoulli

equa-tion, using the equation of continuity, and prefixing the coefficient of discharge as

was done for the bar screen, produce

(5.6)

As in the bar screen, the value of the coefficient can be easily determined

experimentally from an existing microstrainer In the absence of experimentally

determined data, a value of 0.60 may be assumed for C d Also, from the equation,

as the microstrainer clogs, the value of A2 will progressively decrease; thus the head

loss rises to infinity, whereupon, the strainer ceases to function Although the

pre-vious equation has been derived for microstrainers, it equally applies to ordinary

screens where the approach velocity is negligible

Example 5.1 A bar screen measuring 2 m by 5 m of surficial flow area is used

to protect the pump in a shoreline intake of a water treatment plant The plant is

drawing raw water from the river at a rate of 8 m3/s The bar width is 20 mm and

the bar spacing is 70 mm If the screen is 30% clogged, calculate the head loss

through the screen Assume C d= 0.60

Solution:

For screens used in shoreline intakes, the velocity of approach is practically

zero Thus,

From the previous figure, the number of spacings is equal to one more than the

number of bars Let x = number of bars,

-=

Of course, as soon as the solids reach the bottom, they begin sedimenting In thephysical treatment of water and wastewater, settling is normally carried out in settling

or sedimentation basins We will use these two terms interchangeably

Generally, two types of sedimentation basins are used: rectangular and circular.Rectangular settling basins or clarifiers, as they are also called, are basins that arerectangular in plans and cross sections In plan, the length may vary from two tofour times the width The length may also vary from ten to 20 times the depth Thedepth of the basin may vary from 2 to 6 m The influent is introduced at one endand allowed to flow through the length of the clarifier toward the other end Thesolids that settle at the bottom are continuously scraped by a sludge scraper and

20x+70 x( +1) = 5000

x = 54.77, say 55Area of clear opening = 70 55( +1) 2000( )

-2 9.81( ) 0.842

( ) 7.48 0.7[ ( )]2

- 30.49

379.54 - 0.08 m of water

removed The clarified effluent flows out of the unit through a suitably designedeffluent weir and launder

Circular settling basins are circular in plan Unlike the rectangular basin, circularbasins are easily upset by wind cross currents Because of its rectangular shape,more energy is required to cause circulation in a rectangular basin; in contrast, thecontents of the circular basin is conducive to circular streamlining This conditionmay cause short circuiting of the flow For this reason, circular basins are typicallydesigned for diameters not to exceed 30 m in diameter

Figure 5.4 shows a portion of a circular primary sedimentation basin used at theBack River Sewage Treatment Plant in Baltimore City, MD In this type of clarifier,the raw sewage is introduced at the center of the tank and the solids settled as thewastewater flows from the center to the rim of the clarifier The schematic elevationalsection in Figure 5.5 would represent the elevational section of this clarifier at the

FIGURE 5.4 Portion of a primary circular clarifier at the Back River Sewage Treatment Plant,

Baltimore City, MD.

FIGURE 5.5 Elevation section of a circular radial clarifier (Courtesy of Walker Process.)

Effluent weir

Effluent weir Drive

Influent well

Sludge draw-off

Effluent

Influent Sludge concentrator

Collector arm

Back River treatment plant As shown, the influent is introduced at the bottom of thetank It then rises through the center riser pipe into the influent well From the centerinfluent well, the flow spreads out radially toward the rim of the clarifier The clarifiedliquid is then collected into an effluent launder after passing through the effluent weir.The settled wastewater is then discharged as the effluent from the tank

As the flow spreads out into the rim, the solids are deposited or settled alongthe way At the bottom is shown a squeegee mounted on a collector arm This arm

is slowly rotated by a motor as indicated by the label “Drive.” As the arm rotates,the squeegee collects the deposited solids or sludge into a central sump in the tank.This sludge is then bled off by a sludge draw-off mechanism

Figure 5.6a shows a different mode of settling solids in a circular clarifier Theinfluent is introduced at the periphery of the tank As indicated by the arrows, theflow drops down to the bottom, then swings toward the center of the tank, and backinto the periphery, again, into the effluent launder The solids are deposited at thebottom, where a squeegee collects them into a sump for sludge draw-off

Figure 5.6b is an elevational section of a rectangular clarifier In plan, thisclarifier will be seen as rectangular As shown, the influent is introduced at the left-hand side of the tank and flows toward the right At strategic points, effluent trough(or launders) are installed that collect the settled water On the way, the solids arethen deposited at the bottom A sludge scraper is shown at the bottom This scrapermoves the deposited sludge toward the front end sump for sludge withdrawal Also,

FIGURE 5.6 Elevation sections of a circular clarifier (a) and a rectangular clarifier (b).

(Courtesy of Envirex, Inc.)

Sludge withdrawal

Sludge

notice the baffles installed beneath each of the launders These baffles would guidethe flow upward, simulating a realistic upward overflow direction.

Generally, four functional zones are in a settling basin: the inlet zone, the settling

zone, the sludge zone, and the outlet zone The inlet zone provides a transition aimed

at properly introducing the inflow into the tank For the rectangular basin, the transitionspreads the inflow uniformly across the influent vertical cross section For one design

of a circular clarifier, a baffle at the tank center turns the inflow radially toward therim of the clarifier On another design, the inlet zone exists at the periphery of the tank

The settling zone is where the suspended solids load of the inflow is removed

to be deposited into the sludge zone below The outlet zone is where the effluent

takes off into an effluent weir overflowing as a clarified liquid Figure 5.7a and 5.7b

shows the schematic of a settling zone and the schematic of an effluent weir, tively This effluent weir is constructed inboard Inboard weirs are constructed whenthe natural side lengths or rim lengths of the basin are not enough to satisfy theweir-length requirements

respec-5.2.1 F LOW -T HROUGH V ELOCITY AND O VERFLOW R ATE

vp

vo vh vh

to t

0

Effluent

the end of the zone, these solids will have already been deposited at the bottom ofthe settling column The behavior of the solids outside the column will be similar to that

inside Thus, a time t o in the settling column is the same time t o in the settling zone

A particle possesses both downward terminal velocity v o or v p, and a horizontal

velocity v h (also called flow-through velocity) Because of the downward movement,

the particles will ultimately be deposited at the bottom sludge zone to form the sludge

For the particle to remain deposited at the sludge zone, v h should be such as not to

scour it For light flocculent suspensions, v h should not be greater than 9.0 m/h; and

for heavier, discrete-particle suspensions, it should not be more than 36 m/h If A

is the vertical cross-sectional area, Q the flow, Z o the depth, W the width, L the length, and t o the detention time:

(5.7)

The detention time is the average time that particles of water have stayed inside the tank Detention time is also called retention time Because this time also corre- sponds to the time spent in removing the solids, it is also called removal time For discrete particles, the detention time t o normally ranges from 1 to 4 h, while forflocculent suspensions, it normally ranges from 4 to 6 h Calling the volume of

the tank and L the length, t o can be calculated in two ways: t o = Z o /v o and t o = /Q = (WZ o L) /Q = A s Z o /Q Also, for circular tanks with diameter D, t o = /Q = ( Z o)/Q =

A s Z o /Q, also Therefore,

(5.8)

where A s is the surface area of the tank and Q /A s is called the overflow rate, q o

According to this equation, for a particle of settling velocity v o to be removed, the

overflow rate of the tank q o must be set equal to this velocity

Note that there is nothing here which says that the “efficiency of removal isindependent of depth but depends only on the overflow rate.” The statement thatefficiency is independent of depth is often quoted in the environmental engineeringliterature; however, this statement is a fallacy For example, assume a flow of 8 m3/sand assert that the removal efficiency is independent of depth With this assertion,

we can then design a tank to remove the solids in this flow using any depth such as

10−50 meter Assume the basin is rectangular with a width of 106 m With this design,the flow-through velocity is 8/(10+6)(10−50) = 8.0(1044

) m/s Of course, this velocity

is much greater than the speed of light The basin would be performing better if adeeper basin had been used This example shows that the efficiency of removal isdefinitely not independent of depth The notion that Equation (5.8) conveys is simply

that the overflow velocity q o must be made equal to the settling velocity v o—nothing

more The overflow velocity multiplied by the surface area produces the hydraulic

loading rate or overflow rate.

v h

Q A

In the outlet zone, weirs are provided for the effluent to take off Even if v h hadbeen properly chosen but overflow weirs were not properly sized, flows could beturbulent at the weirs; this turbulence can entrain particles causing the design to fail.Overflow weirs should therefore be loaded with the proper amount of overflow(called weir rate) Weir overflow rates normally range from 6–8 m3/h per meter ofweir length for light flocs to 14 m3/h per meter of weir length for heavier discrete-particle suspensions When weirs constructed along the periphery of the tank arenot sufficient to meet the weir loading requirement, inboard weirs may be con-structed One such example was mentioned before and shown in Figure 5.7b Theformula to calculate weir length is as follows:

(5.9)

5.2.2 D ISCRETE S ETTLING

Generally, four types of settling occur: types 1 to 4 Type 1 settling refers to theremoval of discrete particles, type 2 settling refers to the removal of flocculentparticles, type 3 settling refers to the removal of particles that settle in a contiguouszone, and type 4 settling is a type 3 settling where compression or compaction ofthe particle mass is occurring at the same time Type 1 settling is also called discretesettling and is the subject in this section When particles in suspension are dilute,they tend to act independently; thus, their behaviors are therefore said to be discretewith respect to each other

As a particle settles in a fluid, its body force f g , the buoyant force f b, and the

drag force f d, act on it Applying Newton’s second law in the direction of settling,

(5.10)

where m is the mass of the particle and a its acceleration Calling ρp the mass density

of the particle, ρw the mass density of water, the volume of the particle, and g the acceleration due to gravity, f g= ρp g and f b= ρw g The drag stress is directlyproportional to the dynamic pressure, ρw v2/2, where v is the terminal settling velocity

of the particle Thus, the drag force f d = C D A pρw v2/2, where C D is the coefficient of

proportionality called drag coefficient, and A p is the projected area of the particlenormal to the direction of motion Because the particle will ultimately settle at its

terminal settling velocity, the acceleration a is equal to zero Substituting all these into Equation (5.10) and solving for the terminal settling velocity v, produces

(5.11)

assuming the particle is spherical A p= π d2

/4 for spherical particles, where d is the

diameter

weir Rate -

The value of the coefficient of drag C D varies with the flow regimes of laminar,transitional, and turbulent flows The respective expressions are shown next

where Re is the Reynolds number = vρ w d/µ, and µ is the dynamic viscosity of water

Values of Re less than 1 indicate laminar flow, while values greater than 104 indicateturbulent flow Intermediate values indicate transitional flow

Substituting the C D for laminar flow (C D = 24/Re) in Equation (5.11), produces

the Stokes equation:

(5.15)

To use the previous equations for non-spherical particles, the diameter d, must

be the diameter of the equivalent spherical particle The volume of the equivalentspherical particle = π( )3

, must be equal to the volume of the non-sphericalparticle = β , where β is a volume shape factor Expressing the equality and

solving for the equivalent spherical diameter d produces

=

V s 4 3

Solve by successive iterations:

Therefore, v = 0.132 m/s Ans

A raw water that comes from a river is usually turbid In some water treatmentplants, a presedimentation basin is constructed to remove some of the turbidities.These turbidity particles are composed not of a single but of a multitude of particlessettling in a column of water Since the formulas derived above apply only to asingle particle, a new technique must be developed

Consider the presedimentation basin as a prototype In order to design this

prototype properly, its performance is often simulated by a model In environmentalengineering, the model used is a settling column Figure 5.8 shows a schematic ofcolumns and the result of an analysis of a settling test

At time equals zero, let a particle of diameter d o be at the water surface of the

column in a After time t o, let the particle be at the sampling port Any particle that

arrives at the sampling port at t o will be considered removed In the prototype, this

removal corresponds to the particle being deposited at the bottom of the tank t o is

the detention time The corresponding settling velocity of the particle is v o = Z o /t o,

where Z o is the depth This Z o corresponds to the depth of the settling zone of the

prototype tank Particles with velocities equal to v o are removed, so particles of

velocities equal or greater than v o will all be removed If x o is the fraction of all

2.0 3.0 0.16 0.48 0.70 0.85 1.0 0.25 0.35

0.8 0.7 0.6 0.5 0.4 0.4 0.3 0.2 0.1

Sampling port

particles having velocities less than v o, 1 − x o is the fraction of all particles having

velocities equal to or greater than v o Therefore, the fraction of particles that areremoved with certainty is 1 − x o

During the interval of time t o , some of the particles comprising x o will be closer

to the sampling port Thus, some of them will be removed Let dx be a differential

in x o.Assume that the average velocity of the particles in this differential is v p Aparticle is being removed because it travels toward the bottom and, the faster ittravels, the more effectively it will be removed Thus, removal is directly proportional

to settling velocity Removal is proportional to velocity, so the removal in dx is therefore (v p /v o )dx and the total removal R comprising all of the particles with velocities equal to or greater than v o and all particles with velocities less than v o is then

(5.17)

Note that this equation does not state that the velocity v p must be terminal It only

states that the fractional removal R is directly proportional to the settling velocity

v p.For discrete settling, this velocity is the terminal settling velocity For flocculentsettling (to be discussed later), this velocity would be the average settling velocity

of all particles at any particular instant of time

To evaluate the integral of Equation (5.17) by numerical integration, set

(5.18)

This equation requires the plot of v p versus x If the original concentration in the column is [c o ] and, after a time of settling t, the remaining concentration measured

at the sampling port is [c], the fraction of particles remaining in the water column

adjacent to the port is

(5.19)

Corresponding to this fraction remaining, the average distance traversed by the particles

is Z p /2, where Z p is the depth to the sample port at time interval t from the initial location of the particles The volume corresponding to Z p contains all the particles

that settle down toward the sampling port during the time interval t Therefore, v p is

(5.20)

The values x may now be plotted against the values v p From the plot, the numerical

integration may be carried out graphically as shown in c of Figure 5.8

Example 5.5 A certain municipality in Thailand plans to use the water from theChao Praya River as a raw water for a contemplated water treatment plant The river

is very turbid, so presedimentation is necessary The result of a column test is as follows:

=

v p

Z p 2t

-=

What is the percentage removal of particles if the hydraulic loading rate is 25

m3/m2 d? The column is 4-m deep

0.015–0.02 -

=

0.0174 -[0.0162 0.02( ) 0.0125 0.16+ ( ) 0.0092 0.11+ ( )+

=0.0066 0.17( ) 0.0024 0.09( )

5.2.3 O UTLET C ONTROL OF G RIT C HANNELS

Grit channels (or chambers) are examples of units that use the concept of discretesettling in removing particles Grit particles are hard fragments of rock, sand, stone,bone chips, seeds, coffee and tea grounds, and similar particles In order for theseparticles to be successfully removed, the flow-through velocity through the unitsmust be carefully controlled Experience has shown that this velocity should bemaintained at around 0.3 m/s This control is normally carried out using a propor-tional weir or a Parshall flume A grit channel is shown in Figure 5.9 and a propor-tional flow weir is shown in Figure 5.10 A proportional flow weir is just a platewith a hole shaped as shown in the figure cut through it This plate would be installed

at the effluent end of the grit channel in Figure 5.9 The Parshall flume was discussed

in Chapter 3

FIGURE 5.9 A grit channel (Courtesy of Envirex, Inc.)

FIGURE 5.10 Velocity control of grit channels: (a) proportional-flow weir; (b) cross section

of a parabolic-sectioned grit channel.

Practical section

As shown in the figure, the flow area of a proportional-flow weir is an orifice.

From fluid mechanics, the flow Q through an orifice is given by

(5.21)

where K o is the orifice constant,  is the width of flow over the weir, and h is the

head over the weir crest There are several ways that the orifice can be cut through

the plate; one way is to do it such that the flow Q will be linearly proportional to

h To fulfill this scheme, the equation is revised by letting h3/2 = h1/2

reason, for values of h less than 2.5 cm, the side curves are terminated vertically to

the weir crest The area of flow lost by terminating at this point is of no practical

significance; however, if terminated at an h of greater than 2.5 cm, the area lost

should be compensated for by lowering the actual crest below the design crest This

is indicated in the figure

The general cross-sectional area of the tank may be represented by kwH, where k

is a constant, w is the width at a particular level corresponding to H, the depth in the tank Now, the flow through the tank is Q = v h (kwH), where v h is the flow-throughvelocity to be made constant This flow is also equal to the flow that passes throughthe control device at the end of the tank The height of the orifice crest from the bottom

of the channel is small, so h may be considered equal to the depth in the tank, H.

From the equation of continuity,

For grit chambers controlled by other critical-flow devices, such as a Parshallflume (the proportional flow weir is also a critical-flow device), the flow throughthe device is also given by Thus, the following equation may also

be obtained:

(5.26)

Solving for H,

(5.27) which is the equation of a parabola Thus, for grit chambers controlled by Parshallflumes, the cross-section of flow should be shaped like a parabola For ease inconstruction, the parabola is not strictly followed but approximated This is indicated

in the upper right-hand drawing of Figure 5.10 The area of the parabola is

(5.28)

Coordinates of the proportional-flow weir orifice The opening of the weir

orifice needs to be proportioned properly To accommodate all ranges of flow duringoperation, the proportioning should be done for peak flows For a given inflow peakflow to the treatment plant, not all channels may be operated at the same time Thus,for operating conditions at peak flow, the peak flow that flows through a given gritchannel will vary depending upon the number of channels put in operation Theproportioning of the orifice opening should be done on the maximum of the peakflows that flow through the channel

Let l mpk be the l of the orifice opening at the maximum peak flow through the channel The corresponding h would be h mpk From Equation (5.23),

and,

(5.29)

Let l mpk = w and h mpk = Z ompk , where Z ompk is the maximum depth in the channel

corresponding to the maximum peak flow through the channel, Q mpk Then,

(5.30)This equation represents the coordinate of the proportional-flow weir orifice

=

1 3

2

Z ompk

 -

Coordinates of the parabolic cross section Let A mpk be the area in the

para-bolic section corresponding to Q mpk From Equation (5.28),

(5.31)

where w mpk is the top width of the parabolic section corresponding Z ompk From

Equation (5.27) and the previous equation, the following equation for c can be

obtained:

(5.32)From Equation (5.27), again,

(5.33)Substituting in Equation (5.28),

(5.34)

(5.35)Thus,

(5.36)

Example 5.6 Design the cross section of a grit removal unit consisting of fouridentical channels to remove grit for a peak flow of 80,000 m3/d, an average flow

of 50,000 m3/d and a minimum flow of 20,000 m3

/d There should be a minimum

of three channels operating at any time Assume a flow-through velocity of 0.3 m/sand that the channels are to be controlled by Parshall flumes

Solution: Four baseline cross-sectional areas must be considered and computed

as follows:

A mpk

23

-w mpk Z ompk

=1

1/3

w mpk - A2/3

Apeak, three channels 80,000

3 0.3( ) 24( ) 60( ) 60( ) - 1.03 m2 A mpk

Apeak, four channels 80,000

4 0.3( ) 24( ) 60( ) 60( ) - 0.77 m2

4 0.3( ) 24( ) 60( ) 60( ) - 0.48 m2

4 0.3( ) 24( ) 60( ) 60( ) - 0.19 m2

The channels are to be controlled by Parshall flumes, so the cross sections are parabolic Thus,

and determine coordinates at corresponding areas Let w mpk= 1.5 m

Note: In practice, these coordinates should be checked against the flow conditions

of the chosen dimensions of the Parshall flume If the flumes are shown to

be submerged forcing them not to be at critical flows, other coordinates

of the parabolic cross sections must be tried until the flumes show criticalflow conditions or unsubmerged

Example 5.7 Repeat previous example problem for grit channels controlled

by proportional flow weirs

Solution: For grit channels controlled by proportional weirs, the cross-sectionshould be rectangular Thus,

Therefore, the depths, Z o, and other parameters for various flow conditions are asfollows (for a constant flow-through velocity of 0.30 m/s):

1/3

w mpk - A2/3

=

For Apeak four chambers, = 0.77 m2:

Z o

32 -A mpk

1/3

w mpk

- A2/3 3

2 -1.03

1/3

1.5 - 0.77( 2/3) 0.85 m

For Aave = 0.48 m2:

Z o

32 -A mpk

1/3

w mpk

- A2/3 3

2 -1.03

1/3

1.5 - 0.48( 2/3) 0.62 m

For Amin = 0.19 m2:

Z o

32 -A mpk

1/3

w mpk

- A2/3 3

2 -1.03

1/3

1.5 - 0.19( 2/3) 0.33 m

5.2.4 F LOCCULENT S ETTLING

Particles settling in a water column may have affinity toward each other and coalesce

to form flocs or aggregates These larger flocs will now have more weight and settlefaster overtaking the smaller ones, thereby, coalescing and growing still further intomuch larger aggregates The small particle that starts at the surface will end up as

a large particle when it hits the bottom The velocity of the floc will therefore not

be terminal, but changes as the size changes Because the particles form into flocs,

this type of settling is called flocculent settling or type 2 settling.

Because the velocity is terminal in the case of type 1 settling, only one samplingport was provided in performing the settling test In an attempt to capture the changingvelocity in type 2 settling, oftentimes multiple sampling ports are provided Theports closer to the top of the column will capture the slowly moving particles, especially

at the end of the settling test

For convenience, reproduce the next equation

of flocculent settling, would the velocity to be substituted also be terminal?

In the derivation of Equation (5.37), however, nothing required that the velocity

be terminal If the settling is discrete, then it just happens that the velocity obtained

in the settling test approximates a terminal settling velocity, and this is the velocitythat is substituted into the equation If the settling is flocculent, however, the same

does not require that the velocity be terminal but simply that removal is proportional

to velocity, this velocity of flocculent settling can be substituted in Equation (5.37)

to calculate the fractional removal, and it follows that the same formula and, thus,method can be used both in discrete settling as well as in flocculent settling

Each of the ports in the flocculent settling test will have a corresponding Z p

During the test each of these Z p ’s will accordingly have corresponding times t and

thus, will produce corresponding average velocities These velocities and times formarrays that correspond to each other, including a corresponding array of concentration

In other words, in the flocculent settling test more test data are obtained The method

=

v p = Z p /2t

of calculating the efficiency of removal, however, is the same as in discrete settlingand this is Equation (5.37).

Example 5.8 Assume Anne Arundel County wants to expand its softeningplant A sample from their existing softening tank is prepared and a settling columntest is performed The initial solids concentration in the column is 250 mg/L Theresults are as follows:

Calculate the removal efficiency for an overflow rate of 0.16 m3/m2⋅ min Assumethe column depth is 4 m

=

It is not necessary to interpolate the x corresponding to v p = 0.16 m/min From the

sedimen-of figures, although stated in terms sedimen-of the average, really means that it takes anaverage of 1.5 to 2.5 h for a particle of sewage to become septic whether or not theflow is average

Both water and wastewater treatment also need to maintain the flow-throughvelocity so as not to scour the sludge that has already deposited at the bottom ofthe settling tank They also need properly designed overflow weirs, an example ofwhich is shown in Figure 5.7b The particles in both these units are flocculent, sothe flow-through velocity should be maintained at no greater than 9.0 m/h and theoverflow weir loading rate at no greater than 6–8 m3/h per meter of weir length, asmentioned before Some design criteria for primary sedimentation tanks are shown

in Table 5.2 Except for the detention time, the criteria values may also be used forsettling tanks in water treatment