Pumping Station Desing - Second Edition by Robert L. Sanks, George Tchobahoglous, Garr M. Jones

for

the

peak concentration

to

pass

a

downstream point

gives

the

average velocity. Salt

is

frequently

used

for

the

tracer

and its

concentration

is

measured with

a

portable conductivity meter.

If the flow is

steady

and

the

channel

is

prismatic,

an

approximate

flowrate can

be

determined

by

measuring

the

cross-sectional

area.

The

accuracy

is

questionable. Errors

may

well exceed

15%.

The

methods

require

precision.

The

gen-

eral requirements

for the use of

tracers are:

• A

precise method

for

introducing

the

tracer.

•

Enough length and/or turbulence

so

that mixing

is

complete

—

a

critical requirement.

• A

tracer substance

that

is

innocuous (nonhazardous

and

nontoxic), stable,

and not

significantly

adsorbed

on

walls

or

particles.

• A

tracer substance that occurs naturally only

in

very

low

or

insignificant

concentrations (low back-

ground).

• A

means

for

obtaining small samples downstream.

• A

method

of

chemical analysis that

is

sensitive,

accurate, inexpensive,

and

free

from

significant

interferences.

•

Preliminary testing

to (1)

establish accuracy;

(2)

obtain

calibration curves

for the

tracer diluted

with

the

water

or

sewage;

(3)

quantify

possible interfer-

ences, decay,

or

sorption

on

pipe walls

or

particles

so

that corrections

can be

made;

and (4)

determine

the

suitability

of the

means selected

to

preserve

samples

for

shipment

and

analysis.

In

the

slug-addition method,

a

known mass

of

tracer

is

introduced

at

some upstream point

in a

man-

ner to

promote good mixing.

At a

point well down-

stream

after

thorough mixing,

a

series

of

grab samples

is

obtained

and

analyzed. Plotting

the

data yields

a

curve

like that labeled "abd"

in

Figure 3-9.

If the flow-

rate

is

constant over

the

short time needed

for all the

tracer

to

pass

the

downstream point, then tracer intro-

duced equals tracer past

the

downstream point.

M

= vC =

Q\\c-c

0

)dt

(3-26)

^t

1

where

M is the

mass

of

tracer,

v is the

small volume

of

tracer

at

high concentration,

C, Q is the

uniform

flow-

rate,

c is the

measured concentration

of

tracer down-

stream,

and

C

0

is

"blank"

or the

background reading

of

water without tracer. Under ideal conditions,

the

error

in

determining

Q can be

less than

2%. In

Figure 3-9,

blank,

C

0

,

is

shown

to be

large

for

clarity. Actually,

the

peak concentration should

be at

least

100

times

greater than blank.

Accurate results require

a

sufficient

number

of

samples

to

identity clearly

the

time

of first

appearance

and

the

time

of

complete passage

and to

define

the

shape

of the

curve.

It is

prudent

to

take many samples

before

the

expectation

of first

appearance

and

many

more samples

after

expected complete passage.

The

tracer concentrations should

be

determined with

the

same care

as

described below

for the

constant-rate

injection

method.

In the

more versatile continuous constant-rate

injection

method,

a

small stream

of

concentrated

tracer

is

added

at the

upstream point.

If

possible,

the

concentration

of

tracer past

the

downstream point

should

be

monitored until

uniform

instrumental read-

ings,

as

indicated

by

point

"e"

in

Figure 3-9,

are

obtained.

If

monitoring

is

impractical, estimate

the

waiting

period

for the

axial dispersion

to

stabilize

and

for

a

uniform

concentration

of

tracer

to

invade

all

water

in

pockets (such

as

valve bonnets). Then take

a

series

of

grab samples

for

precise analysis.

The

remainder

of

this discussion applies

to

continuous

constant-rate injection, although much

of it

would

apply

to

slug addition

as

well.

Figure 3-9.

Downstream

concentration

distribution

of

tracer resulting

from:

(a)

slug

addition

of

tracer

(curve abd)

and (b)

continuous

constant-rate

injection

of

tracer (curve

ae) at an

upstream

point.

If

the

objective

is to

calibrate

a flowmeter,

obtain

simultaneous readings

of the flowmeter in

engineering

units

and in raw

sensor analog output.

The

latter

can

be

measured

by

means

of a

digital meter with much

greater accuracy than

a

visual reading

of the flow

indi-

cator,

and the

multiplier

and

offset

coefficients

to

con-

vert sensor signal

to flow can be

calculated directly.

Flowmeter signals typically

fluctuate as

much

as 10%

over short periods

of

time

due to

turbulence

at the

sen-

sor, and, therefore, many data points

are

needed

to

establish

a

norm.

If

practical, obtain pump speed

and

pump motor current draw

to

compare pump perfor-

mance with predicted performance

and to

check

the

reasonableness

of the

test results.

If

the

objective

is to

calibrate

a flowmeter in an

open channel,

it is

useful

to

obtain simultaneous

depth measurements manually

for

comparison with

the

flowmeter

measurements

and to

establish

an

inde-

pendent

flow

rating curve.

If a flow

sensing element

is

replaced,

the

manual rating curve allows

a

quick

check

of the

meter rating data. Record

the

measure-

ment

location on-site

and

document

it in the

report

so

the

same point

can be

identified

and

used

in the

future.

The

accuracy

of the

method depends directly upon

(1) the

accuracy

and

uniformity

of

tracer injection

and

(2)

complete mixing

at the

second sampling point.

Tracer

can be

metered with precision either

from

a

positive displacement

fluid

metering pump

or

from

a

Marriot

jar

feeding

an

orifice,

as

shown

in

Figure

3-10.

The

Marriot

jar is

useful

only

for

open channels,

whereas

the

pump

can

inject tracer

at

high pressure.

To

ensure accuracy, however,

the

pressure must

not

change during injection.

It is

possible

to

inject tracer

into

the

low-pressure side

of a

small pump that

"chases"

the dye to the

point

of

application with

a

small stream

of

water. Constant speed metering

pumps

can be

obtained

from

Fluid Metering Inc. [37]

for

12 v

battery operation, whereas variable speed

pumps

can be

obtained

for

operation only

on

1

10

v ac

current.

The flowrates can be

adjusted

by

changing

the

piston angle

to

alter

the

piston stroke length. Even

more adjustment

in flowrate can be

made

by

changing

the

pumping heads

(on

either kind

of

pump).

The

res-

ervoir

of

tracer should

be

calibrated either volumetri-

cally

or

gravimetrically

so

that

the

accuracy

of

dispensing

can be

measured with

a

stopwatch.

By

the

time

the

tracer

reaches

the

sampling loca-

tion, mixing must

be

complete

so

that

the

concentra-

tion

of

tracer

is

uniform.

One

hundred pipe diameters

downstream

of the

injection point along

a

straight sec-

tion

of

pipe

is

considered

sufficient,

but

sometimes

that distance

can be

reduced substantially.

Dye can be

injected

at the

inlet side

of a

centrifugal

pump

and

sampled

on the

discharge side.

Or it can be

injected

into

a

pipe through

a

ball

valve

or a

corporation cock

(wherein leakage between probe

and

valve

is

pre-

vented

by

means

of

O-rings)

and

sampled downstream

by

the

same means.

It

helps

to

have several ejection

ports

in the

injection (probe) tubing. Always test

for

complete mixing

by

withdrawing samples

from

vari-

ous

points across

the

pipe

and

also

by

comparing con-

secutive samples. Extreme care must

be

taken

to

ensure that none

of the

tracer escapes

by

recirculation

or

by

leaking through check valves.

(Close

all

isola-

tion valves

for

pumps that

are not

running during

the

test.)

If the wet

well

is

contaminated with tracer,

it

will

take

a

long time

to

remove

all of it, and it

will

compromise

the

data.

Of

the

recommended tracers shown

in

Table 3-2,

Rhodamine

WT is the

best choice

for

municipal water

and

wastewater,

because

(1)

flow-through fluorometers can be

Figure 3-10. Constant head

device

for

metering

tracer.

used

in the field to

determine when stability

has

occurred

and

when

the

more accurate grab sampling

procedure

can

start;

(2) the

tracer

is

innocuous, inex-

pensive,

and

provides linear instrumental response

in

concentrations

from

the

limit

of

detection (about

0.01

ppb

depending upon

the fluorometer

used)

to 100

ppb;

(3)

sorption

on

walls

or

particles

is

usually very slight;

(4)

background fluorescence

is low

(usually less than

0.2

ppb);

(5)

determinations

are

quick

and

relatively

convenient;

and (6)

determinations

can be

made

in the

field. The

disadvantages

are (1) fluorometers are

expensive

and

rarely

found

in

chemical laboratories

(although

they

can be

rented);

(2)

rhodamine

is

very

temperature-sensitive

and is

attacked

by

chlorine;

and

(3)

samples should

not

contain particles

or air

bub-

bles,

so if the

water

is

dirty, samples must either

be

centrifuged

or

tediously

filtered

through glass

or

MiI-

lipore

filters.

If

no

tracer

is

lost (through leakage, reaction,

absorption,

etc.),

a

material balance yields:

Qc

0

+

qC =

(Q

+ q)c

(3-27)

tracer

in

tracer

out

Table

3-2.

Recommended

Tracers

and

Analyses

Concentration

(mg/L)

Lower

detection Advisable

Substance

Use

Analytical method

limit

range

Comments

Fluoride Excellent

for

Specific

ion

0.0500

0.5-2.5

If

utility adds

fluoride to

water,

potable water.

electrode.

3

no

added spike needed, hence

it may be the

best

field

tracer.

Calibrate

fluoride

feeder

or

substitute solution feed

and

metering

jump

or

Mariott

jar

(Figure

3-9).

Glucose Excellent

for

Colorimetry

by 1

1-10

Occurs naturally

in

some

fruits

potable water.

Park-Johnson

and is a

food ingested

by

method

[38].

everyone. Sterilize

any

tracer

solution

to be

injected into

potable water. Little affected

by

chlorine.

Protect

samples

from

bacterial attack.

Rhodamine

Excellent

for

Fluorometry,

b

0.00001

0.0002-0.4

Fluorometers uncommon

in

WT

[39]

sewage. easiest

of all

commercial laboratories.

Approved

for

tracer methods There

is

little background

drinking water

for use in fluorescence.

Adsorption

on

by

the EPA

laboratory

or

pipe walls

and

particles

[4O].

field.

insignificant.

Lithium Good

for

Electrothermal

0.001 0.005-

Very

low

natural background,

chloride manufacturing atomic

0.025

used medicinally (but

in far

plants

and

adsorption larger

quantities),

water

or

spectroscopy,

sewage. laboratory only.

Sodium Sewage

Conductivity,

0

good

1

100-1000

High

background

(1000

umhos)

chloride

for field

use.

requires

massive

spikes

(~100

mg/L

NaCl)

and

large

flow (q

=

1/2%

Q)

of

brine.

Flame atomic

0.002

0.03-1

Must dilute samples.

adsorption.

Chlorine Water

DPD

colorimetry

—

0.2-4

Usually unacceptable

due to

[41],

(can

be

rapid reaction

and

decay,

used

in the field).

a

SPADNS

colorimetric

method

can be

used,

but it is

less

convenient, more expensive,

and

subject

to

more interferences.

b

Temperature

sensitive:

variation

of

0.4

0

C

in

samples gives

1 %

error;

use a

water

bath

or

correct

mathematically.

c

Correct

for

temperature:

use a

temperature-conductivity

calibration

chart

in the field.

where

Q is flowrate in the

pipe before

the

stream

of

tracer

is

added,

C

0

is

blank

or the

apparent background

concentration

of

tracerlike substance,

q is the flowrate

of

tracer,

C is the

concentration

of the

tracer

feed

solu-

tion,

and c is the final

concentration

of the

tracer

downstream.

If Q is

greater than

10Og

(as it

should

be),

Q + q

approximates

Q and

Equation 3-27

can be

modified

to

G

=

Co

(3

-

28)

The

highest accuracy with Rhodamine

WT

cannot

be

achieved, however, without accounting

for the

effects

of the flow

stream

on the dye

(such

as

degrada-

tion

or

sorption)

and on the

actual

fluorescent

mea-

surement itself

(by

masking

the

background

fluorescence).

Before

and

after

every

flowrate

test,

background

samples should

be

collected

upstream

of

the

injection point

and

composited

in

sufficient

vol-

ume

(5 L) to

produce

a

spiked background standard

and

a

blank sample.

The

spike should

be

added

in the

field

soon

after

collection

at a

concentration reason-

ably

close

to

that expected

in the

downstream sam-

ples.

Use

only

Class

A

volumetric glassware

for

dilution

and

pipetting.

Wastewater

characteristics typically change under

varying

flow

conditions.

Solids

increase

significantly

in

raw

domestic wastewater

as the flow

increases

from

early morning

to

midmorning,

and

they

can

signifi-

cantly

affect

the

measured

dye

concentration. Under

certain conditions, background sampling

is the

only

way

to

detect

dye

recirculation through,

for

example,

leaking valves into

the wet

well. Furthermore, there

may

be

some unknown material that degrades

the dye

or

absorbs

it

over time

in the flow

stream.

These background samples should

be

analyzed

in the

same

manner

as the

downstream samples

and

used

to

adjust

the

measured sample

dye

concentrations

as

shown

by

the

following

equation developed

by

McDonald

[42]:

C

a

=

(C

m

-»)[

(Cs

5

_J

(3-29)

where

C

a

is the

adjusted

concentration

of the

sample,

C

m

is the

measured concentration

of the

sample,

b is

blank

(or

background concentration),

C

8

is the

mea-

sured

concentration

of the

spiked background,

and S is

the

true concentration

of the

spiked background based

on

the

volumetric dilution calculations.

The

true

flow-

rate

is

calculated

from

Q

=

q(£)

(3-30)

V^

a'

where

q is the flowrate of the dye

injected

at

concen-

tration

C.

As

an

absolute minimum, samples should

be

col-

lected

in

groups

of

three

for

each

flowrate

tested.

It is

often

difficult

to

predict

how

long

it

will take

to

reach

steady-state conditions,

so it is

prudent

to

obtain extra

grab samples

to

demonstrate that steady-state condi-

tions were actually achieved.

The

concentration

variability between samples

in a

group should

be

less

than

±2%

with complete mixing

and

steady-state

conditions.

A flow-through fluorometer

cell

is

useful

for

con-

tinuously

monitoring downstream

dye

concentrations

for

determining completeness

of

mixing, equilibrium,

and

optimal

dye

concentration.

But if

precision

is

needed (for example,

to

calibrate

flowmeters), use

these data only

for

guidance.

Use

only grab samples,

centrifuged

and

brought

to

uniform

temperature,

for

precise

results.

Although

less

than

20 ml of

sample

is

required

for

measurement,

the

sample volume must

be

sufficient

to

allow

for

centrifuging

or filtering the

sample

and for

rinsing

containers. Therefore,

250 to 500 ml of

sample

should

be

collected

in

groups

of

three

and

kept

in

borosilicate glass bottles. Decanting

after

settling

by

gravity

instead

of

centrifuging

is

sometimes adequate,

although

it is

time consuming. Borosilicate cuvettes

(test

tubes) should

be

acid-washed before each

use

and

either dried

or rinsed

with sample prior

to

deter-

minations. Mark cuvettes

so

each

can

always

be

inserted into

the fluorometer

with

the

same orienta-

tion,

and

test each

for

blank with distilled water.

Use

only those cuvettes with

the

same blank reading.

Fluorometers

are now

made with automatic tem-

perature compensation

for flow-through

cells,

and

the

flow-through

cell

can be

used with large

(1-L)

grab samples

by

pumping

the

samples through

it.

But

unless enough experience

is

gained

to

trust

a

particular instrument

or

procedure,

it is

wiser

to put

grab samples into small cuvettes

and

immerse them

in

a

circulating water bath long enough

(at

least

20

min)

for the

samples

to

reach

a

predetermined

stable temperature.

After

insertion into

the fluorom-

eter, obtain

the

instrument reading

as

soon

as it

sta-

bilizes,

because

the

temperature

of the

sample rises

in

the

instrument

due to the

heat

from

the

lamp,

and

readings change 2.6%

per

degree

centigrade.

A

liq-

uid-cooled

cuvette holder

(if one is

available

or can

be

custom made)

is

very desirable.

Run all the

sam-

ples without pause

to

obtain

the

best temperature

control. Good advice

on the

details

of fluorometric

measurements

is

given

by

Turner Designs [43,

44].

This

company also rents

fluorometers and

metering

pumps.

Lithium

chloride

is

also

a

good tracer. Lithium

is

rare

in

nature,

so the

background

is

low.

It is not

degraded

by

sunlight

or

chemicals,

and

sorption

on

walls

and

particles

is

less

of a

problem than

it is

with

rhodamine.

It can be

measured

by

means

of

electro-

thermal atomic absorption spectroscopy

or by

induc-

tively

coupled plasma (ICP) emission spectroscopy.

These

instruments

are

common

in

chemistry labora-

tories,

but

(unlike

fluorometers,

which

are

easily

operated) they require considerable skill

for

opera-

tion,

and

they

are

more expensive than fluorometers.

The

samples can, however,

be

measured

by

trained

personnel

in

commercial

or

university

laboratories.

Usually, samples

are

acidified

and

digested,

but it

seems likely that

for

constant injection where

the

concentration

is

near optimum,

the

samples

can be

measured much more economically without

the

usual

preparation.

It

would

be

wise

to

make prelimi-

nary

tests

to

determine whether accuracy

is

thus

compromised.

The

disadvantages include

the

neces-

sity

of

taking samples

to a

laboratory

for

analysis,

high

cost

per

sample,

and

uncertainty

or

delay

in the

field

for

determining either contamination

or

stability.

Calculation

of

Pipe Friction

Coefficient

With

pipe diameter, headloss,

and flow as

known

quantities,

the

Hazen-Williams

roughness

coeffi-

cient,

C, can be

calculated

by

Equation

3-9a.

Rear-

ranging

it

into

a

more convenient

form

gives

C

=

\51QD~

263

hf-

54

(3-3Ia)

where

Q is in

cubic meters

per

second,

D is the

pipe

ID in

meters,

and

h

f

is

meters

per 100

meters.

In

U.S.

customary

units Equation

3-9b

becomes

C

=

\49QD~

2

'

63

hf-

54

(3-3Ib)

where

Q is in

gallons

per

minute,

D is in

inches,

and

h

f

is

feet

per

1000

feet.

It

is

desirable

to

make

two or,

better, three tests, pref-

erably

at

different

flowrates. The C

values should

be

rea-

sonably

close.

If C is

less than about

130,

investigate

for

excessive

mineral deposits

or

obstructions. Note

that

buried

pipe

can be

both cleaned

and

relined

in

place with

cement

mortar

or

plastic

at a

total

of

20-40%

of the

cost

for

new

pipe

in a

"turnkey" operation (which includes

all

facets

of the

job

—

even

a

temporary bypass). Cost data

and

practical

field

methods

for

cement-mortar lining

have

been discussed

by

Walski

[45].

3-10.

Flow

of

Sludges

The

preceding

equations

for

friction

headloss

in

pipes

(Equations

3-8 and

3-10,

for

example)

are

limited

to

Newtonian

fluids

—

those

in

which shear stress

is

pro-

portional

to

shear rate

and

thus

to

velocity (see

Figure

3-

11).

But in

thick sludge,

the

shear stress

increases very rapidly

at low

shear rates

and

increases

only moderately with

an

increase

of

shear rate

at

higher velocity. Consequently,

at low

velocity

the

headloss

for

sludge

is

many times

the

headloss

for

water, whereas

at

high velocity

the

headloss

for

sludge

may

be

only marginally higher than that

for

water.

In

general,

the

headloss

for

sludges with

less

than

2%

solids

is

nearly

the

same

as for

water. Most sec-

ondary sludge

and

water treatment plant sludge would

fall

into this category.

The

headloss

for

thicker sludge

(usually

primary sludge)

can be

approximated

as

explained

in

Section

19-1

by

calculating

the

headloss

of

water

and

then multiplying

by a

factor obtained

from

Figure 19-4

or

19-5.

But

sludges

are

unique

and

the

headloss

for a

"worst

case"

could

be

double

the

factors

shown

in

Figure 19-3.

For

long pipelines

where pressure loss

is

important,

it is

wise

to

test

the

friction

properties

of the

sludge. Sludge

flow and

pumping

are

considered

in

greater detail

in

Chapter

19

and

by the EPA

[46].

3-11.

Unsteady

Flow

In

all of the

preceding sections,

it is

assumed that

the

flowrate

is

steady

and

continuous

and

that Equation

3-1

(the continuity equation)

is

valid,

so the flowrate

Figure

3-11.

Shear rate

relationships

for

representative

fluids.

at

one

point equals that

at

another.

In

reality, this

assumption

is

often

only

an

approximation.

Pipe

material

is not

rigid

and

water

is not

incompressible.

When valves

are

closed

or

opened quickly

or

when

pumps

are

started

or

stopped, pressure waves

are

gen-

erated

and

travel back

and

forth

in the

pipe,

which

expands

and

contracts

(as

does

the

water)

and

causes

the

flow to

become unsteady.

These violent pressure changes

can

have serious

consequences

on

pumps, especially

if the

pressure

changes continue

for

many cycles

and if the

head-

discharge curve

of the

pump

is

relatively

flat. The

intersection

of the

pipe system curve

and the

pump

curve

is the

operating

point

of the

pump

—

but

only

during

steady

flow

when

the

pressure

at

discharge

is a

function

only

of

static

and

friction

head.

If

the

pressure

increases

somewhat,

for

example,

because

of the

partial closure

of a

valve,

the flow

decreases greatly.

If the

pressure

is

reduced slightly

below normal,

the flow

increases substantially. Thus,

a

component

of flow (in

which

the

water sloshes back

and

forth)

is

superimposed upon

the

average discharge

of

the

pump.

If

that component

is in

harmony with

the

natural

frequency

of the

pressure waves

in the

pipe,

resonance occurs,

the

pressure waves continue,

and

the

pump

can be

destroyed

in a few

hours.

The

problems associated with pressure waves

can

be

even more severe

and

insidious with variable-speed

pumps

because

the

pumps operate over

a

considerable

portion

of the

family

of

head-discharge curves.

The

problem

can be

avoided

or

alleviated

in a

number

of

ways.

•

Choose pumps that

do not

have

a flat

head-

discharge curve

at the

operating point.

•

Design

the

system

so

that

the

pump does

not

oper-

ate for

more than

a few

seconds

at any

point where

the

phenomenon described

can

occur.

•

Make

a

transient analysis (see Chapters

6 and 7)

and

design

the

entire system

to

limit

the

magnitude

and

repetition

of

pressure

waves.

3-12. Model Studies

Some types

of

problems

defy

traditional mathematical

analysis

and

must

be

solved

by

extraordinary means.

One

such problem type

is the flow

regime

in

forebays

and

pump intake

facilities.

For

structures

of

reasonable

size that

are

based upon proven,

successful

designs,

it is

usually

sufficient

to

follow

established rules

or

guide-

lines.

For

very large structures

or

those that

differ

sig-

nificantly

from

designs known

to be

successful,

a

model

study

is

usually

the

only means

to

ensure success.

Model studies

of wet

wells and/or forebays

are

indicated whenever:

• The

design does

not

adhere

in all

respects (such

as

bay

width,

bell

clearance,

side

slopes,

piping, dis-

tance

from

obstructions,

and

change

in

direction

of

incoming

flow) to the

guidelines presented herein

or

to

established designs proven

to be

successful.

• The flow is

greater than about

9000

m

3

/h

(40,000

gal/min)

per

pump

or

23,000

m

3

/h

(100,000

gal/min

or

140

Mgal/d)

for the

station.

•

Excavation cost

for

size

or

depth

is at a

premium,

or

where achieving maximum design

flow is

critical.

• The

approach

flow is

asymmetrical

or

nonuniform

or

there

is a

change

in

direction

of

incoming

flow

due,

for

example,

to

some pumps

not

operating.

• An

existing sump

is

malfunctioning,

and

retrofitting

is

required.

Conducted

by

experienced personnel, model stud-

ies can be

used

to

evaluate measures

for

alleviating

the

undesirable hydraulic conditions described under

"Pump Sump

Problems"

in

Section 12-6.

Model

Similitude

True similitude requires that

(a) the

Froude number

(F

= v/

JgL),

a

dimensionless

function

of

gravita-

tional

and

inertial forces;

(b) the

Reynolds number

(R

=

vD/V

,

Equation 3-11),

a

dimensionless

func-

tion

of

gravitational

and

viscous forces;

and (c) the

Weber number

(W = v

Dp/c),

a

dimensionless

function

of

inertial

and

surface

tensile forces

be the

same

for

both

the

prototype

and a

geometrically sim-

ilar model.

The

velocity

is v, g is the

acceleration

due

to

gravity,

L is a

length such

as the flow

depth,

D is a

length such

as the

intake diameter,

V is

kinematic

viscosity,

a is

surface tension,

and p is

mass density.

All

dimensionless numbers cannot

be

satisfied

simul-

taneously unless

the

model/prototype scale ratio

is

unity,

so a

compromise must

be

made. When

a

free

surface

exists,

such

as in a

pump intake basin,

flow

patterns

are

influenced

primarily

by

gravitational

and

inertial forces, and, therefore, similitude

is

based

on

the

Froude number. Although

the

Reynolds number

is

much less important,

it

must

be

greater than

3 x

10

4

at the

suction bell mouth

to

ensure minimum vis-

cous

effects.

The

Weber number should

be

greater

than

120

for

minimizing

surface

tension

effects.

For

practicality

in

observing

dye

patterns

and

obtaining

adequate measurements

of

velocity

in the

bell,

the

throat diameter

of the

suction should

be at

least

75

mm

(3

in.).

The

linear scale ratio,

L

m

/L

p

,

of

models

is

typically about

VIQ*

but

L

m

/L

p

for the

models used

for

developing

the

guidelines

in

Section

12-7

was

close

to

V

4

,

so

that

for

equal model

and

prototype

values

of F,

other model/prototype

scale

ratios were

close

to:

•

Velocity:

v =

(L

m

/L

p

)

0

'

5

=

V

2

•

Time:

t =

(LJL^

=

V

2

•

Volume:

V =

(LJL

p

f

=

V

64

•

Flowrate:

Q = V/t

=

(L

m

/L

p

)

2

'

5

=

V

32

Construction

The

geometry

of the

model

and

prototype must

be

simi-

lar,

and in

particular,

a

sufficient

amount

of the

approach

structure

or

water body must

be

included

to

simulate

accurately prototype

flow

patterns into

the

sump.

At

least

one

side

of the

model must

be

constructed

of

clear

plastic

or

glass

for

observing

flow

patterns. Likewise,

suction

bells

and

pipes should also

be

formed

from

clear

plastic.

It is

advantageous

—

in

spite

of

extra

cost

—

to

construct

the

model

so

that

selected dimensions,

such

as

floor

clearance

for

bells, depth

of

trench,

or

slope

of

floors,

can

be

changed (possibly

by

adding

or

removing

inserts)

without rebuilding

the

model.

Impellers

are not

modeled, because

the

objective

is

to

evaluate

flow

patterns approaching

the

impeller.

Instead,

the

suction intake

is

equipped with

a

swirl

meter consisting

of

four

neutrally pitched vanes that

rotate

freely

on a

centered

shaft.

The

outer diameter

of

the

vanes

should

be 75% of the

intake pipe diameter

and

the

axial length

of the

vanes should

be 0.6

pipe

diameters.

The

swirl meter should preferably

be

located about

four

suction pipe diameters downstream

from

the

mouth

of the

suction bell.

Measurements

Water level should

be

measured with

a

model accu-

racy

of 3 mm

(V

8

in.).

Flowmeters should

be

cali-

brated

to

achieve

an

accuracy

of at

least

±2% of

upper

range value. Alternatively,

a

standard ASME

orifice

could

be

used without calibration.

Very

low

approach

velocities

to

pump intakes

can

sometimes

be

mea-

sured with

dye by

means

of a

stopwatch

and a

back-

ground

grid.

Dye is

introduced through tubing small

enough

to be

essentially nonintrusive. Higher veloci-

ties

can be

measured with

a

small propeller meter

or

by

other suitable means

at

enough points

to

define

the

flow

pattern

and its

stability.

For the final

design,

the

distribution

of

axial veloc-

ity

in the

throat

of the

suction bell should

be

taken

with

velocity traverses along

two

perpendicular axes

with

a

device capable

of a

repeatability

of ±2% or

bet-

ter. Pitot tubes

can be

used,

but a

laser velocity meter

with

a

computer readout, although

an

incredibly

expensive device, provides much more extensive data

and is

completely nonintrusive.

The

intensity

of flow

rotation,

0,

is

measured

by

the

swirl angle computed

from

Q

.

-\(ndri\

,„

--.

9

= tan

(3-32)

\

u

J

where

d is

pipe diameter,

n

is

revolutions

per

second

of

the

swirl meter,

and u is

average axial velocity

at the

swirl meter. Swirl

is

unsteady.

The

meter

may

only rock

slightly

for

short

or

long periods followed

by

slow,

rapid,

or

even reversing rotation. Hence, average rota-

tion

is not a

complete description,

and

data

on the

per-

centage

of

time versus swirl angle should

be

obtained.

As the

swirl meter

may

sometimes rotate

too

rapidly

to

count revolutions,

a

good system

is to

photograph

the

swirl

meter

for 10

min

with

a

video camera that over-

lays time

in

seconds

on the

images. This permanent

record

can be

analyzed

(at

slow speed when necessary)

for

any

type

of

time-rotation rate distribution wanted.

Vortices

are

measured visually with

the aid of dye

and

artificial

debris

by

comparing them

to

Figure

3-12. Vortices

are

usually unsteady

in

both location

and

strength

and

intermittent

in

occurrence. Vortices

should

be

observed

at, for

example, every

15

seconds

during

a

10-min

interval

to

obtain vortex type versus

frequency.

Video recording

is

recommended.

Acceptance

Criteria

The

pump manufacturer, station designer, client,

and

research

organization should agree

on the

acceptance

criteria, because

the

criteria

may

vary

with

the

size,

application,

and

kind

of

pumps.

In

general,

the

follow-

ing

provisions

are

satisfactory.

•

Surface vortices

of

Type

3 or

more

and

subsurface

vortices

of

Type

2 or

more

are

unacceptable, except

that

in

some stations they

may be

acceptable

only

if

they occur less than

10% of the

time

or

only

for

infrequent

pump operating conditions.

Be

cautious,

however, because

a

weak

effect

in a

small prototype

can

become

stronger

in a

larger prototype.

•

Swirl angles should

be

less than

5°,

except that

6°

may

be

acceptable

only

if

they occur

less

than

10%

of

the

time

or

only during infrequent pump operat-

ing

conditions.

• The

time-average velocities

at

specific

points

in the

bell throat should

be

within

10%

of the

area average

velocity. Time-varying

fluctuations

should have

a

standard deviation

of 10% or

less.

Tests

General observations should

first be

made

on the

ini-

tial design

to

identify

any

problems before making

time-consuming

detailed tests (unless detailed tests

are

wanted

by the

client

for

comparison with

a final

design).

Modify

the

model until

the

general observa-

tions

are

consistent with satisfactory design. Then test

operating conditions

at

minimum, intermediate,

and

maximum

flows and

water levels. Include

all

possible

pump

operating conditions

and

combinations

of

pumps.

Selected tests

for the

formation

of

free-surface

vortices should

be

made

at 1.5

times

the

Froude num-

ber

to

compensate

for

possible

scale

effects.

Some-

times

strong vortices

can

organize

unexpectedly

—

at

the low

velocities that occur with

HWL and low flow,

for

example.

Vortices

and

swirl angles should

be

observed

in all

tests.

Axial velocity determinations should

be

made

for

each

pump

—

but

only

in the final

design. Document

tests

of

swirling

and

vortexing

with

a

video camera

and

include

a VHS

cassette

of the

tests with

the final

report.

Comparison

with

HI

Standards

Part

of

this section

is

adapted

from

(and

all of it is

compatible with) more detailed guidelines prepared

by

Hecker [47]

for the

(circa

1998)

of

Hydraulic

Institute Standards.

1 •

Swirl

2. Dye

core

3. Air

and/or vapor

core

or

bubbles

b

Subsurface vortices. Floor vortices (not shown), centered under

the

intake,

are

similar

but

stronger

for the

geometry shown.

Figure 3-12. Classification

of

vortices.

Courtesy

of

Alden

Research

Laboratory,

Inc.

3

Surface vortices

Surface swirl.

Dye

core

to

intake,

coherent swirl

throughout water

column.

Vortex

pulls

air

bubbles

to

intake.

Surface

dimple,

coherent swirl.

Vortex

pulls

floating trash

but not air

to

intake.

Full

air

core

to

intake.

Vortex

type

Vortex

type

3-13.

Computational

Fluid

Dynamics

(CFD)

Computational

fluid

dynamics (CFD)

is a

powerful

method

for

predicting

fluid

motion

in a

continuum

by

using

numerical techniques.

The

Navier-Stokes

equa-

tions

governing

fluid

motion

are

assumed valid

at all

points, but,

as it is not

feasible

to

calculate velocities

at

every

point,

the

equations

are

solved

at a finite

number

of

points called

"nodes."

Typically, nodes

are

closely

spaced

at

discontinuities (such

as

walls

and

corners)

where velocity gradients

are

large, whereas nodes

are

spaced

farther

apart where velocity gradients

are

low.

Node spacing depends

on the

phenomena

and

geome-

try

to be

studied

as

well

as on the

numerical solver

and

the

computer used. Computational time

can

vary

from

a few

minutes

to

several days.

An

increasing number

of

engineers

are

using CFD,

because programs (called

"codes")

are

being devel-

oped

for

high-speed, relatively

low

cost computers.

Over

30

codes were available

in

1996. Engineers with

basic

fluid

mechanics backgrounds can, with minimal

training,

use

these tools

to

analyze

flow

patterns.

The

most versatile codes include

the

ability

to

deal with

several types

of fluids

(compressible,

incompressible,

Newtonian,

non-Newtonian, etc.); change

of

phase,

multiphase, steady

and

unsteady

flow;

shock waves;

body forces;

and

even chemical reactions.

Fluid

flow is

described

by

partial

differential

equa-

tions

of

mass, momentum,

and

energy conservation.

Equations that

describe

fluid

properties

such

as

viscos-

ity

and

density

are

needed. Using

the

time-averaging

technique,

several terms that cannot

be

mean

flow

quantities

are

generated.

These

quantities

are

called Reynolds stresses.

It is

impossible

to

solve

the

time-averaged equations unless certain assump-

tions

are

made

for the

Reynolds stresses. Various tur-

bulence models

are

available depending upon those

assumptions,

and it is the

responsibility

of the

user

to

select

the

appropriate turbulence model.

After

the set

of

differential

equations

is

derived

for a

particular tur-

bulence assumption, these equations

are

converted

to a

set

of

nonlinear equations

by

discretization.

These

simultaneous, nonlinear equations

are

then solved

at

all

nodes

to

obtain

the flow field by

iteration

to a

pre-

determined level

of

accuracy.

A

limitation

of

current

(1996)

codes

is

their inabil-

ity

to

predict turbulence with accuracy.

The

energy

in

turbulence

is

contained

in

eddies whose sizes

can

range over

ten

orders

of

magnitude.

To

resolve

the

smallest

eddies

in

three dimensions, about

10

30

nodes

would

be

required

—

well

beyond

the

present limit

of

10

6

nodes.

Instead,

special

functions

or

turbulence

models

are

used

to

estimate

the

production, transport,

and

dissipation

of

turbulent energy without dramati-

cally increasing

the

number

of

nodes.

The

equations

used

to

model turbulence contain constraints that

are

adjusted

for the

type

of flow, for

example,

a

free

jet or

flow

over

a

backward-facing step. Turbulence levels

and

mean

flow

characteristics

can be

predicted

for

conditions near those

for

which

the

code

was

cali-

brated

and

verified.

Research

is

currently being con-

ducted

to use

direct numerical simulation

to

minimize

assumptions

for

modeling turbulence.

CFD is

useful

for

predicting overall

flow

distribu-

tion

in

pump sumps

and

forebays

to

within about

one

bell

diameter

of a

pump intake. Approach

flows to a

pump

intake

(or to a

pump

bay

from

a

forebay)

can be

influenced

by

withdrawals

by

other pumps,

and

such

influences

can be

readily predicted

by

CFD.

But flow

details, such

as

free

surface

and

subsurface vortices,

cannot

be

predicted

by

CFD,

nor can CFD

predict

objectionable phenomena such

as

swirling

or

asym-

metrical

flow

within pump suction bells. Obtaining

accurate data

for

such phenomena will require physi-

cal

model studies until

CFD

codes

are

developed that

can

accurately

model

the

smallest turbulent

eddies

that

affect

a flow field. The use of CFD in

conjunction

with physical model testing

can

sometimes reduce

the

total cost

of

modeling.

3-14.

References

1.

Ten-State Standards, Recommended

Standards

for

Sewage

Works,

Great

Lakes—

Upper

Mississippi River

Board

of

Sanitary Engineers Health Education Service,

Inc., Albany,

NY

(1978) (revised periodically).

2.

Benedict,

R. P.,

Fundamentals

of

Pipe

Flow, John

Wiley,

New

York (1980).

3.

Williams,

G.

S.,

and A.

Hazen,

Hydraulic

Tables,

1st

ed., John Wiley,

New

York

(1905);

3rd

ed.,

llth

printing, Hazen

and

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