DESIGN OF LOW PRESSURE
AIR CURTAINS FOR ENVIRONMENTAL
PROTECTION OF SURFACE WATERS *
By
Herbert Mascha
and
B.A. Christensen
Hydraulic Laboratory
Department of Civil Engineering
University of Florida
Gainesville,Florida 32611
Project No. R/OE19
Technical Papers are duplicated in limited quantities for specialized
audiences requiring rapid access to information and may receive only limited
editing. This paper was compiled by the Florida Sea Grant College with
support from NOAA Office of Sea Grant, U.S. Department of Commerce, grant
number NA80AAD00038. It was published by the Marine Advisory Program
which functions as a component of the Florida Cooperative Extension Service,
John T. Woeste, Dean, in conducting Cooperative Extension work in Agri
culture, Home Economics, and Marine.Sciences, State of Florida, U.S.
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TECHNICAL PAPER NO. 30
July 1983
Also published as Report No. HY 8303, Hydraulic Laboratory, Department of
Civil Engineering, University of Florida.
FOREWORD
The design procedures developed and presented in this report will
allow professional engineers and state and local officials to design
economical low pressure air bubble screens for the protection of coastal
water quality from pollution originating in marinas and residential canal
systems.
The methodology is based on researchrelated to the air system of
low energy bubble screens and the secondary currents created by such
screens at the tidal entrances to marinas or canal systems.
Verification of the design methods advanced in this document is
provided by experimental screens setup in the Hydraulic Laboratory's
large research flume. The size of this flume has allowed the construction
and testing of air bubble screen systems of almost prototype scale.
CHAPTER Page
1 INTRODUCTION . . . . . 1
2 REVIEW OF THE PHYSICAL PROCESSES AND RELATED
LITERATURE . . . .... .. 3
2.1 Generation of Bubbles . . . 3
2.2 Turbulent Buoyant Jets and Plumes . . 5
2.3 Bubble Screens . . . . 7
TABLE OF CONTENTS
FOREWORD . .. ... .. . ii
LIST OF FIGURES ... . . . .. v
LIST OF SYMBOLS . .. . .. vii
4.4. Ine n orizonrai niow . .. .. .
2.5 The Application of Bubble Screens . . 9
2.6 Spreading of Pollutants on the Water Surface 11
Z.4 mne .low Field Generated by an Air Bubble
Screen . ....... . .. 7
2.4.1 The Vertical Flow ......... 7
SA1 l r .'.~' 'rt q I I l. 7 .. .. .I . .
3.3.1.2 Requirement 2 . . .. 24
3.3.1.3 Requirement 3 . . 24
3.3.2 Constraint of f' . . . 25
3.3.3 The Optimum Pipe Diameter d . .. 26
3.3.4 Pressure p at Location x . 27
3.3.5 Pressure pe at the Entrance of the Pipe 30
3 BASIC EQUATIONS AND THEIR DERIVATION . .. 13
3.1 Formulas Describing the Air Discharge . 13
3.1.1 Linearization of the Vertical Velocity
Distribution . . . 13
3.1.2 Linearization of the Shape of the Bubble
Screen in Flowing Water . . .. 14
3.2 Spacing of the Discharge Holes . . 18
3.3 The p/peCurve . . . .. 18
3.3.1 Requirements for the p/peCurve . .24
1 I 1 1 Doanlti raman+ 1 9
CHAPTER Page
A runIfAli nVrTdAtt ^ir tir rTn nTrUfunoeCr
4.z Ine inTruence OT Lne oDUDDue ZUire un JuacuUSu
Load . . . . . 37
4.3 The Influence of the Bubble Screen on Floating
Material . . . . . 45
4.4 Considerations for Designing a Bubble Screen 45
5 THE EXPERIMENT ... . . . . 48
5.1 The Setup of the Experiment . . .. 48
5.1.1 The Sediment . . . ... 48
5.1.2 The Sediment Release Device . ... 51
CV LU l' uThheMixinn Tank .. ... . ... 51
4.1 Evaluation of the Air Discharge for Bedload 31
4.1.1 Efficiency of the Bubble Screen for
Bedload ............... 31
4.1.2 Relationship Between the Air Discharge Qa
and Vertical Travel Time t . .. 32
4.1.3 The BedloadEfficiencyDiagram of a Bubble
Screen (BED) . . . 34
4.1.4 The Influende of the Bubble Screen on
Sediment Transport . . 35
t.?. Tlme RcStirv vi fi.lih;L+,, 1" i" .<'*t' 
5.3 Conclusions . . . . 70
5.1.4 The Sampling Device ........... 57
5.1.5 The Bubble Screen . . .. 62
c J r % I s9 *h. Cv.n im nt . .n 62
7.4 The Air Discharge Qa . . ... 91
8 CONCLUSIONS . . . .. 95
LIST OF REFERENCES . . . .... ..... 96
6 A PROGRAM TO CALCULATE THE AIRU1lb.AKtL a ANU i n
PRESSURE pe . . . . . 75
6.1 The Setup of the Program. . . 75
6.2 The Use of the Program . . ... 76
6.3 Listing of the Program . . ... 79
7 EXAMPLE MARINA (A Guide to Use the Formula) . 86
7.1 The Pipe Diameter d . . . 86
7.2 The Spacing of the Nozzles . . ... 88
7.3 The Shape of the Centerline of the Bubble
rr on . . . . 89
LIST OF FIGURES
Figure Page
2.1 The flow field induced by the bubble screen ...... 6
2.2 The horizontal flow field induced by the bubble
screen . . . . ... . 10
3.1 Linearization of the distribution of the vertical
velocity . . . . ... .... .. .15
3.2 Linearization of the centerline of the bubble screen
in flowing water .... .. . . . .. 17
3.3 Distribution of the vertical velocity. . ... 19
3.4 Mass flux in the pipe . . . .... 19
3.5 The p/p distribution . . . 20
3.6 A nozzle in the pipewall . . . .. 28
4.1 Traveling distance for bed material . . .. 33
4.2 The bubble screen efficiency diagram for bedload (data
from the example in Chapter 7) . . .. ..36
4.3 The vertical flow field above the manifold ...... 38
4.4 Proposed device for improvement of the efficiency of
the bubble screen . . . .... 39
4.5 Influence of the bubble screen on the distribution of
suspended material . . . .... 40
4.6 The Re, versus Wcurves. . . . 44
4.7 Distribution of suspended material lighter than
water . . . . . . 46
5.1 The setup of the experiment . . . .. 49
5.2 The setup of the experiment (not to scale) ...... 50
5.3 Distribution of the suspended silica powder
concentration . . . .. .52
Page
53
The sediment release device (dimensions in mm)
The sediment release device . .
The setup of the sediment release device
The sediment release device in operation
The mixing tank (schematic) . .
Result of the test of the mixing tank .
The sampling device . . .
The setup of the sampling device .
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19 Average concentration distribution profile
. . 54
. . 55
. . 56
. . 58
. . 59
. . 60
. . 61
. 63
. . 64
. . 65
. . 66
. . 67
. . 68
. . 69
s ...... .71
Relationship between N and the rising velocity
Relationship between the rising velocity and the
depth for constant air discharge . .
Layout of Marina I . . . .
. 72
. 73
. 87
Figure
5.4
The compressor . . .
The air discharge monitor . .
The bubble screen in operation .
Concentration distribution profiles
Concentration distribution profiles
Concentration distribution profiles
Concentration distribution profiles
5.20
5.21
7.1
. ..
LIST OF SYMBOLS
Ah entrainment coefficient
aT tidal amplitude
b width of the vertical airflow
C constant for the calculation of the air discharge
S average concentration
Ca concentration at depth a
Cb constant for the linearization of the centerline of the
bubble screen
CD drag coefficient
Ck discharge factor defined by Kobus
C1, C2 dimensionless constants
C',C2' constants
Db bubble diameter
d diameter of the air manifold
d effective grain' diameter
ds grain diameter
d wall thickness of the air manifold
w
f bubble production frequency
f' friction factor related to R
f friction factor related to R for a nozzle
n
g acceleration due to gravity
H thickness of the oil layer
H atmospheric pressure as head of water
h depth of submergence
h* depth of the horizontal flow field
k equivalent sand roughness
z length of the air manifold
Li circumference of the injector
m mass flux per unit length and unit time
n number of nozzles within the influence of a nozzle
P wet perimeter
p pressure at x=x in the air manifold
Pa atmospheric pressure
e pressure at the entrance of the manifold
Qa air discharge
R hydraulic radius
Re, wall Reynolds' number
S slope of the energy grade line
s spacing of the nozzles
T tidal period
t spreading time
tH horizontal traveling time
t vertical traveling time
Vb bubble volume
Vi oil volume
vf friction velocity
vH horizontal velocity
vH average horizontal velocity
Hmax maximum horizontal velocity
Hmax
v average velocity
viii
vs
v
vV
v
vmax
W
X
xb
Ay
y*
GREEK
a'
6
Y
CS
v
Pa
PO
p5
Ps
PW
 spreading velocity
 settling velocity
 vertical velocity
 average vertical velocity
 maximum vertical velocity
 dimensionless constant
 characteristic grain size of the bed material
 displacement of the centerline of the bubble screen
 distance of the vertical source under the bed
 distance from the bed to the point where the bubble screen
is fully developed
SYMBOLS
 momentum coefficient
 entrainment coefficient
 specific weight
 diameter of a nozzle
 factor of safety
 diffusivity
 angle of repose
 ratio of relative spread
kinematic viscosity
density of air under atmospheric pressure
density of oil
density of air under pressure p
density of the sediment
density of water
a surface tension coefficient
o sum of surface tension of oil/water and water/air
T critical shear stress
T wall shear stress
x

CHAPTER 1
INTRODUCTION
When air is released from a perforated pipe at some depth in a
body of water it breaks up into individual bubbles. As a result of
their buoyancy and their injection momentum, the bubbles rise and drag
the surrounding water particles along. When reaching the water surface
a horizontal current is created with direction away from the vertical
curtain of bubbles. This flow phenomenon is used to prevent pollu
tants generated in for instance a marina from entering cleaner waters.
Bubble screens have previously been used for a great number of
other purposes. They have proved a success for the control of oil
spills, or as pneumatic break waters, for the prevention of ice
formation, or as barriers against saltwater intrusion into surface
waters, and for the absorbtion of shock waves caused by blasting.
Bubble screens have even been proposed to be used to contain manatees
in specific areas of coastal waterways.
A bubble screen barrier is easily installed. The air is released
through a perforated pipe. 'This pipe is usually placed on the bottom
but may also be tied to floats in deeper waterbodies. The advantage
of bubble screens in comparison with mechanical devices, such as tur
bidity curtains, is that they allow boat traffic across the barrier
and that their installation is very simple, easily made to conform
with the bottom geometry.
2
The objective of the present work is to find an analytical ap
proach to the effect of an air bubble screen on the transport of sus
pended and floating material and to design air bubble screens to reduce
the transport of bed load. The results of this investigation were com
pared with experimental results.
These results are used to develop a guideline for design of air
bubble screens for marinas or similar bodies of water that may generate
floating or suspended pollutants or debris being transported as bed
load (saltation).
CHAPTER 2
REVIEW OF THE PHYSICAL
PROCESSES AND RELATED LITERATURE
When air is released into water and energy and/or mass exchange
takes place between the two media. The air being released from a
nozzle, or an orifice, or a similar structure disintegrates into
bubbles of various sizes. This leads to a large contact area between
the two media causing the exchange.
As this phenomena is of a very complex nature, a large number
of investigations have been done. Therefore this review will focus
only on the appropriate generalities and those details which are used
in this work.
Ecuyer and Murthy (1965) studied the heat transfer from the sur
rounding liquid to the bubbles. Speece et al. (1973) investigated the
flow induced by a bubble screen as well as the mass transfer between
the air bubbles and the surrounding liquid. Haberman and Morton (1954)
and Chao (1963) examined details of the individual bubbles.
The main concern of these papers was the estimation of the shape
and size of the bubbles, the rising velocity of the individual bubble
as well as the swarm of bubbles, and the induced mass and energy
transfer.
2.1 Generation of Bubbles
Eucyer and Murthy (1965), Wallis (1969), and Speece and Reyyan
(1973) presented papers in which the progress of bubble formation and
the influencing factors were discussed. These factors are the gas in
jection rate, the gas and liquid properties, and the size and shape of
the injector and the gas supply line. Their influences appear in the
form of dynamic and interfacial forces due to injection momentum,
inertia of the displaced liquid, buoyancy, drag on the bubbles during
rise, and surface tension.
Two main regimes of bubble .formation have been identified. At
very low gas flow rates (Qa< 1 cm3 s ) the terminal bubble volume Vb
can be determined by equating the buoyancy and surface tension forces,
L a
V = i (2.1)
b (P pa) g
w a
in which Li is the circumference of the injector, pw and pa are the
densities of liquid and gas respectively, and a is the surface tension
coefficient. This regime is referred to as the static regime.
If Qa is increased beyond 1 cm3 s the regime is called dynamic.
The bubble size Ds depends only on the buoyancy and the liquid inertia
forces, while the frequency, f, has been found to be constant. Ds can
be written as:
2
s= 1.38 ( )1/5 (2.2)
in which g is the acceleration due to gravity. For both regimes Qa
can be written as the product of the bubble volume Vb and the production
frequency f.
Qa = Vb f
(2.2)
In both regimes bubbles whose sizes are unique for a given Qa, are
formed periodically.
For higher flow rates Ecuyer and Murthy (1965) distinguished a
third regime, which they called turbulent regime. Leibson et al.
(1956) investigated this regime and found that bubble sizes as well as
the formation frequency vary randomly.
2.2 Turbulent Buoyant Jets and Plumes
When one of two miscible fluids, called the effluent, is dis
charged through a submerged outlet into the other, called the ambient
fluid, the resulting behavior is similar whether they are gases or
liquids. In addition to its initial momentum the effluent may possess
buoyancy forces due to differences in density. The relative influence
of each fluid is described by the densimetric Froude number.
P U 2 p U2
F T a a : a a
F = a a (2.4)
S( P ) gd pw gd (2
When the momentum is the dominant factor the resulting flow is
called a buoyant jet. If buoyancy is dominating, the flow is referred
to as a plume.
Both jets and plumes consist of three distinct zones. In the
zone of flow establishment (ZFE), the jet enters the ambient fluid.
Except for simple plumes this zone is dominated by the initial momentum.
In the zone of established flow (ZEF), the flow pattern depends on
the local velocity, the buoyancy, and the ambient flow conditions.
The third zone is called the far field. Here the ambient charac
teristics dominate and the excess velocity of the jet is depleted
(see Figure 2.1).
ZEF
WATER
ZFE
I
WATER
r BED
y=O
AIR MANIFOLD \ y
VIRTUAL SOURCE
Figure 2.1 The flow field induced by the bubble screen.
WATER
SURFACE
2.3 Bubble Screens
At the injector the bubble screen possesses
buoyancy. The relative effect can be observed by
Froude number (2.4). For a typical set of Kobus'
both momentum and
the densimetric
(1968) data
F = (150) = 0.14
800 980 0.2
As just above the injector F is even smaller, the
classified as a bubble plume using the previously
bubble screen can. be
discussed classi
fiction.
2.4 The Flow Field Generated by an Air Bubble Screen
2.4.1 The Vertical Flow
Miyagi (1929) already showed that the rising velocity of the air
bubbles is approximately constant and does not depend on their size.
Taylor (1955) describes the maximum velocity at the centerline
(vmax) by using the analogy between the vertical flow of the bubbles
and the hot air stream from an heat source.
and the hot air stream from an heat source.
h 1/3 1/3
vmax = 1.9 (1 + ) (g Qa1/3
0
(2.5)
in which H is the atmospheric pressure head, and h is the depth of
0
submergence of the injector.
Sj6berg (1969) found the following expression by experiments:
1 1/2 Qa2/3
Vmax T= (g y) for y 9 1/2
Q2/3
max 1.2 (g Qa)1/3 for y 9 (2.7)
9
The distribution of the vertical velocity was investigated by Charlton
(1961) and Kobus (1968). It was approximated by a Gaussian Distribution,
2
kfx
e (2.8)
max
in which b is the width of the plume and k is a dimensionless constant,
which was found to be 40 (Figure 2.1).
Further studies done by Cederwall and Ditmars (1970, 1974) derived
the following equations for the centerline velocity vv and the width, b,
of the plume:
(1 + I 2) 1/6 h 1/3 1/3
vmax + [5(1 + T)] (g Qa)1/3 (2.9)
Equation (2.9) can be simplified to
Vv.max = C Qal/3 (2.10)
b = 2 v1/2 B(y + Ay) (2.11)
in which Ay is the distance of the virtual source under the bed and y
is the distance above the real source (see Figure 2.1), B is the en
trainment coefficient, and x is the rate of the relative spread of the
lateral density and the velocity distribution. Using Kobus' data
Tekeli and Maxwell (1970, 1974) found B to vary between 0.085 and 0.115
for the 2D case. They set A to 0.2 after different values were tried
and the sensitivity for the change was not apparent.
2.4.2 The Horizontal Flow
The depth of the surface current, h*, and the maximum horizontal
velocity, vHm were expressed by Bulson (1961):
max
h* = 0.32 H In (1 + ) (2.12)
0 (2.12)
0
Vm( h 13 1/3
H = 1.46 (1 + (g 1/3 (2.13)
max 0 (
Sj6berg (1969) found the velocity distribution in the surface layer to
vary linear with depth, while it is approximately constant in the lower
layer (see Figure 2.2)
for h
max
for 0 < y
fo yh H max
2.5 The Application of Bubble Screens
Bubble screens have been used for numerous purposes. Kobus (1973)
discusses the use of the bubble screen for the control of heavy oil
spills, the control of stratification by using an artificial mixing
caused by the bubble screen, improvement of the water quality in lakes
and reservoirs by artificial aeration, prevention of icing of navigation
waterways and hydro power plant intakes, absorption of shock waves
caused by blasting, and control of shoaling in estuaries and harbors.
The advantage of the bubble screens in comparison with mechanical
devices is that they allow traffic across the barrier and that their
installation is very simple.
"max WATER SURFACE
i
S BED
y=0 i
Figure 2.2 The horizontal flow field induced by the bubble screen.
According to its application either the vertical velocity field
or the horizontal velocity field or both are taken into consideration.
Using the bubble screen as an oil barrier the induced horizontal
velocity has to be greater than the spreading velocity of the oil to
keep the pollutant from crossing the barrier. For the control of
stratification the vertical exchange depends on the induced vertical
velocity.
In this work both types of flow will be taken into consideration.
2.6 Spreading of Pollutants on the Water Surface
To stop pollutants which float on the water surface from crossing
the bubble screen the induced horizontal velocity has to be greater
than the spreading velocity of the pollutant. This velocity may be in
creased by wind, tide, or waves.
Kobus (1973) derived the formula for the maximum spreading velocity
of the oil film,
vs =gH (w 2 o )1/2 (2.16)
s g w p, g H
where Po is the density of oil and a is the sum of the surface tension
oil/air and oil/water. Blooker (1964) found the following for the
thickness of the oil layer, H:
H= K (2.17)
where t is the spreading time and K can be written as
V. 1/3 p 2/3
K () [ w P3 (2.18)
0 03 K
where Vi is the volume of oil and K is a constant for oil.
In order to stop the oil spill from crossing the bubble screen the
induced horizontal velocity found from equation (2.13) has to be greater
than the spreading velocity of oil. As the velocity induced by the
bubble screen is fluctuating and equation (2.13) gives only a maximum
value, a factor of safety e.has to be taken into consideration. Kobus
(1973) suggest e to be in the order of 1.5.
H s
max
1.46 (1 + 1/3 (g Q )1/3 > [gH (W P
H a PW
2 )]1/2 (2.19)
p g H
Equation (2.19) yields the required air discharge:
Q a 0.32 (1 + ) gl/2 [H(P a
a Ho PW
2) 3/2 (2.20)
Po g H
CHAPTER 3
BASIC EQUATIONS AND THEIR DERIVATION
3.1 Formulas Describing the Air Discharge
In the previous chapter the equations which are used to describe
the velocity distribution of the rising bubbles and the relationship
between air discharge and rising velocity were explained and the related
literature was mentioned.
In order to make the use of these equations simpler with regard
to their integration, the profile of the vertical velocity distribution
and the shape of the bubble screen in flowing water were linearized.
3.1.1 Linearization of the Vertical Velocity Distribution
With 3 0.1 as suggested by Tekeli and Maxwell (1978) equation
(2.11) yields
b = 0.113 (y + Ay) (3.1)
When using equation (2.8) for one half of the profile the ratio (L) can
be described by
n v )]l/2 (3.2)
2 max
where x is the horizontal distance from the centerline of the bubble
screen.
V
Figure 3.1 shows the result when vs (v ) according to
(b) vv
2 max
equation (3.2) are plotted. For x = 0.3 equation (2.8) gives
vb
v
v 0.027. This indicates that the distribution outside the distance
V
max
x = 0.017 (y + Ay) from the centerline can be neglected.
Using linear regression the remaining curve may be represented quite
well by the straight line
v
V = 1 7.19 (g) (3.3)
max
as seen in Figure 3.1.
3.1.2 Linearization of the Shape of the Bubble Screen in Flowing
Water
When bubbles rise in flowing water a certain displacement in the
downstream direction takes place. In his thesis Mechrez*(1981) found for
the shape of the bubble screen's centerline in flowing water:
= 2.5 vf y [In 29.7 y 1] (3.4)
Xb = k
v
v
in which xb is the distance the bubble screen's centerline is moved by
the current, vf is the friction velocity, k is the equivalent sand
roughness of the bed, while vv is the average vertical velocity.
This average vertical velocity v may be written
1 f0.15
v v [1l 7.19 d ()
SV max 0
by use of Equation (3.3) from which
*See also Appendix B.
.Eqn. (3.2)
THE INFLUENCE OF
NEGLECTED
Eqn. (3.3)
v CAN BE
0 0.1 0.2 0.3 0.4 0.5
Figure 3.1 Linearization of the distribution of the vertical velocity.
V
V
V
Vmax
v = 0.79 v (3.5)
max
Further the friction velocity vf is defined as
v = / .= (g RS)1/2 (3.6)
vf p
where R is the hydraulic radius and S the slope of the energy grade line.
If it is assumed that the flow takes place in the MRange (i.e.
4.32 < R < 276 and Re, > 70) vf can be represented by
vf = 0.121 vH k(1/6) R(1/6) (3.7)
in which vH is the average horizontal flow velocity. Introducing
equations (3.5) and (3.7) into (3.4) yields:
VH /6 /6)
xb = 1.532 () y k16 R(16
max
S[n 29.7 1] (3.8)
Using linear regression it can be seen that equation (3.8) may be
approximated by the straight line
xb = Cb y (3.9)
in which Cb is a constant which has to be evaluated by linear regression
for every case.
This approximation was checked with various sets of data and found
to be reasonable. Figure 3.2 shows equation (3.8) for the set of data
used in the example MARINA I described in Chapter 7.
Eqn. (3.8)
y[m]
4.0
3.0
2.0
1.0
0 0.5 1.0 1.5 2.0 xb[m]
Figure 3.2 Linearization of the centerline of
in flowing water.
the bubble screen
Eqn. (3.9)
3.2 Spacing of the Discharge Holes
As shown in section 3.1.1, the distance from the centerline of the
bubble screen to the point outside which the vertical velocity can be
neglected is 0.017 (y + Ay). Assuming that Ay << y and setting y = h**
we get
n.s = 0.017 h** (3.10)
in which s is the distance between the discharge holes and n is the
number of holes within the range of influence of one hole. To find the
right spacing the hole at the end of the pipe has to be considered because
it receives contribution of vertical velocity components only from one
side. The sum of the vertical velocities can be written as follows
(see Figure 3.3)
2 )l2 2
2x 2(xs 2(xns)
v 40( ) 40(2b 40(2 ns)
z e + e +... +e (3.11)
max
To check if the spacing was chosen sufficiently close, a point
between the last two holes is chosen (e.g. at x = 0.5 s). Using equation
v
(3.11) it can be checked if the value of z is not less than a
v
reasonable value (e.g. 1.0). max
3.3 The p/peCurve
When a fluid or a nearly incompressible gas is discharged through
a manifold, the velocity head decreases because of the decreasing volume
of fluid or air. This effect may cover up the friction loss and increase
the pressure term according to the energy equation. Figure 3.5 shows a
p/pedistribution, p is the pressure at a point x=x along the manifold
EV I I
I I
NOZZLES
Figure 3.3 Distribution of the vertical velocity.
 dx *
M+dM
p+dp L
LT1T
M
j p
CLOSED END OF MANIFOLD
Sx=x x=0
CONTROL SURFACE
Figure 3.4 Mass flux in the pipe.
llllllll
I I
I &
20
Pe
1.0   
x.0
XPe
X=Z =XXm X=O
Figure 3.5 The p/pedistribution.
and pe is the pressure at the entrance of the manifold location at x=z.
The deadend of the manifold is x=O.
In the following the properties of the p/pecurve are used to derive
equations for the pipe diameter d and the necessary pressure at the pipe
entrance pe"
The momentum equation applied.on a control volume as shown in
Figure 3.4 yields:
P' p v 2 A a' pp (v + dv )2 A
= (p + dp) A p A T0 Pdx (3.12)
where a' is the momentum coefficient, p is the density of air at pres
sure p, To is the wall shear stress, and P is the wetted parameter.
The mass flux per unit length and per unit time can be defined
as:
m = (3.13)
The mass flux through the control volume shown in Figure 3.4 can
be described by
M + dM = mdx + M
Integrating and using the boundary condition that at the end of
the pipe (i.e. x=O) all air has left the manifold (i.e. M=O) yields
M = m x (3.14)
The average velocity vm can be expressed by
m = (3.15)
m p A
p
The wall shear stress To can be written as
T = yRS (3.16)
where S is the slope of energy grade line or energy loss per unit length
of the conduit. DarcyWeisbach's equation gives the following expression
for S:
f' v
S 2 R (3.17)
2g R
where f' is the friction factor based on the hydraulic radius. Intro
ducing equations (3.14) through (3.17) into (3.12) yields
SM2p a (M2 + 2MdM + dM2)
^ P p A
1 f' M2
= dp A  dx (3.18)
p
The term dM2 is very small and therefore it can be neglected. The
general gas law for constant temperature yields
P Pa
= a (3.19)
where pa is the density of the gas at atmospheric pressure and pa is the
atmospheric pressure. Introducing equation (3.19) into (3.18) and
integrating f'm2 2 2
2 f m p a' m p
+ C = x x (3.20)
6 pa A R Pa A
is obtained.
To evaluate the integrating constant C, the boundary condition ex
pressing that p=pe at x=2 may be used. Substracting equation (3.20) for
2
Pe
x=t and p=pe from equation (3.20) and dividing by to make it dimen
sionless yields:
2
(2) =1
e
f' m2 Pa 2
2 a [1
3 p A RPe.
2 2
2 a' m pa a
+ A2 2 C 
Pa A Pe
3
(]
2
(x)]
(3.21)
where z is the length of the pipe and p now is expressed in terms of the
pressure pe"
The dimensionless constants Cl and C2 can be defined as:
1 2
2 a' m2 Pa 2
Cl A2 2
Pa A pe
f' m2 Pa a3
C2 2
3 pa A2 R pe2
(3.22)
(3.23)
Using these expressions equation (3.21) reduces to
S= [1l + Cl [1 
Pe
(X)] C2 [1 ()]]1/2
2 V ]
(3.24)
This equation gives the pressure distribution along the manifold.
24
3.3.1 Requirements for the p/peCurve
To find formulas for the optimum pipe diameter d and the pressure
at the pipe entrance pe the p/pecurve is used. To find these values
the following requirements for the p/p curve are made.
3.3.1.1 Requirement 1. It is required that  > yh at all xvalues
Pe
ensuring a positive ai.r discharge at all holes.
3.3.1.2 Requirement 2. At = 0, A has to be a minimum. Ap is
SPe
defined as p p. Fulfilling this requirement the ratio of  is kept as
ee
big as possible.
3.3.1.3 Requirement 3. The value for pe is calculated for p at
xm where the p/p curve has a minimum (see Figure 3.5).
xm can be found bydifferentiating equation (3.24) with respect to
( ) and setting equal to 0 which yields:
2
1 [2 C1 (I + 3 C(
2 3 = 0 (3.25)
[1 + C1 [1 () ] C2 [1 () ]]
Consequently solving for yields
x
0 (3.26)
x 2 Cl
l 1 (3.27)
2
x
To check if the p/pecurve has a minimum at the second de
rivative of equation (3.24) with respect to (X) is found. It must be
positive.
d e 1 + C )] C2 () J]/2 [6C2() 2C]
d E ++ C^ 2 [6C2 () 2C1
2 = 2 3
d ( ) 1 + CI [1 () ] C2 [1 ( C)]
2 3
[1 + C11 (1) ] C211 (x) 1/2
1 + C [1 () ] C2 [1 
x C .
When the value for is introduced and 1,
C2
most realistic dimensions, the nominator yields
54 C19 + 48 C112 > 0
[2C )+ 3C2() 2
3
(21) 3
(3.28)
which is true for
(3.29)
Therefore the p/pecurve must have a minimum at x m/ = 2C1/3C2.
3.3.2 Constraint of f'
Using requirement 1 a constraint for the friction factor f' and
therefore for the material of the pipe.can be developed. Requirement 1
(3.3.1.1) states
x
7<0
2.
setting equation (3.24) equal to 0 yields
2 3
0 = 1 + C C () C2 + C ()
and solving for () yields:
C2 C2 C
(3.30)
(3.31)
(3.32)
26
If is less than 0 the right side of the equation is less than
0, too, for both C1 and C2 greater than 0, which is always true.
1 C1
1 < 0 (3.33)
C2 C2
with expression (3.22) for C1 and (3.23) for C2 this yields
2 2
3 Pa A R pe R
1 a2 3e a R < 0 (334)
f' m pa
a
and solving for f' yields
2 2 2 2
3 Pa A R e + 6 a' R m p, 2
f' < a m2 a (3.35)
m p a
This constraint can be used to check if a proposed material for the
pipe is appropriate.
3.3.3 The Optirum Pipe Diameter d
To find a formula for the optimum pipe diameter d, requirement
2 (3.3.1.2) is used. Ae can be written as
pe
2 = 1 (3.36)
Pe Pe
At = 0 and using equation (3.24) for we get
Se
2= 1 (1 + Cl C2) 1/2 (3.37)
e
C1 and C2 can be written in terms of the pipe diameter d
C1' = C1 d4 (3.38)
C2' = C2 d"5 (3.39)
To get the dvalue that makes minimum the first derivative of
Pe
Switch respect to d has to be 0, which yields
Pe
4 CI' d + 5 C2' d6 = 0 (3.40)
then, solving for d and introducing the result in the expressions for
C1' and C2' yields
5 f' 2
d = 6 (3.41)
3.3.4 Pressure p at Location x
As shown in Figure 3.6, the energy equation may be applied between
the shown crosssections 1 and 2 as an approximation although the
streamlines are not normal to section 1.
p + p v2 = H + h ) Y + Pp V p p Z AH (3.42)
where the index p refers to the density of the air under the pressure p
at a location x=x in the pipe.
Kobus (1973) defines a discharge factor for bubble screen nozzles
Ck*
4 Q P
Ck a2 (3.43)
v 7 p
~ I
WATER OUTSIDE
/ d, = WALL
PIPEWALL I / / THICKNESS
Figure 3.6 A nozzle in the pipewall.
where 6 is the diameter of the nozzle. Kobus (1973) found Ck to vary
between 0.5 and 0.9. From equation (3.31) an expression for the
velocity v through the nozzle can be found.
4 Pa
v = a (3.44)
Ck I Pp
When equation (2.10) and (3.32) are plugged into (3.30) and the
equation is solved for p one obtains
(H+h)y (H+h) 222 2016 Q a
a 2 a a
(Ho+h)v + [(Ho+h) YW2~ pa 4 62 (1 PC2 a2/3 gaH)]/2
6 64 Ck2 d 3
p =
2(1 a C2 Q2/3 PZ
2( a g AH)
a a
(3.45)
In this equation the solution with the negative sign would give
results for p which are smaller than the pressure outside the pipe
(i.e. p < (H +h) y). Therefore the result with the negative sign
can be neglected. SAH is the sum of the friction loss in the nozzle
and the exit loss. EAH can be written as follows
ZAH = n a d C1 C Qal/3 )2 (3.46)
2g A2 R C k k a
where f is the friction factor for the nozzle, and dw is the wall
thickness of the pipe.
3.3.5 Pressure pe at the Entrance of the Pipe
To evaluate pe, requirement 3 (3.3.1.3) is used.
at Yields
= 1[ +C1
Pe
Equation (3.47)
3
C 4 .] 1/2
 C 1C2
C2
and solving this equation for pe yields
C,3
p = [2 Ci + C + 4 11/2 (3
2
where p is evaluated by equation (3.33) and Ci' and C are defined as
,, 2 a' m2 p 2
C1 = A2 (3
Pa A
f' m2 Pa z 3
S3 A2 R (3
.48)
.49)
.50)
CHAPTER 4
EVALUATION OF THE AIR DISCHARGE
To evaluate the necessary air discharge three modes of material
crossing the screen have to be considered: 1) floating material,
2) suspended material, and 3) bed material. Each case leads to dif
ferent solutions. For designing a bubble screen the mode which is
considered to be the most important, has to be chosen to find the
corresponding values for the air discharge and the pressure. The other
modes of transport may then easily be checked for importance after the
design.
4.1 Evaluation of the Air Discharge for Bedload
In the following two types of bedload have to be distinguished:
1) sediments and 2) objects, which are light enough to be moved along
the bed (i.e. cans or similar containers, etc.). Solutions for these
two cases can be approached in the same way. Some considerations though
will have to be different because of the different qualities of the
two types of bedload.
4.1.1 Efficiency of the Bubble Screen for Bedload
Before a formula for the necessary air discharge is developed, the
efficiency of the bubble screen will be defined.
Consider a particle moving along the bed. Einstein (1950) states
that the average length of a particle jump is about 100 grain diameters.
This distance is called L'. Assuming that a bubble screen is located
in flowing water, the centerline of the screen will be moved a distance
xb downstream from the vertical axis. xb is given by equation (3.4).
To keep a particle from crossing the screen, it must be moved into the
zone of backwards flow while it travels the distance L which is the sum
of L' and xb, i.e. the time it takes to travel the vertical distance,
tv, must be smaller than the horizontal travel time tH (see Figure 4.1).
If tv gets smaller, a particle may move closer to the bubble
screen to start its movement while it is still moved to the zone of
backwards flow. The distance the particle may move closer to the bubble
screen is called AL.
The ratio of AL to L is defined as the efficiency of the bubble
screen for bedload,
edoad L (4.1)
bedload L
4.1.2 Relationship Between the Air Discharge Qa and Vertical
Travel Time t
The vertical travel time tv can be expressed by
t = dy (4.2)
0 VV Vss
where h**is the distance from the bed to the level where the air induced
horizontal flow starts to develop (see Figure 2.1 and Figure 2.2), v
is the vertical velocity induced by the bubble screen which is described
by equation (3.3), and vss is the settling velocity of the particle.
Introducing the linearized functions developed in Chapter 3 into equation
(4.2) we get
CENTERLINE OF BUBBLE
SCREEN (STAGNANT WATER)
WATER SURFACE
CENTERLINE OF BUBBLE
I /SCREEN (FLOWING WATER)
L
FLOW L L xbb7
L I
/ AIR MANIFOLD
BED
S/////// / / /
Figure 4.1 Traveling distance for bed material.
(4.3)
(1 + 63.63 Cb) v 63.63 v x
max (Y + y
By integrating and using equation (2.10) for vmax
expression for the vertical travel time is obtained
pression for the vertical travel time is obtained
the following ex
h** 4 At
63.63 C Q 1/3 x
t = +
SC Qa1/3 (1 + 63.63 Cb) vs [C Qa/3 (1 + 63.63 Cb) vss
[C Qa1/3 (1 + 63.63 Cb) vss] (h**+Ay)
1/3
63.63 C Q, x
a
 1}
(4.4)
4.1.3 The BedloadEfficiencyDiagram of a Bubble Screen (BED)
The horizontal travel time tH is evaluated by integration of the
velocity profile over a distance h1 from the bed. hi is the vertical
distance a particle is moved from the bed into the flow when it travels
downstream.
h
^1
2.5 vf ln (29 7k ) dy
(4.5)
(4.6)
L
tH =
vH
The distance AL can then be expressed hy
AL = (tH tv) H
h**
vma
Vvmax
(4.7)
When AL is evaluated for various values of the air discharge Qa
using equation (4.4), a BedloadEfficiencyDiagram .BED) can be plotted.
In the same way using equation (3.36) and (4.4) a BED with respect to
the pressure at the pipe entrance pe may be plotted. Figure 4.2 shows
BEDs which were plotted using the data from the later numerical example
given in Chapter 7.
Using the BED makes it possible to compare the influence of an
increase in pressure or the air discharge on the efficiency of the
bubble screen, i.e. the economy of the bubble screen.
4.1.4 The Influence of the Bubble Screen on Sediment Transport
Einstein (1950) found the following expression for the velocity
to which a grain is exposed
vH = v 2.5 n 297 0.35 X (4.8)
H f k
where X is a characteristic grain size of the bed material. 0.35 X is
the distance from the bed where the velocity v is found. This distance
m
is usually very small.
A distance y* is defined as the distance from the bed to the level
where the vertical flow field of the bubble screen is fully developed.
At this point must be equal Hence,
1 1
0.113 y* = s
or
or
y* = 8.85 s
(4.9)
Qa[l06 m3 s1]
20
(LEFT SCALE)
(RIGHT SCALE)
1.5
0 20 40 60 80 100 [%]
Figure 4.2 The bubble screen efficiency diagram for bedload (data
from the example in Chapter 7).
P [atm]
3.0
2.5
2.0
When compared to 0.35 X it is seen that y* is much bigger. As a
result triangular areas originate where the vertical velocity field of
the bubble screen is not fully developed. The sediment will cross the
screen at these locations (see Figure 4.3).
To avoid this "transparency" effect these areas must be blocked.
Figure 4.4 shows device which will accomplish that and may be easily
attached to the pipe. The shape of the device forces the flow, and
with it the sediment, to pass through the area where the velocity field
of the bubble screen is developed and the sediment may be moved into
the upper layer of backwards horizontal flow.
4.2 The Influence of the Bubble Screen on SuspendedLoad
The bubble screen is not able to reduce the total amount of sus
pended load. Although a part of the suspended material is sent back
with the horizontal flow in the upper layer it is added to the incoming
flow upstream of the bubble screen.
The improvement the bubble screen can do is by mixing, thereby
reducing the concentration.of the pollutant. A pollutant in suspension
approaches the bubble screen with a concentration profile which depends
on the settling velocity of the material and the diffusivity coefficient.
After passing the screen due to the mixing a uniform distribution
profile takes place (see Figure 4.5).
Such a process improves the situation for the bottom layer where
usually the high concentrations are located by reducing the near bed
concentrations. It also helps the spreading due to natural forces such
as wind and waves, if the canal feeds into a large waterbody such as the
ocean or a big lake. The assumption of complete mixing effected by the
bubble screen was investigated in the experiment described in Chapter 5.
WATER
SURFACE
AREAS OF BUBBLE SCREEN
LEAKANCE
4 1AOZZLE
AIR MANIFOLD
BED
7
Figure 4.3 The vertical flow field above the manifold.
FLOW
BED
IB
I CENTERLINE OF BUBBLE SCREEN
NOZZLE
AIR MANIFOLD
Figure 4.4 Proposed device for improvement of the efficiency of the
bubble screen.
T
8.85 s
j
FLO
S ULL
OF B
WATER
SURFACE
 I
IW
C
C_
F F
/ /
UTANT CONCENTRATION UPSTREAM
UBBLE SCREEN
POLLUTANT CONCENTRATION
OF BUBBLE SCREEN
I
CENTER OF
I BUBBLE SCREEN
I
A AIR MANIFOLD
DOWNSTREAM
BED
Figure 4.5 Influence of the bubble screen on the
suspended material.
distribution of
z/ I/ z, /' /, 77
41
The efficiency of the bubble screen is defined as the ratio of
the average concentration C to a reference concentration Ca at a depth
a. a is chosen according to where the maximum concentration is ex
pected.
The concentration distribution corresponding to a steady state
condition may be written as
s (ya)
= e s (4.10)
a
where as is the momentum transfer coefficient assumed equal to the mass
transfer coefficient. Hurst (1929) and Rouse (1938) showed by experi
ment that the distribution given by equation (4.10) is correct.
es was expressed by Elder (1947):
s = KVf (h y) (4.11)
where K is Karman's constant (K = 0.4).
Lane (1941) and Brown (1950) suggest to assume as to be constant
for engineering purposes.
vf h
s = V (4.12)
The average concentration C can be calculated from
vss (y a) 15
h dy (4.13)
C h f h
_a 0
Integration of (4.13) yields
15 v a
( ss
CVf e
a 15 ss
15 v
( ss)
Vf
[1 e
The friction velocity vf can be expressed in terms of the wall
Reynold's number Re,
Re* v
v 
f k
(4.15)
where v is the kinematic viscosity of water. For small grain sizes the
settling velocity vss can be expressed by Stoke's.law:
S2 Ps Pw
Vss s pg v
Introducing equations (4.15) and (4.16) into (4.14) yields
10 d,
(
T 3 Re* v w
S2 e
Ca 10 k ds2 g (Ps 
O k g (P5 )PW
l (e ds23ew
3 Re, v pw
[1 e
2
2 g ka (P P
2 )
w v Re. h
(4.17)
(4.14)
(4.16)
The dimensionless constant W is defined as
2
P v
W 2= (4.18)
ds kg (ps P)
Using this definition of W in equation (4.17) yields
(a3.33 a 33
(3.33 h Rw
hW Rwe e W Re*
S=0.3 W Re e [1 e ] (4.19)
a
In most cases the exponent (3.33 Re) is very small and the
corresponding term can be set equal to 1. With this assumption equation
(4.19) yields
3.33
= 0.3 W Re, [ e W Re* ] (4.20)
Ca
Figure 4.6 represents a family of curves which may be plotted by
use of equation (4.20). These curves allow evaluation of the change of
efficiency of the bubble screen for suspended load for a given case
(i.e. W = constant) for different flow conditions (i.e. Re, f constant).
If the exponent (3.33 ) has a too high value (> 0.01) it is
not possible to set the corresponding term equal .to unity anymore.
Therefore it is not possible to use the plotted curves based on equation
(4.20). In these cases equation (4.19) has to be used to calculate
the efficiency.
The Re* versus Wcurves.
Jul U M,
C LC
NkU
Figure 4.6 
D
II
o)
4
c
0
C
0
U0
Oin
r^
It is also possible to use equation (4.19) or (4.20) for materials
with a unit weight smaller than that of water. In such cases the
distance a must be measured from the surface (see Figure 4.7).
4.3 The Influence of the Bubble Screen on Floating Material
As mentioned in Chapter 2, the influence of the bubble screen on
floating material has been discussed by many authors. Kobus (1973)
discusses the use of the bubble screen to prevent oilspills. In his
thesis Pineros*(1981) investigated the influence of the surface velocity
and the depth of submergence on the.air discharge.
The equations for evaluating the air discharge are listed in
Chapter 2. The pressure at the pipe entrance pe is given by equation
(3.36).
4.4 Considerations for Designing a Bubble Screen
When a bubble screen is designed the decision has to be made
whether to design it according to the bedloadformula or the formula
for floating material. The decision is made after considering which
case is most important. Once this decision is made and the air dis
charge is calculated for one case the efficiency of the bubble screen
according to a BED or a maximum surface velocity, respectively, should
be evaluated.
When the bedloadcase is discussed for different types of particles
the different settling velocities have to be considered when using
equation (4.4). The distance L' (the length of a particle jump) has to
be kept within a reasonable magnitude. For sandgrains Einstein's
100 diameters criterion can be used. For a can this would lead into a
region which is outside the range of influence of the bubble screen.
*See also Appendix A.
WATER
SURFACE
a
SBED
//////////
Figure 4.7 Distribution of suspended material lighter than water.
Plotting BEDs for different types of bedload yields different re
sults for each case. Here it is possible, too, to set priorities for
the more important types of bedload. In Chapter 7 an example is dis
cussed which shows the use of the BED and the different design criteria.
CHAPTER 5
THE EXPERIMENT
To justify the assumption that a complete mixing of suspended
material is obtained by the bubble screen an experiment was done. It
was setup in the flume of the Hydraulic Laboratory at the University
of Florida. The flume is 2.44 m wide and 30 m long. The still water
depth was 0.5 m. At 0.10 m sl surface velocity the depth was 0.46 m
in the test section.
Measurements of velocity profiles in the flume showed that the
roughness is 5 104 m on the painted concrete surface and 5 107 m
on the galvanized steel plates. To increase the roughness a layer of
rocks was placed in the flume.. The average diameter was about 0.03 m.
Now the roughness was found to be 0.74 m on the average after a
distance of about 15 m downstream from the beginning of the flume.
This distance was needed to assure a fully developed velocity profile.
5.1 The Setup of the Experiment
The setup of the experiment is shown in Figures 5.1 and 5.2.
5.1.1 The Sediment
As sediment, silica powder was used. Silica powder is an arti
ficially grained material with a grain diameter of 4 105 m and a
settling velocity of 1.2 103 m s" at 200C. The unit weight is
25985.9 N m3 corresponding to a specific gravity of 2.65.
48
F.* ..
Figure 5.1 The setup of the experiment.
FLOW
SEDIMENT/WATER PUMP
MANIFOLD
BUBBLE SCREEN
*^^_^^
.MIXING TANK
PLATFORM
COMPRESSOR
ORIFICE
SEDIMENT
RELEASE
DEVICE
SAMPLING
DEVICE
AIRTIGHT
 PLEXIGLAS BOX
 VACUUM PUMP
PLATFORM
Figure 5.2 The setup of the experiment (not to scale).
a
According to equation (4.10), these qualities give a ratio be
tween the concentration at 90% depth and close to the bottom (a = 0.02 m)
of 1:1.74. The measurement of the concentration distribution profile
without the bubble screen in operation showed very good agreement with
the theoretical result (see Figure 5.3)
At first a material for which the difference between the concen
tration at 90% depth and close to the bottom is of at least one order of
magnitude was used. But the settling velocity of a material with the
appropriate qualities (e.g. fine sand with a grain diameter of 104 m)
was too high to keep it from settling in the experimental system. There
fore the silica powder was used.
5.1.2 The Sediment Release Device
The sedimentwater mixture was released at three locations across
the flume 1 m upstream of the bubble screen. At each location seven
tubings with the same diameter (4.8 103 m) and the same length
(0.90m) were mounted at depths determined according to the expected con
centration profile of the silica powder (see Figure 5.4, 5.5, 5.6, 5.7).
These tubings were connected to a manifold mounted about 0.35 m above the
water surface.
By this setup it is provided that the discharge in all tubings
is the same.
5.1.3 The Mixing Tank
To provide a constant discharge with a constant concentration of
the sediment water mixture throughout the time of the test a mixing
tank had to be designed. A tank with a volume of 415 liters was used.
The tank was made air tight except for an opening at the top
through which a PVCpipe was put. This pipe was mounted moveable to
/ WATER SURFACE
1.0.
0.9 
MEASURED PROFILE WITHOUT BUBBLE
SCREEN IN OPERATION
0.55
THEORETICAL DISTRIBUTION
PROFILE
0.25
0.08
0 CONCRETE SURFACE
0 0.5 1.0 1.5 C
0.08 d
Figure 5.3 Distribution of the suspended silica powder concentration.
IRON PIPE
Figure 5.4 The sediment release device (dimensions in mm).
CONCRETE
SURFACE
Figure 5.5 The sediment release device.
Figure'5.6 The setup of the sediment release device.
'Iy
'SI
.~.. .
6
.41
Figure 5.7 The sediment release device in operation.
adjust the head in the tank which is determined by the elevation of the
lower end of the PVCpipe.
Through that setup a pressure lower than the atmospheric pressure
is created above the water surface in the tank. At the lower end of the
PVCpipe the pressure equals the atmospheric pressure when water in the
tank is replaced by air entering through the PVC pipe. Thus the head and
therefore the discharge out of the tank stay constant as long as the water
surface is above the lower end of the PVCpipe (see Figure 5.8).
To keep the sediment in mixture a pump to circulate the sediment
water mixture'was installed. The discharge of the pump was 0.46 V/s.
The outlet of the pump was attached to a hose entering the tank at the
top as shown in the figure (Figure 5.8). Thus a vertical flow in the up
wards direction was created.
To make sure that mixing in the tank takes place as assumed the
tank was tested with different concentrations. Concentrations of 0.5 g
silica powder/l of water, 2.5 g/z, and 5.0 g/. were tried. The dis
charge was kept constant at 0.066 z/s. Samples were taken every 10
minutes over a period of 50 minutes. The concentrations of these samples
were compared with a fluorometer.
With the fluorometer it is possible to compare the different con
centrations by their turbidity. The results of these tests are shown in
Figure 5.9.
For a concentration of 5.0 g/z the change is less than 5% over a
50 minute time period. This concentration was used for the experiment.
5.1.4 The Sampling Device
The samples were taken at four locations across the flume 3 m
downstream of the bubblescreen. At each location four tubes were
ATMOSPHERIC PRESSURE
7
H
const.
TO SEDIMENT RELEASE
LL _DEVICE
WATER/SEDIMENT PUMP
Figure 5.8 The mixing tank (schematic).
Relative Concentration
1.0
S5 g/a
2.5 g/l
0.5 g/l
20
50 t[min]
Figure 5.9 Result of the test of the mixing tank.
1.5
0.5.
0
ICIII~ILCI
 
Figure 5.10 The sampling device.
Figure 5.11 The setup of the sampling device.
fixed at depths of 0.08 d, 0.25 d, 0.55 d, and 0.9 d. These tubes were
connected to glass probes in an airtight plexiglas box. With the aid
of a vacuum pump water samples were transferred into the glass probes.
The sampling device is shown in Figures 5.10 and 5.11.
The turbidities of these samples were determined by the fluorometer.
5.1.5 The Bubble Screen
For the bubble screen a PVCpipe of 0.0127 m diameter with holes
of 0.001 m diameter, 0.015 m apart was used. Theair was supplied by a
compressor. The air .discharge was monitored by an orifice which had
been built following the specification of the VDI for previous studies.
The discharge at atmospheric pressure is given by:
(10330 + 702.72 P1) /2
Q = 0.00549 (AH 29.3 (273 + T0 ) (5.1)
where AH is the difference in the manometer readings between both sides
of the orifice and is read in meters, P1 is the gage pressure in PSI,
and To is the temperature in OC.
5.2 The Result of the Experiment
For the experiment the surface velocity was kept constant at 0.10
m s1. The total air discharge was varied beginning with 1.1 2/s. With
a discharge smaller than 1.1 S/s the bubble screen was found to be
unstable. For every discharge three sets of data were collected.
Figures 5.14 through 5.17 show the distribution profiles at the
four locations across the flume which were obtained by averaging the three
sets of data. These profiles are compared with the induced profile.
Figure 5.12 The compressor.
ILi .B
Figure 5.13 The air discharge monitor.
Figure 5.14 The bubble screen in operation.
i ~
II 
( a'811
Q, = 0.0011 m3 s"
* induced profile
 x location 1
. C location 2
A location 3'
. location 4
Qa = 0.0012 m3 sl
C
0.08 d
o induced profile
 . x location 1
location 2
location 3
* o location 4
I I
C
0.08 d
Figure 5.15 Concentration distribution profiles.
0.5 +
Y
d
1.0.
0.54
_
I
Qa = 0.0013 m3 s1
a
a. ,
0.5
* induced profile
x location 1
o location 2
A location 3
o location 4
C
C0.08 d
Qa = 0.0014 m3 s1
a
induced profile
  location 1
 O location 2
 location 3
 o location 4
0.5 1.0 1.5 C
C0.08 d
Figure 5.16 Concentration distribution profiles.
d
1.0
0.5 4
d
1.0.
0.5+
I i i
Q, = 0.0015 m3 s"1
a
1.0 4.
0.5 4
0.5 1.0 1.5
0.5 1.0 1.5
 induced profile
location 1
 O location 2
 location 3
o location 4
C
C0.08 d
aQ = 0.0016 m3 s
 
induced profile
location 1
location 2
location 3
location 4
I
1.0
C
0.08 d
Figure 5.17 Concentration distribution profiles.
1.0+
0.5,
Q, = 0.0017 m3 s1
a
1.0+
iP I
! 'b
0.5
0.5
* induced profile
 x location 1
 O location 2
A location 3
... o location 4
C
CO.08 d
' 
Qa = 0.0022 m3 s1
a
1.0+
* induced profile
. location 1
O location 2
A location 3
o location 4
0 0.5 1.0 1.5 C
0.08 d
Figure 5.18 Concentration distribution profiles.
I 1
It can be seen that with increasing air discharge the profiles
resemble more and more an uniform distribution. This tendency is even
stronger when the average of all profiles across the flume is taken and
the result is plotted as shown in Figure 5.19.
For total discharges smaller than 1.5 2/s the distribution profile
of location #4 behaves quite irregularly. A reason for this might be
that this location is on the side of the bubble screen which is opposite
to the air supply. For small air discharges the screen is not stable at
the far end of the pipe. The irregularity of the flow conditions in
this region could cause the irregular shape of the concentration profiles.
5.3 Conclusions
N can be defined as the ratio of profiles with a change from bottom
to top of less than 20% to the number of profiles measured. If N is
plotted against the total air discharge or the rising velocity of the
bubbles a relationship can be seen. By linear regression a straight line
was found to represent this relationship. The correlation coefficient R
was found to be 0.89 (see Figure 5.20).
For N equal 0.75 the air discharge is slightly less than 1.5 z/s
which is in agreement with the test results described above. For this
number a rising velocity of 0.085ms is obtained. In Figure 5.21 the
vertical velocity is plotted against the depth of the water according to
equation (2.9) and the air discharge Qa is kept constant. When the
depth is increased to 4 m the rising velocity decreases by 10%. Using
the relationships plotted in Figure 5.20, it can be seen, that the
vertical velocity is not sufficient anymore to obtain a complete mixture.
Due to the limited depth of the flume, it is not possible to repeat
the experiment with greater depths. If a model scale of 1:5 is applied,
Profiles Compared to
Profiles
0.5+
0.5
* induced profile
x 0.0011 m3 s1 a'
O 0.0012 m3 s1 a'
A 0.0013 m3 s1 a'
o 0.0014 m3 s"1 a
* 0.0015 m3 s1 a'
A 0.0016 m3 s1 a'
* 0.0017 m3 s1 a'
1.5
average
average
average
average
average
average
average
C
0.08 d
Figure 5.19 Average concentration distribution profiles.
Average
Induced
Y.
d
1 .0
profile
profile
profile
profile
profile
profile
profile
I
1.0
/4
0.75
0.50
0.25
/I I
0.970 0.975 0.080 0.085 0.090 vy[m s1
Figure 5.20 Relationship between N and the rising velocity.
v [m s1]
0.090 
0.085 
0.080
0.075
0.070
Q = 9.14 106 m3 s"1
a
i n 2.0 3.0 4.0 h[m]
Figure 5.21 Relationship between the rising
for constant air discharge.
velocity and the depth
the surface velocity of 0.10 m s in the flume corresponds to a sur
face velocity of 0.22 m s in the field. This is a very high velocity.
Therefore it does not seem necessary to repeat the experiment with
higher surface velocities.
The total air discharge used in the experiment is much smaller
than the air discharge which is obtained by designing the screen for
keeping bedload from crossing. For the setup of the experiment the
difference is of about one order of magnitude. Thus the assumption
that a complete mixing is obtained by the bubble screen can be used to
describe the efficiency of the bubble screen as done in Chapter 4.
CHAPTER 6
A PROGRAM TO CALCULATE THE
AIRDISCHARGE Qa AND THE PRESSURE pe
In this chapter a program is presented to solve equation (4.4)
for the air discharge Q equation (4.1) for the efficiency Ebedload'
and equation (3.48) for the pressure at the manifold entrance pe.
The program was developed for the Texas Instruments TI59 with printer
PC10OC. After a short discussion of the setup of the program a
guideline for the use with sample printouts and a complete listing of
the program will be provided.
6.1 The Setup of the Program
The input of the data is assigned.to five different labels. To
each label a differentgroup of data is related. Label A is used to
store the data of the environment (i.e. water depth, density of water,
etc.), label A' for the data of the manifold, label C' for the data of
the nozzle and the bubble screen, label B' for the data of the sediment,
and label B for the air discharge. This setup allows one to very easily
vary different parameters and to compare the results. Label B is also
used to evaluate equations (4.4) and (4.1). Label C is used to solve
equation (3.45) while the labels D, 0', E, and E' are used for printer
routines.
6.2 The Use of the Program
First the data memory has to be repartitioned. This program
uses 30 memories and 718 steps. The necessary partition isachieved
by pressing 3 2nd Op 17. The display then should show 719.29.
The program is started by pressing label A (display 0.0000).
Now the data are put in in the following order:
f the environment:
Pa specific weight of air under atmo
3
[kg m]
pa atmospheric pressure [N m2]
pw specific weight of water [kg m3
h depth of submergence [m]
spheric pressure
Data of the manifold:
d diameter of the air manifold [m]
Z length of the manifold [m]
a energy coefficient
a' momentum coefficient
f' friction factor related to R
P
Data of the nozzle and the bubble screen:
a diameter of the nozzle [m]
d wall thickness of the manifold [m]
f' friction factor of the nozzle related to R
n
a energy coefficient
c, discharge factor defined by Kobus
Data c
s spacing of the nozzles
x ratio of the relative spread
B entrainment coefficient
Ay distance of the virtual source under the bed [m]
cb constant for the linearization of the centerline of the
bubble screen
Data for the sediment:
v settling velocity [m s ]
x closest horizontal distance from the bubble screen
(e.g. half a grain diameter [m]
L sum of L' and xb [m]
vH velocity of the surrounding water [m s ]
After all the data are entered, the program moves on to label B.
The air discharge Qa is entered and the efficiency of the bubble
screen Ebedload and the necessary pressure at the entrance of the mani
fold pe are calculated. The printout shows the air discharge Qa, the
efficiency AL/L, and the pressure pe. After the calculations, the
program moves again to label B. A sample printout may look like this:
QA (M3/S)
1.0005
AL/L
90.34
PE (ATM)
1.73
If the value
Qa is chosen
out then may
of pe is smaller than one atmosphere (this may happen if
too big), the printout shows: QA TOO BIG. A sample print
look like this:
QA
AL/L
(M3/S)
1.0003
98.37
QA TOO BIG
6.3 Listing of the Program
000 76 LBL 040 91 R/S
001 11 A 041 42 STO
002 01 1 042 07 07
003 32 X$T 043 91 R/S
004 25 CLR 044 42 STO
005 58 FIX 045 11 11
006 04 04 046 91 R/S
007 91 R/S 047 42 STO
008 42 STO 048 09 09
009 22 22 .049 91 R/S
010 91 R/S 050 42 STO
011 42 STO 051 10 10
012 23 23 052 91 R/S
013 91 R/S 053 42 STO
014 42 STO 054 08 08
015 00 00 055 91 R/S
016 91 R/S 056 42 STO
017 42 STO 057 16 16
018 01 01 058 91 R/S
019 16 A' 059 42 STO
020 76 LBL 060 12 12
021 16 A' 061 91 R/S
022 91 R/S 062 42 STO
023 42 STO 063 13 13
024 02 02 064 91 R/S
025 91 R/S 065 42 STO
026 42 STO 066 14 14
027 03 03 067 91 R/S
028 91 R/S 068 42 STO
029 42 STO 069 15 15
030 04 04 070 42 RCL
031 91 R/S 071 01 01
032 42 STO 072 55 +
033 05 05 073 01 1
034 91 R/S 074 00 0
035 42 STO 075 93
036 06 06 076 03 3
037 18 C' 077 03 3
038 76 LBL 078 85 +
039 18 C' 079 01 1
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
95
65 x
43 RCL
13 13
95 =
35 1/X
65 x
53 (
43 RCL
12 12
33 X2
85 +
01 1
54 )
34 /X
55 +
02 2
34 X
95 =
45 yx
93
03 3
03 3
65 x
02 2
93
01 1
02 2
04 4
02 2
95 =
42 STO
25 25
02 2
93
07 7
06 6
02 2
02 2
52 EE
05 5
65 x
43 RCL
05 05
65 x
43 RCL
03 03
33 X2
55 
43 RCL
02 02
45 yx
04 4
55 
134 43 RCL
135 16 16
136 33 X2
137 95 =
138 42 STO
139 26 26
140 01 1
141 93
142 08 8
143 04 4
144 01 1
145 05 5
146 52 EE
147 05 5
148 65 x
149 43 RCL
150 03 03
151 45 yX
152 03 3
153 65 x
154 43 RCL
155 06 06
156 55 +
157 43 RCL
158 02 02
159 45 yX
160 05 5
161 55 +
162 43 RCL
163 16 16
164 33 X2
165 95 =
166 42 STO
167 27 27
168 43 RCL
169 01 01
170 55 +
171 01 1
172 00 0
173 93
174 03 3
175 03 3
176 85 +
177 01 1
178 23 LNX
179 65 x
180 01 1
181 00 0
182 93
183 03 3
184 03 3
185 65 x
186 93
187 03 3
188 02 2
1
02 2
95 =
42 STO
29 29
61 GTO
17 B'
76 LBL
17 B'
25 CLR
91 R/S
42 STO
21 21
91 R/S
42 STO
17 17
91 R/S
42 STO
18 18
91 R/S
42 STO
19 19
61 GTO
12 B
76 LBL
12 B
98 ADV
25 CLR
91 R/S
42 .STO
20 20
22 INV
52 EE
71 SBR
15 E
01 1
85 +
06 6
03 3
93
06 6
03 3
65 x
43 RCL
15 15
95 =
65 x
43 RCL
25 25
65 x
43 RCL
20 20
45 yX
93
03 3.
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
03 3
75 
43 RCL
21 21
95 =
42 STO
12 12
35 1/X
65 x
53 (
43 RCL
01 01
75 
43 RCL
29 29
85 +
43 RCL
14 14
54
42 STO
13 13
85 +
06 6
03 3
93
06 6
03 3
65 x
43 RCL
25 25
65 x
43 RCL
20 20
45 yX
93
03 3
03 3
65 x
43 RCL
17 17
55 
43 RCL
12 12
33 X2
65 x
53 (
43 RCL
12 12
35 1/X
43 RCL
13 13
55 +
06 6
03 3
297 93
298 06 6
299 03 3
300 55 +
301 43 RCL
302 25 25
303 55 t
304 43 RCL
305 20 20
306 45 yx
307 93
308 03 3
309 03 3
310 55 
311 43 RCL
312 17 17
313 75 
314 01 1
315 54 )
316 23 LNX
317 95 =
318 22 INV
319 52 EE
320 58 FIX
321 02 02
322 94 +/
323 85 +
324 43 RCL
325 18 18
326 55 4
327 43 RCL
328 19 19
329 95 =
330 65 x
331 43 RCL
332 19 19
333 95 =
334 55 +
335 43 RCL
336 18 18
337 65 x
338 01 1
339 00 0
340 00 0
341 95 =
342 42 STO
343 24 24
344 71 SBR
345 14 D
346 61 GTO
347 13 C
348 76 LBL
349 13 C
350 01 1
351 75 
352 43 RCL
353 22 22
354 55 4
355 43 RCL
356 23 23
357 65 x
358 43 RCL
359 10 10
360 65 x
361 43 RCL
362 25 25
363 33 X2
364 65 x
365 43 RCL
366 20 20
367 45 yx
368 93 .
369 06 6
370 06 6
371 75 
372 43 RCL
373 22 22
374 55 +
375 43 RCL
376 23 23
377 55 +
378 02 2
379 65 x
380 53 (
381 01 1
382 93
383 06 6
384 02 2
385 01 1
386 65 x
387 43 RCL
388 24 24
389 65 x
390 43 RCL
391 20 20
392 33 X2
393 55
394 43 RCL
395 07 07
396 45 yX
397 04 4
398 55
399 43 RCL
400 08 08
401 33 X2
402 85 +
403 06 6
404 93
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
45
452
453
454
455
456
457
458
04 4
08 8
05 5
65 x
43 RCL
09 09
65 x
43 RCL
20 20
33 X2
65 x
43 RCL
11 11
55 +
43 RCL
08 08
33 X2
55 z
43 RCL
07 07
45 yX
05 5
85 +
53 (
01 1
93
02 2
07 7
03 3
02 2
65 x
43 RCL
20 20
55 
43 RCL
07 07
33 X2
55 +
43 RCL
08 08
75 
43 RCL
25 25
65 x
43 RCL
20 20
45 yx
93 .
03 3
03 3
54 )
33 X2
54
95 =
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
48
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
42 STO
28 28
65 x
03 3
93
02 2
04 4
02 2
65 x
43 RCL
22 22
65 x
43 RCL
23 23
65 x
43 RCL
20 20
33 X2
55 +
43 RCL
07 07
45 yx
04 4
55
43 RCL
08 08
33 X2
75 
06 8
33 X2
75 
53 (
01 1
00 0
93
03 3
03 3
85 +
43 RCL
01 01
54 )
33 X2
65 .x
09 9
06 6
93
01 1
05 5
07 7
06 6
65 x
43 RCL
00 00
33 X2
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
56
562
563
564
95
94 +/
34 vX
85 +
53 (
01 1
00 0
93
03 3
03 3
85 +
43 RCL
01 01
54
65 x
09 9
93
08 8
00 0
06 6
65 x
43 RCL
00 00
95 =
55 
02 2
55 
43 RCL
28 28
95 =
33 X2
75 
43 RCL
26 26
65 x
43 RCL
20 20
33 X2
85 +
43 RCL
27 27
65 x
43 RCL
20 20
33 X2
85 +
93
01 1
04 4
08 8
01 1
65 x
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
'585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
43 RCL
26 26
45 yX
03 3
55 +
43 RCL.
27 27
33 X2
65 x
43 RCL
20 20
33 X2
95 =
34 /X
55 "
43 RCL
23 23
95 =
22 INV
77 GE
10 E'
42 STO
24 24
71 SBR
19 D'
61 GTO
12 B
76 LBL
14 D
69 OP
00 00
00 0
00 0
07 7
05 5
02 2
07 7
06 6
03 3
02 2
07 7
69 OP
01 01
69 OP
05 05
43 RCL
24 24
99 PRT
92 RTN
76 LBL
19 D'
00 0
00 0
03 3
619 03 3 .673 06 6
620 01 1 674 00 0
621 07 7 675 00 0
622 00 0 676 00 0
623 00 0 677 00 0
624 00 0 678 00 0
625 00 0 679 00 0
626 69 OP 680 00 0
627 01 01 681 00 0
628 05 5 682 69 OP
629 05 5 683 03 03
630 01 1 684 69 OP
631 03 3 685 05 05
632 03 3 686 52 EE
633 07 7 687 43 RCL
634 03 3 688 20 20
635 00 0 689 58 FIX
636 05 5 690 02 02
637 06 6 691 99 PRT
638 69 OP 692 92 RTN
639 02 02 693 76 LBL
640 69 OP 694 10 E'
641 05 05 695 98 ADV
642 43 RCL 696 03 3
643 24 24 697 04 4
644 99 PRT 698 01 1
645 92 RTN 699 03 3
646 76 LBN 700 00 0
647 15 E 701 00 0
648 00 0 702 03 3
649 00 0 703 07 7
650 03 3 704 03 3
651 04 4 705 02 2
652 01 1 706 69 OP
653 03 3 707 01 01
654 00 0 708 01 1
655 00 0 709 04 4
656 00 0 710 02 2
657 00 0 711 04 4
658 69 OP 712 02 2
659 01 01 713 02 2
660 05 5 714 69 OP
661 05 5 715 02 02
662 02 3 716 69 OP
663 00 0 717 05 05
664 00 0 713 12 B
665 04 4
666 06 6
667 03 3
668 03 3
669 06 6
670 69 OP
671 02 02
672 05 5
CHAPTER 7
EXAMPLE MARINA I
(A Guide to Use the Formula)
In this chapter an example for the use of the formula which were
developed in the previous chapters is presented. Marina I is arbitrary.
The shape of the marina is shown in Figure 7.1.
The tidal period was chosen to be 12.42 hr and the tidal ampli
tude aT = 0.20 m. These are common values for coastal Florida.
The bed roughness k was set to 0.25 m. It is assumed that there
are no other than the tidal induced velocities.
The material for the pipe was chosen to be PVC. The kvalue is
1.5 105 m. The energy coefficient a is assumed to equal 1. Thus
the momentum coefficient a' is equal to 1 also. The diameter of the
nozzles 6 is 0.001 m.
7.1 The Pipe Diameter d
The pipe diameter d is calculated by using equation (3.29) and an
equation for the friction factor f' in the rough range (i.e. Re' > 580,
Re, > 70).
1.171 + log k (7.1)
4
When equation (3.29) is introduced into (7.1) the result is
PLAN VIEW
15 m
e 150 m I
CROSS SECTION OF T
AIR MANIFOLD
*HE CANAL
WATER SURFACE
15 m
Figure 7.1 Layout of Marina I.
250 m
I
T
4.0 m
i
= 0.643 + 1.131 log10 d (7.2)
This equation can be solved by iteration. Using the given data equation
(7.2) gives
d = 0.05 m
The friction factor f' is found from equation (7.1)
f' = 0.0037
The value for f' satisfies equation (3.35).
7.2 The Spacing of the Nozzles
The distance between the nozzles is selected as 0.10 m. As ex
plained in 3.2, it has to be checked if this assumption is sufficient.
Equation (3.1) solved for b yields
b = 0.226 (y + Ay) = 0.226 4.0 = 0.904 (Ay = 0)
For a point halfway between the last two nozzles (x = 0.05 m) equation
(3.11) yields
2 2 2
40(0.10 ) 0.10 0.30
vv 40(04i.,) 40(0 90) 40(0.90 )
vv e 0. + e 0.904 + e
vmax
v
z . = 0.61 + 0.61 + 0.01 = 1.23 > 1.0
v
max
Thus the spacing is sufficient.
7.3 The Shape of the Centerline of the Bubble Screen
As explained in 3.1.2, the shape of the centerline of the bubble
screen in flowing water is approximated by a straight line.
The maximum horizontal flow velocity induced by the tide is given
by
Marina 2r (7
H A T T
Hmax Acanal T
whereAmarina and A canal are the surface area of the marina and the
cross section area of the canal, respectively. With the given data we
get
150 250 2n 1
v 150 250 27r 0.2 = 0.018 m s1
Hmax 15.4 12.41 3600 2 018
Assuming that Manning's power formula can be used, the friction
velocity vf is calculated
Hma
vf mx R0.16
f M
where M is written as
,.8.25 /( 8.25 t/Wi06' ,
M = 8.25 = 8.25 V7 = 32.55
k/6 0.251/6
and R is written as
S15 (4 + 0.1) 2
15 + 2 (4 + 0.1)
With the values for M and R, vf is evaluated
S=0.018 2.650.6 = 0.0015 m 1
To check the assumption that using Manning's power formula was
right the Reynolds' number and the ratio R/k are calculated
Re f k =0.0015 0.25 343.09 > 70
v 1.093 106
R 2.65
k 2.65. 10.6 > 4.32
Thus the assumption was correct.
To evaluate the vertical velocity induced by the bubble screen
vmax, an air discharge has to be estimated. Qa is assumed to be in the
4 3 1
order of magnitude of 10 m s This assumption has to be checked
after the required air discharge is evaluated. As suggested by Tekeli
and Maxwell (1970, 1974) x is 0.2 and 6 is 0.1. With these values
equation (2.9) yields
v +0.2 )1/6 [0.1 (1 + T0 )11/3 1/3 i04/3
max
= 0.172 m s1
The average vertical velocity vv can be calculated from equation
(2.8) using () = 0.15.
