FUNCTIONING AND SIZING OF AIR VALVES
By Luís M.M. da Silveira e Silva
Abstract: The three main functions of
1
air valves in water supply pipelines
are: I) air release under pressure, II) air admission during vacuum
conditions, and III) release of large amounts of air during filling. In the
present paper, they are presented
the two basic types of air valves (small
orifice and large orifice), analyzed the fundaments of their functioning
and reviewed the usual location criteria. They are established general
formulas for the flow of air through orifices (isentropic flow) which can
be used to pre-size any air valve. Finally it is presented a detailed
discussion concerning Function I air valves; topics include air inception,
air release from flow, removal of air by water flow and pratical sizing
criteria.
--------------------------------------------
1
Civil Engineer, Hydraulics and Water Resources Specialist
COBA SA, Av. 5 Outubro,323. 1600-Lisboa. Portugal. 1996
Key words: Air valves, air removing, air release, isentropic flow, pipeline
design
INTRODUCTION
Air in pressure pipelines is known to be a potential source of
problems particularly if it comes out of solution and forms air pockets.
Obviously, the best way to avoid air in a pipe is to avoid its entry trough
careful design and proper operation of the systems; however the world is
not perfect and as stated by Lescovitch (1972), “air can enter a pipeline
in many insidious ways”.
In the other hand, as reported by Wisner et al.
(1975) the velocities required to hydraulically clear out all air-pockets,
are too high, and consequently uneconomical, to be recommended. For these
reasons mechanical venting is normally adopted, being air valves are the
most popular choice.
The present paper addresses some key questions concerning the role,
location and sizing of air valves in water supply systems, and in
particular along the profile of transmission pipelines.
The presentation starts with the basic functions of air valves in a
water system, functioning principles,
main types of
air valves, and the
laws of air flow through orifices, whose knowledge is essential to
correctly size these devices. A brief vocabulary, with some of the most
common designations is presented.
It follows a summary of the usual criteria for the location of a
these valves according with the function of the air valve.
In the final part it is presented a detailed discussion concerning
the location and dimensioning criteria of the so-called Functions I air
valves, i.e. valves to purge small air volumes released from the line. The
focus of the discussion is directed to air inception, air conservation and
to the mechanism of air release from a saturated air-water solution.
FUNCTIONS
The three basic functions of air valves in a pressure system are:
I.
air release at service pressure
II.
air admittance under vacuum conditions at atmospheric pressure (vacuum
breaker)
III. release of large amounts of air at atmospheric pressure
Air release under pressure corresponds to the purging of small
amounts air which came out from solution as a
result of a reduction of
the air solubility capacity of water, or a decrease of the hydraulic
carrying capacity of air in the form of bubbles released earlier.
Admission of large amounts of air at atmospheric pressure is done to
avoid vacuum conditions (as for example, during the draining of the
pipeline), or to impose a fixed pressure condition in a certain section of
the line (as for instance, in a transition of pressure flow to free surface
flow). Vacuum impose a significant underpressure (given by the difference
between atmospheric and vapor pressure) which may lead to the pipe rupture,
loss of ability due to excessive strain and sucking of joints,
deterioration of interior lining and contamination by impurities or
contaminated groundwater.
Exhaustion of large amounts air at atmospheric pressure occurs during
the pressurization of a line in the sequence of a previous
depressurization. The most typical example is the filling of a line.
The main difference between Functions I and III, concerns the
pressure at which air is exhausted and not the absolute magnitude of air
flow-rate; in fact as it will be seen below, air valves intended for
Function III are not able to deaerate flow under pressure.
FUNCTIONING PRINCIPLES
The basic functioning principle of a classic air release valve is
buoyancy.
In the figure below are represented the forces that act over the
float of a simple non-guided air release valve; for simplicity they are
neglected interaction between air ant the float and inertia forces
(relevant in unsteady flows).
Fig. 1- Simple air release valve
For the air valve to function it is necessary that the apparent
weight (total weight minus buoyancy) overcomes the resultant of pressure
forces caused by the difference between interior pressure and outside
atmospheric pressure; i.e.:
V (gf - gw m) > (p - patm) Ao
(1)
in which m is the immerse fraction of the float (immerse volume divided by
total volume, 0 m  1) and Ao the area of orifice
Dividing by gw and rearranging (1), one obtains:
m <
df - hw Ao/ V
(2)
in which hw= (p - patm) /gw, is the piezometric height (pressure head in
mwc) and df= gf /gw, é a the relative float density.
For a given air valve, df, Ao e V are fixed data. The right member of
(2) depends only of
hw as indicated in Fig. 2.
Fig. 2- Zone of operation of a Function I air valve
The completely emerged condition of the float (m=0) is obtained for:
hcol = V df /Ao
(3)
This pressure head is designated by gluing pressure and it represents
the maximum possible operating pressure for a given air valve; for
operating pressures bigger than that value, the float is unable to descend,
being compressed (glued) against the orifice.
The Figure illustrates the classical solutions to extend the
operating region:
− augmenting
df - limited improvements, since its is convenient to have d f
< 1;
− augmenting
V - used by some manufacturers (e.g. GEC (1978)) but not by
the majority since it leads to an increase of the overall dimensions of
the valve;
− reducing Ao - the most common solution, which however implies a decrease
in the venting capacity
Supposing for example a spherical float 100 mm diameter and df= 0.9;
for a maximum pressure head of 100 m (10 bar), the orifice diameter must
be smaller than 4 mm.
It is not therefore difficult to conclude that the evacuation of
large amount of air as in Function III, requiring large venting areas,
is
not compatible with the purging under pressure which imposes relatively
small venting areas.
For these reasons there are
normally two basic types of air valves:
− small orifice ones, intended for Function I, with areas calibrated for
the water line pressure, governed by buoyancy.
− large orifice ones, intended for Functions II and/or III, functioning
with pressures near the atmospheric pressure, governed by the laws of
flow of air trough orifices
For the large orifice valves buoyancy is used, but only to close the
valve after the complete exhaustion of air. In fact, in order to prevent
valve to blow shut, the valve is designed so that the float is kept outside
of
air draft, or that, the resultant of aerodynamic forces of escaping air
maintain the valve open (aero-kinetic principle, Lescovitch, 1972).
Air-valve opening is achieved by pressure difference the very same
way as a classic check valve.
AIR FLOW TROUGH ORIFICES
The isentropic flow of air trough orifices is governed by the
following equations (Wylie & Streeter, 1978):
− Air entry. Subsonic regime:

 p
'
m = CdiAi 7p00   
  p0 

with
1.4286
p0 > p > 0.53 p0
 p

 po 
−
1.714



(4)
− Air entry. Sonic or critical regime :
−
'
m =C
0.686
with
p < 0.53 p0
diAi
RT0
p0
(5)
− Air outlet. Subsonic regime:
  p 1.4286  p 1.714

m' = Cdo Ao 7p   0 
−  0

p
p




with
p0 /0.53 > p > p0
(6)
− Air outlet. Sonic or critical regime:
−
0.686
m' = CdoAo
p
RT0
with
p > p0 / 0.53
(7)
in which m’ is the mass flow-rate of air. Considering m’=  Qar and the gas
state equation p/ = RT, the above equations can be transformed and
expressed only in terms of the volumetric flow-rate of air referred to the
interior pipe conditions, Qar. Introducing
p’= p/p0 , and assuming p0 
1 bar = 105 Pa, T 10 ºC= 283 K; T0  20 ºC= 293 K, the following equations
are obtained:
− Air entry. Sonic or critical regime :
Qar = 754CdiA i
with
p'1.4286 − p'1.714
p'
1 > p’ > 0.53
− Air entry. Sonic or critical regime :
(8)
Qar =
with
195CdiAi
p'
p’ < 0.53
(9)
− Air outlet. Subsonic regime:
Qar = 754CdoAo (1/p' )
1.4286
with
− (1/p')
1.714
1 / 0.53 > p’ > 1
(10)
− Air outlet. Sonic or critical regime:
Qar = 195 Cdo Ao
with
p’ > 1 / 0.53
(11)
Fig. 3 presents the graphical plot
Qar / Cdi Ai or Qar / Cdo Ao versus p’
correspondent to the above equations. The plot is completely general and
may be used to pre-dimension any air valve.
Fig. 3- Air flow trough orifices
Example 1: Pre-dimension an air valve to admit 1.5 m3/s of air (air
flow referred to pipe interior conditions) with a maximum vacuum head of
3 mwc. Supposing p0= 10 mwc, one has p= 7 mwc and p’= 0.7. From Fig. 3 (or
equation 4.5, valid for subsonic air inlet), Qar / Cdi Ai, = 260 m/s.
Assuming Cdi = 0.6 one calculates
equivalent to an orifice 111 mm
Ai = 1.5/ 260/ 0.6 = 0.0096 m2, which is
diameter.
As a rule, air valves manufacturers present in their catalogues
dimensioning graphs or formulas relating air flows
with pressure (gauge or
absolute). These abacus or formulas take into account the particular
characteristics of each valve and should always be preferred for the final
dimensioning. It is however important to note that volumetric flow-rates
presented in the catalogues are normally referred to standard atmospheric
conditions and for this reason they cannot used straightforward in the
dimensioning. Designating Qar
atm
the volumetric flow-rate at standard
atmospheric conditions, and Qar air flow-rate at pipe conditions (Note: Qar=
Qwater), the continuity gives:
Qar= Qar
atm
p0/p
T0/T
(12)
I.e., standard atmospheric air flow-rates have to be multiplied by:
p0/p T0/T p0/p= 1/p’
to get air flow-rates referred to interior pipe
conditions.
CLASSIFICATION AND USUAL TYPES
In the technical literature multiple classifications and designations
of air valves can be found. Very frequently they are hybrid designations
which mix construction characteristics (point of view of the manufacturer)
with function (point of view of the user).
This non-uniformity is closely associated technological progress,
which has produced in the last years
many different designs, combining the
same valve, functions and operating principles very different. It is
therefore very difficult, and most probably useless, to conceive an unique
classification.
Nevertheless, for the sake of clarity, it is recommended that
function (or functions) of the apparatus should be always indicated.
Some examples of currently used designations are given below:
− Small orifice air valve, basic type defined above, primarily intended
for Function I
− Small orifice air valve. basic type defined above, intended for
Functions II and/or III
− Simple effect air valve, normally, Function I
− Double effect air valve, hybrid designation to be avoided. Normally it
refers to large orifice air valves previewed Functions II and/or III;
some other times it designates double air valves, for triple function
− Triple function air valve, valve performing functions I, II and III.
− Double air valve, apparatus composed by two air valves, a small orifice
one, and a large orifice one, in a single body. It is the most popular
type of triple function air valve.
− Combined air valve, usually it is a double air valve. There are however
some manufacturers that use this name to designate valves with a single
float which drives a nozzle, or as in some other designs, a membrane,
which in its ascending movement, shut different venting areas. As a rule
they are triple function air valve
− Piloted air valves. Usually globe or angle regular valves, piloted by a
small orifice air-valve. They are normally used as triple function
valves in special conditions such as high air flows and/or very high
pressures.
− Air inlet valves, ordinary or specially profiled check valve which only
let air in (Function II air valves).
AIR VALVE LOCATION
Most of the authors agree that air valves should be located in the
following points along the pipeline profile (cf. Fig. 3):
a) peaks
b) upstream of isolating valves in ascending stretches
c) downstream of isolating valves in descending stretches
d) points of sharp decrease in slope in ascending stretches
e) points of sharp increase in slope in descending stretches
Fig. 4-Air valves location along pipe profile
In addition, some authors, recommend to place double air valves
(i.e., triple function) every 500 m to 1000 m (Lescovitch, 1972).
Stephenson (1981) does this very same recommendation but without specifying
the type of valve.
Triple function air valves are normally recommended at peaks.
Lescovitch (1972), indicates that peak should be referred to the hydraulic
grade line rather than horizontal; Stephenson (1981), goes further and
defines peaks relative to both lines- horizontal and hydraulic grade.
Points b) and c) are particular cases of peaks; they are so when the
isolating valve is closed. In these points recommendations are - triple
function air valves (Stephenson, 1981), or, more simply - air valves for
Functions II and III (Cary, 1992).
For points d) and e) recommendations vary between small orifice air
valves for Functions I (Lescovitch 1972, Stephenson 1981), to large orifice
air valve Functions II and III (Cary, 1992).
Some manufacturers (e.g. A.R.I., 1990), recommend to install air
valves at all
changes in slope, including low points.
Bedsides aforementioned points, concerning the pipeline profile, air
valves are usually recommended in the following points:
− downstream of pumps
− downstream of regulating valves and controlling diaphragms
− upstream of convergents or diaphragms
− upstream of meters
Obviously placement and types of air valves depend of assumed
criteria. For example, if one admits that vacuum is not a problem, it is
possible to dispense Function II air valves at points d) and e); further,
if it is considered that there will not be any release or significant
accumulation of air at those points, one may avoid to install any air valve
there. On the other hand, in a very long stretch with a slope near the
hydraulic gradient, it may be necessary to place air valves at regular
intervals.
In the next section, there shall be refined criteria concerning the
Function I air valves.
DIMENSIONING FUNCTIONS I AIR VALVES
Usual Criteria
The most common criterion for sizing air release valves is due to
Lescovitch (1972), which considers an air flow-rate of 2 % of water flow
rate at atmospheric pressure. The 2 % value is proposed by this author as
the normal solubility coefficient of air on water, which ranges between 1.5
% at 30 ºC to 2.9 % at 0 ºC.
One immediate criticism of this criterion is that it does not take
into account the number of air valves. For example, systems on Fig. 5 would
have similar air flows per valve.
Fig. 5. Identical systems with different number of air valves
Pont à Mousson (1990), presents an example of calculation of an air
release valve, where it is introduced the concept of pressure reduction
along the path. The example considers a pumping main, 2036 m3/h water flow,
11 bar absolute pressure at an initial section (where it is implicitly
assumed water is air saturated) and a 1.75 bar pressure decrease between
the said initial point and the point where the air valve is placed.
Admitting a solubility coefficient C= 0.0252, released gas flow-rate is
given by:
−
0.0252 x 1.75 / (11-1.75) x 2036 =
9.7 m3/h.
It is noticeable that only 19 % of all potentially soluble air is
released in the aforementioned air valve (potentially soluble air is
2.52 % x 2036 m3/h= 51 m3/h).
Denoting with subscript 1 the initial section and the air valve
section with subscript 2, the generalization of the reasoning gives the
following equation (Note: valid for constant temperature):
Qar
released
=
C
(p1 -p2) / p2
Qw
(13)
On the cited reference it is not given any indication concerning the
way to implement the methodology in a real system (either a pumping system
or gravity) with several air valves.
Cary (1992) proposes for pumping mains an equation similar to (13),
but divided by a reduction coefficient which can assume values 1, 2 or 3,
depending on the number of neighboring air valves near the point under
consideration. For this author p1 represents the pressure at the first
section of
the line (discharge flange of the pump).
To compare above criteria, one must convert first air flow from
Lescovitch criterion which refers to standard atmospheric conditions to
interior pipe conditions; denoting p0
the atmospheric pressure and p2 the
pressure at the section containing the air valve, the Lescovitch criterion
is given by:
Qar
released
=
0.02
p 0 / p2
Qw
(14)
Assuming a solubility coefficient C= 0.02, one can see that (14)
coincides with (13) for p1 - p2 = p0 .
Air Release
Equation (13) may be easily demonstrated
applying Henry’s law and
the continuity principle to the air mass between two arbitrary sections 1
and 2, as follows:
− Assumed existing air mass at section 1= C Qw p1 / (RT1)
(Air dissolved
assuming saturation)
− Existing air mass at section 2 = Existing air mass at section 1 (steady
flow)
− Dissolved air mass at section 2
= C Qw p2 / (RT2) (Air dissolved assuming
saturation)
Released air at section 2 is given by the difference between total
air mass constant) and dissolved air mass, i.e.:
Qar
released 2
=
C Qw (p1 T2/T1 - p2) /p2
(15)
Note that (15) transforms itself in (13) for constant temperature.
Coherence with the continuity principle requires that equation (15 or
16) is recurrent; i.e., the amount of air available to be discharged on the
further downstream air valves is the one that is maintained dissolved at
pressure p2.
On the other hand, if pressure increases (p2 > p1 ) one would have
from (15) (Qar < 0); i.e., air will not release. More precisely, for air to
release in a given vent it is necessary that the elevation at that vent is
higher than the highest elevation of all upstream air valves, as
illustrated on Fig. 6.
Fig. 6. Differentiated air release along pipe profile
Generalization of
equation (15), assuming constant temperature,
gives:
Qar j= Qw
C
(pm -pj) / pj
with
pm >pj ;
pm= min{p1, p2 ... pj-1}
(16)
where j denotes the section with the air valve under analyis and m the
section uspstream with the smallest absolute pressure.
Note: It is assumed in the present derivation that the only existing
air is dissolved and that each air valve is adequately sized to exhaust all
incoming free and/or released air; if that does not happen and flow-rate is
able to hydraulically drag air downstream and/or reabsorb it, this same
air, or part of it, will be available to be released in the next air
valves, which, incidentally, may be situated at lower elevations.
Criticism of Usual Criteria. Sources of Air
Referred criteria assume that air to be exhausted is air that
saturates water at a given pressure, forgetting the obvious fact that air
valves can only vent air previously existent an that there is not air
creation by the simple fact of raising the pressure.
Usual sources of air within water supply systems are:
i) vortices at reservoirs and intakes
ii)deficient sealing in pump glands or pipe joints in systems with negative
gauge pressures
(e.g. suction pipes)
iii)localized depressions originating sub-atmospheric pressures, as for
instance, downstream of near closed constrained regulating valves
iv)low pressures arising from bad layout design, or too low operating flows
compared with the design capacity of the pipeline. This last situation
is very typical of gravity systems underfed from upstream
v) remaining air not totally removed during a previous filling operation
vi)negative gauge pressure transients due to waterhammer phenomena (pump
stoppage, rapid valve closure, etc.)
vii)temperature raise along the line
viii)free fall and/or hydraulic jump, in dissipating energy devices,
breaking tanks, reservoir arrivals, etc.
ix)deliberated air injection for anti-cavitation protection or as a mean of
alleviating waterhammer overpressures.
Besides air from source v) and, sometimes vi) and vii), which will
always be present in a pipeline (however not for long), it can be stated
that in most cases, a pipeline correctly designed, built and operated, will
not release air along its extent.
The amount of air a pipeline carries coincides with the mass amount
of air contained at the departure reservoir; i.e., approx. 2 % at
atmospheric pressure, and this will not be released unless pipe is subject
to vacuum or temperature raises.
On the other hand, other sources such as i) and ii), point to
situations where large amounts of air can be entrained, eventually
overcoming the solubility capacity and originating an over-saturated flow.
In the case of vortex at intakes, Lescovitch (1972) and Pont à
Mousson (1990) refer air flow-rates from 5 to 10 %, in volume, of water
flow-rate.
For hydraulic jumps, the U.S. Army Corps of Engineers (1966) presents
the following envelope formula:
max = 0.03 (Fr -1)
1.06
(17)
in which Fr, is the Froude number upstream of upstream supercritical flow
(Fr > 1) and  the gas fraction given by
Qar/Qw.
Example: Let there be a pipeline D= 1 m, Qw= 1m3/s, i= 5 %,
rug= 0.3 mm. For uniform supercritical flow: y= 0.28 m, V= 5.6 m/s, Fr= 4,
from where one obtains max 0.1; meaning that the jump may entrain an
airflow of about 10 % of liquid flow.
Depending on particular conditions air-flows up to 40 % of liquid
flow are possible.
In short it is necessary to analyze each case with the necessary
precautions in order to identify and quantify possible air sources.
Hydraulic Removal of Air
Another important aspect to be taken into consideration, is the
capacity of the flow to remove (clear) by itself
bubbles or air pockets
that they may raise or accumulate in certain sections of the pipeline,
provided velocity is high enough.
A comprehensive analysis of this problem is presented by Wisner et
al., (1975), who present the following envelope for the minimum clearing
velocity, Vc , of air pockets:
Vc/ (g D)1/2 = 0.25 sin1/2  + 0.825
in which
(18)
 is the pipe angle with the horizontal in a descendent reach.
Table 1 shows the resolution of such an expression for some typical
values.
TABLE 1: Air Clearing Velocity, Vc (m/s)
Data from some other authors suggest that the influence of slope on
the clearing velocity is stronger. However it is noted that the above
expression is an envelope formula and not a functional relationship.
Summary. Proposed Criteria
Air valves for Functions I must be installed:
− in special systems (e.g. pipelines with alternating stretches free flow/
pressure flow; pipelines with flow or pressure regulating valves and
energy dissipators; pipelines with air injecting devices or Function II
air valves, for cavitation control; pipelines subject to temperature
gradients or local variations)
− in badly conceived or operated systems subject to transient or permanent
depressurizations, vortexes and insufficient submergence at sumps and
intakes, unexpected temperature variations
− to prevent situations arising from accidents and aging of the materials
that may ultimately lead to air ingestion and subsequent release (e.g.,
ruptures, corrosion holes, loss of sealing ability in pumps and suction
pipes)
− as a means to control airflow and ensure complete air exhaustion in the
case of usage of Function II air valves for waterhammer protection
However in the majority of the cases, there will not be big needs for
Functions I air valves. The feeling that these devices do not work
properly, may well result from the very simple fact that, usually, there is
not air to exhaust.
One of the exceptions to this rule is the remaining air not totally
removed by Function III air valves during a previous filling operation.
This situation justifies per si the need of air valves at all peaks.
An aspect which has deserved little attention in the technical
literature so far, is the mechanism of air release. Air release is due to
the diminishing of the solubility capacity of the water caused by a
reduction of pressure or a raise in the temperature. The analysis of the
mechanism of air liberation, together with the continuity equation, shows
that, theoretically, the only effective air valves are the ones placed in
peaks which are higher than the preceding highest peak, counting from the
point of air inception; air valves in intermediate peaks or downstream of
the highest peak will not release air.
Still, one should bear in mind that not all air that may be present
is dissolved an that there is a strong (and complex) interaction between
air and water flows. It is therefore possible that air may be dragged by
flow and accumulate at an intermediate peak, or some other, quite far from
the point of inception.
In short, it is recommended to install function air valves in all
peaks relative to hydraulic grade line and horizontal line. Except for
special cases it is not necessary to install air valves in the middle of
ascending stretches.
To determine air release flows it is proposed to adopt the Lescovitch
(1972) criterion, which gives sensible results, in spite its physical
background is doubtful.
Air sizing flows must be raised in cases where there is evidence of
significant air production/ inception, specially for the dimensioning of
the air valves nearer the air source. In these cases equations (15) or
(16) or a more comprehensive model considering both advection and air
absorption, could be used for a more precise evaluation.
Selection of air release valves shall be done taking into account air
flows and pressure. In systems where static pressure is very different from
service(s) pressure(s) there may be a need of installing two sets of air
release valves in the same profile, with different operating pressures.
CONCLUSIONS
Basic air valves types have been presented and the principles of
operation discussed. It is proposed to class air valves according to its
function on a water supply system, viz. I)- small volume air release, II)
large volume air inlet, and III) large volume air outlet valves.
Functions I air valves are usually small orifice valves and they
function according to the buoyancy principle. The analysis of the factors
governing the equilibrium of the buoyant body explained why the size of
orifices decrease with the pressure and the existence of
a limiting
pressure beyond which the air release valve is unable to function.
Function II and III air valves are large orifice ones and its
functioning is governed by air flow laws trough orifices. In the paper they
are presented the isentropic flow laws concerning air mass and they are
deduced general expressions relating volumetric air flow-rate referred to
inside pipe conditions with pressure and orifice area; these expressions
can be used to pre-dimension any air valve.
Principal rules for placement of air valves in a water supply systems
were reviewed; these cover function I, II and III air valves.
In the last section of the paper it is presented a detailed
discussion concerning criteria for sizing Functions I air valves. Focus has
been directed to the concepts of
“generation” and “conservation” to
conclude that in most of the cases there will not be significant air flows
to purge; still some situations have been identified that may lead to air
release flows bigger than those usually assumed in practice.
The other factors involved in the Functions I air valves problematic
are the air-release mechanism, which indicates that only valves higher than
previous are able to purge dissolved air, and the too much complex air
water-flow interaction which may entrain non-released free air to points
where it would not normally expected. The only general conclusion is that
each case should be analyzed per si; the equations presented could be
helpful in such an analysis.
As a safety measure it is recommended the installation of Functions I
air valves at all peaks relating both the piezometric line and the
horizontal static line, considering a minimum air release flow of 2 % of
liquid flow at atmospheric conditions (Lescovitch criterion).
ACKNOWLEDGMENTS
The author acknowledges the facilities given by
COBA, SA.
Appendix I. References
Ahmed A.A. et al. (1982) “The process of aeration in closed conduit
hydraulic structures.” Proc. Symposium on Scale Effects in Modelling
Hydraulic Structures. Technische Akademie Essligen, Germany.
A.R.I. Kfar Charuv (1990?) Water supply accessories. A.R.I. Kfar Charuv,
Israel.
Glenfield -Kennedy , ex-Neptune-Glenfield. (1978). Apex. Air relief valves
for water systems. Biwater, UK.
Cary, E. (1992). “Definition and sizing of air valves.” Revista Industria
da Agua, December 1992, EPAL,Lisboa (in Portuguese).
Dupont, A. (1974). Hydraulique Urbaine. Tome II. Eyrolles, Paris (in
French).
Ervine, D.A. & Himmo, S.K. (1982) “Modeling the behaviour of air pockets in
closed conduit hydraulic systems.” Proc. Symposium on Scale Effects in
Modelling Hydraulic Structures. Technische Akademie Essligen, Germany.
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Appendix II. Notation
Ai
=
orifice area (air inlet)
Ao
=
orifice area (air outlet)
C
=
solubility coefficient of air in water
Cd
=
discharge coefficient (of air valve or valve)
Cdi
=
discharge coefficient(air inlet)
Cdo
=
discharge coefficient(air outlet)
d
=
air valve orifice diameter
df
=
float density
D
=
pipe diameter
Fr
=
Froude number
g
=
gravitational acceleration
hcol
=
gluing pressure head
hw
=
piezometric head
i
=
pipe slope (sinus of pipe angle with horizontal)
m
=
degree of immersion (air valve float)
m’
=
mass flow-rate of air
p
=
absolute pressure
p’
=
pressure ratio (p’= p/p0 )
p0
=
atmospheric pressure
pi
=
absolute pressure at section i
Qar
=
air flow-rate (inside pipe conditions)
Qar
atm
=
air flow-rate (atmospheric conditions)
Qar
j
=
released air flow at section i
Qw
=
water flow
R
=
gas constant, 287 Nm/ kg
S
=
pipe section
T
=
absolute temperature
T0
=
absolute temperature of atmospheric air
V
=
float volume. Velocity
Vc
=
air clearing velocity

=
gas fraction (= Qar / Qw)
f
=
specific weight of air valve float
w
=
specific weight of air valve float

=
air mass density
0
=
air mass density at atmospheric conditions

=
pipe angle with horizontal
TABLE 1: Air Clearing Velocity, Vc (m/s)
D
Slope (%)
(m)
0.5
1
5
20
100
(1)
(2)
(3)
(4)
(5)
(6)
0.25
1.3
1.3
1.4
1.5
1.6
0.5
1.9
1.9
1.9
2.1
2.3
1
2.6
2.7
2.8
2.9
3.2
1.5
3.2
3.3
3.4
3.6
4.0
FIGURE CAPTIONS
Fig. 1- Simple air release valve
Fig. 2- Zone of operation of a Function I air valve
Fig. 3- Air flow trough orifices
Fig. 4-Air valves location along pipe profile
Fig. 5. Identical systems with different number of air valves
Fig. 6. Differentiated air release along pipe profile