ALBERT L KIMMEL
Assistant Research Engineer
Chemical Engineering Section
Bulletin No. 17
FLORIDA ENGINEERING AND INDUSTRIAL EXPERIMENT STATION
COLLEGE OF ENGINEERING * UNIVERSITY OF FLORIDA * GAINESVILLE
The Florida Engineering and Industrial
The Engineering Experiment Station was first approved by the Board
of Control at its meeting on May 13, 1929. Funds for the Florida Engineer-
ing and Industrial Experiment Station were appropriated by the Legislature
of the State of Florida in 1941. The Station is a Division of the College of
Engineering of the University of Florida under the supervision of the
State Board of Control of Florida. The functions of the Florida Engineering
and Industrial Experiment Station are:
(a) To develop the industries of Florida by organizing and promoting
research in those fields of engineering, and the related sciences, bearing on
the industrial welfare of the State.
(b) To survey and evaluate the natural resources of the State that
may be susceptible to sound development.
(c) To contract with governmental bodies, technical societies,
or industrial organizations in aiding them to solve their technical problems.
Provision is made for these organizations to avail themselves of the facilities
of the Engineering and Industrial Experiment Station on a co-operative
financial basis. It is the basic philosophy of the Station that the industrial
progress of Florida can best be furthered by carrying on research in those
fields in which Florida, by virture of its location, climate, and raw
materials, has natural advantages.
(d) To publish and disseminate information on the results of
experimental and research projects. Three series of pamphlets are issued:
Bulletins covering the results of research and investigations by staff mem-
bers; Technical Papers, reprinting papers or reports by staff members
which have published elsewhere; and Leaflets, reprinting articles by staff
members which have been published in the more popular periodicals.
For copies of Bulletins, Technical Papers, Leaflets or information on
hou the Station can be of service, address:
The Florida Engineering and Industrial Experiment Station
College of Engineering
University of Florida
RALPH A. MORcEN, Director
TABLE OF CONTENTS
Review of Corrosion and its Mitigation Page
Introduction ................. .. . . .. .. .. .. 7
The Corrosion Process ..... . .. ......... . 7
Methods for the Mitigation of Corrosion
M echanical .............. ........ ... 11
Chem ical ... . ...... .... ...... .. .. .. . ... ..... .. 12
Electrical . . .. 12
Nomenclature ... --... ... . . .... .... ... 15
Engineering Data Relative to the Installation of Cathodic
Protection Systems in Water Tanks
O bject .. .....- - ... .... . .. . . . . . .. ......... 17
Introduction ............. -- ... ....... .. . ... .... 17
Method and Equations
Current Requirements . . .. .. . . . .... 18
Electrode ,. ......... . ..... .. . .. 21
Voltage Requiremenits .......... 26
Cost ... ......... .. . .. . ..... . ... .. .... ......... .. .......... 26
Nomenclature - - ..... .. ......... 31
Appendix I ..... .... . . . .. . .. . ............... .. .. .. 30
Appendix II ................ .......... 31
Bibliography .... . ... ....... .. . . .................. 39
1. Salt Spray Cabinet for Testing Protective Coatings .. . 10
2. Galvanic Protection Installed in Water Tank and on Pipe Line 12
3. Cathodic System on Water Tank and Pipe Line ........ -.... .. 13
4. Typical Britton Curve --..-- --------.......................... 18
5. Apparatus for Preparing Britton Curves ........... .. . . . 19
6. Britton Curves for Three Types of Waters Common in Florida 20
7. Britton Curves for Waters of Different pH Values ........ - -- 22
8. Electrode Factor Curve for Multiple Electrode Systems .... 25
9. Polarization Potential Curve --................ . .. .... 27
10. Britton Curve for Water Used in Illustrative Example . . 27
1A. Water Shape in Tank .---.- - ..-.....- ............ . 31
2A. Component Parts of Water Shape ...................................... 32
3A. Water Shape for Calculating Rs ......-- ...................... ......... 33
4A. Water Shape for Calculating Rb ....- ... ....-................. .. ........... 35
5A. Water Shape for Calculating Rt by Equation 13 . ......._.... . 36
Fundamentally corrosion is an electrochemical reaction, therefore, the
process should be studied from this standpoint. Accelerated corrosion can,
in most cases, be studied as simple cells or battery action, however, sections
of the corroded structure must be viewed as isolated bodies. In most cases
numerous factors are involved in the corrosion on any system and no one
thing can safely be given as the cause.
Corrosion mitigation methods in present use may be divided into three
groups-mechanical, chemical, and electrical-and combinations of these.
The method selected for any one purpose always depends largely on the
structure, the location, and the engineer in charge.
Cathodic protection systems for water tanks may be designed and
installed by a consideration of the physical properties of the water handled
and the tank dimensions. These factors are pH. dissolved salts, specific
resistance, height of tank, diameter of tank, and height diameter ratio. A
specific design example is given for cathodic protection of a commercial
size water tank. By the proper use of this information other cathodic
protection systems can be designed and specified.
ALBERT L. KIMMEL
Assistant Research Engineer
Chemical Engneering Section
FLORIDA ENGINEERING AND INDUSTRIAL EXPERIMENT STATION
COLLEGE OF ENGINEERING * UNIVERSITY OF FLORIDA * GAINESVILLE
Bulletin No. 17- September, 1947
Permission is give to reproduce or quote any
portion of this publication providing a credit lae is
given acknowledging the source of the information.
Throughout Florida as in other parts of the country
industries and individuals hate suffered economic loss
directly or indirectly as a result of the problem of cor-
rosion of metals.
Industries have felt the problem through damage to
pipe lines, boilers, production equipment, and. in some
cases. products. Individuals hade been affected indirectly
by industrial losses and in many instances have also
experienced damage to their personal property.
In these pages the research engineer reviews the
subject of corrosion and describes mechanical, chemical,
and electrical methods for its mitigation. He also supplies
engineering data relative to thdie installation of cathodic
protection systems in water tanks.
It is hoped that the compilation of information and
the diligent research conducted in regard to corrosion will
materially benefit Florida's industries and its citizens.
RALPH A. MORCEN
The author wishes to express his appreciation to Dr.
J. D. Warner, Vice Director of the North Florida Agri-
cultural Experiment Station at Quincy, Florida, who
allowed him the use of the water tank located on that
property for experimental work. Sincere appreciation is
also expressed to Dr. E. S,. Quade of the Mathematics
Department at the University of Florida who assisted in
the derivation of the equations found in this bulletin.
REVIEW OF CORROSION AND ITS MITIGATION
Modern civilization has reached its present level largely through the
development and use of the structural metals. Without the use of iron,
steel, brass, aluminum and the other metals skyscrapers, bridges and the
numerous methods of transportation would be impossible and man would
still be living in community life with very little knowledge of the outside
The important structural metals known to man are rarely found free
in nature. but as compounds, commonly called minerals or ores. In order
to prepare the pure metals the mineral or ore is processed chemically by
the use of heat and other agents. Once prepared- these metals will again
slowly revert to their compounds. This process of a free metal changing
to one of its compounds, due to atmospheric or other chemical conditions,
is called corrosion.
The Corrosion Process
In discussing the process of corrosion it is necessary to have some
knowledge of the metals being handled, their chemical activity, and a few
of the factors which will affect their rate of destruction. In general, most
corrosion problems involve many factors. therefore, no simple statement
could be made to cover the entire field.
Corrosion from the standpoint of the chemist or chemical engineer
is an electrochemical process. Modern theory divides electrochemical re-
actions into two parts-an anode and a cathode. The anode reaction con-
sists of a discharge of metallic ions to the solution, accompanied by a flow
of electrons to the external circuit. At the cathode, metal or gas is deposited
accompanied by an absorption of electrons from the external circuit. Take,
for example, iron corroding in water At the anode iron goes into solution
as ferrous ion accompanied by the flow of electrons to the cathodic area.
In the cathode area the hydrogen ions absorb these free electrons resulting
in the formation of hydrogen gas.
The ease with which a metal can change from the metallic state to
one of its compounds is known as its chemical activity. The fact that metals
have different activities explains why some metals corrode more rapidly
Elements Potential (volts)
Workers in the field of theoretical chemistry have prepared a list of
metals according to their activity, Table 1. The activities of the metals
decrease from the top of the table to the bottom. Any metal in the series
will displace the ones below it from solutions of their salts (2) *. The table
lists a "potential (volts)" opposite each metal. This is the single electrode
potential of the metal when in a solution of its ions at unit activity. This
value also represents the solution potential of the metal under ideal
The actual conditions encountered in the field are far from ideal. Also
variation in surface conditions of some metals, due to chemical environment,
makes them behave like the more noble metals resulting in a change of their
solution potentials, The electrochemists and corrosion engineers have pre-
pared a second table known as the galvanic series. This series, Table 2,
predicts the activities of the metal for conditions commonly met in practice.
It was prepared primarily for use in studies concerning galvanic cells, and
THE GALVANIC SERIES OF METALS
Nnnmerals in italics denote source of material as listed in bibliography.
In Table 2 no potential (volts) is listed with the metals since each
metal has a different solution potential for every electrolyte. The solution
potential changes both with materials and concentration, therefore- in a
generalization of this type they are not listed. However, it should be
remembered that the single electrode potential of any metal with respect
to the medium around it is an indication of its ability to liberate inons. This
is a measure of its corrodibility.
If two different metals were connected together and placed in a
corrosive medium, the more electronegative metal would be destroyed.
while the other would be unaffected. This is known as galvanic action and
is present in many corrosion problems. The explanation for this is that the
more electronegatike metal acts as the anode, the other metal the cathode.
Sinte in electrochemical reactions only the anodic area sends metal into a
Solution. this area is the only one destroyed. Any conditions which will
produce isolated anodic and cathodic areas can result in galvanic corrosion.
Conditions conducive to galvanic corrosion may be listed as follows:
1. Bimetallic Couples.
Bimetallic couples are two dissunilarmetals in contact with one another
and floated in a corrosive medium. These include brass valves and fittings
in iron pipe lines, and external metallic objects in contact with a structure
2. Nonuniformity in the structural metal.
Nonuniformity in the metal includes spots or areas of different
chemical composition, and all strained, stressed, or work hardened areas.
3. Concentration Effect.
When a metallic structure is located in an area where two different
soils exist, or where there is a difference in the aereation of the soils sur-
rounding the structure, galvanic action takes place and the metal is
destroyed in the anodic portion due to concentration cell effects.
In making corrosion studies anodic and cathodic areas on any strue-
ture. surrounded by the corrosive medium. may be located by single eled-
trode potential methods. The portions being corroded will always be more
In dealing with corrosive mediums-water- soil, solutions. etc.-a
term which finds wide use is pH I I. The term pH is defined as the log of the
reciprocal of the hydrogen ion concentration. For practical purposes pH
is an expression of the acidly or alkalinity of the material. The pH values
below 7 are acid, and the lower the number- the more acid the soil or water-
In like manner, values above 7 are basic or alkaline- and the higher the
number, the more basic the substance 191 -
The fact. that in the corrosion process of most common metals.
hydrogen is liberated makes it an important factor in the determination of
the corrosion rate. In the case of iron or steel. below a pH of 5. the rate
of corrosion is directly proportional to the hydrogen ion concentration if
all other factors are kept constant.
Another factor which will influence the rate of corrosion on a metal
is the quantity of oxygen in the corrosive medium. This is generally re-
fe red t[, a. the d s~,led oxygen i content. When oxygen. aids I he orrosion
lipro. n dIi a. , in two "A's. First, if the metal is A.bove hydrogen oi
hlie VilIuliocll-mi rl sei" it mam react with metal i.ons cl if$ng into Ithe
'oluioln Ib, fo.rm insolublic products which settle out and [acilitate the soul-
ion of additional retail. Se-onid. if the metal -hould Ihe below hydroge. n
m the -,erI'. it ,-an cait sith the surface to form metal oxides which tlhen
real I ihulnlr ilth the jaids present to form meal salts and water. There
are c(-.s ilere o'x gevn in a corrosi'e medium helps prevent I orrosion. In
the case of aluiniumiin it will form an impervious coating of aluminum oxide
on thl surface whih " ill preenlt further metal destrur'tion. In any selnem
llc, role oxAgeI will pla i must be detennined by experiment.
The attack in metals bI water or soul can I)e accelerated or decelerated
1h, .ont ell ral mio' of various salts. The salt solutions are good electrical
corndup tor, and aid the electrocheinical pro< ess. This property is made use
of in the -tandard alt spraV machine where accelerated corrosion tests are
nmade on paint filns. plated metals, and treated metal su faces, Fig. 1.
Polacrlzattiii. Ihe phenomenon of gases collecting on the surface of the
Fig. I -Sail -pray cabonel for testing prolecti'e coalmng,
metals in a corrosion system, tends to decrease the rate of corrosion. This
is noted particularly in himnetallic couple systems where, when the cathode
area i, small, it is completely covered with gas. This film of gas on the
cathode surface will offer a high resistance tn the flow of destructive electric
Corrosion is alctars accompanied by a physical change in the metal.
This change is usually in the form of a surface discoloration, a weakening
of the internal structure or a combination of both. On copper it is an
opaque green film. In the case of cast iron, corrosion causes not only a
red brown surface coat but a weakening of the metal known as graphitiza-
tinr or spongosis.
As mentioned above . when metal a L-e coiudeid hy the natural elements
the compound formed usually will be thle same as onr' of the natural ores of
that metal- Table 3 gives a few of the common metals, their ores. and the
products of corroion under natural conditions.
Natural Product of
Metal Ore Chenwcal Name Corrosion
Iron Hematite Iron Oxide I Fe20, I Iron Oxide I FeO0a)
Magnetite Iron Oxide (FO,)! Iron Oxide (FeaO4)
Copper Malachite Green Basic Copper Green Basic Copper
Aluminum Bauxite Aluminum Oxide Aluminum Oxide
In the case of equipment in chemical industry, the compounds formed
when corrosion takes place depend on the material handled. If iron equip-
ment is uted in the manufacture of dilute sulfuric acid, iron sulfate will
be formed. It is for this reason that the choice of metals and alloys for
industrial equipment depends to a considerable extent on their corrosion
Methods for the Mitigation of Corrosion
I rom the time metals were first produced from their ores man has
worked on methods for the prevention of their destruction. The corrosion
engineer classifies all the methods presented to date into three groups-
mechanical, chemical, and electrical.
MECHANIcuL. The mechanical method of corrosion mitigation con-
sists of walling off metallic surface w ith a film of some nonreactive material
such as paint- lacquer, or varnish. These methods find extensive use on
all types of iron and steel structures.
For a mechanical film to offer complete protection to a metal structure,
it must he impervious to water, it muibt be resistant to cliciinal and abrasive
attacks, and it must not crack on aging or exposure to rapid temperature
changes. No one film will meet all of these requirements. but the better ones
will retard rnrrosinn to such an extent that they are important in all
corrosion mitigation problems.
Bridges and other steel structures exposed to atmospheric corrosion
are usually treated with a primer of red lead and two finishing coats of
paint. This method is almost standard practice on outdoor structures. The
treatment should be repeated every two or three years.
On buhaed iron pipe the problem is different. The pipe can not be dug
up at intei;als for painting, therefore a coating must be applied that will
last the estimated lifetime of the pipe. The oil and the public utilities com-
panies have led the field in developing long lasting pipe coatings. The most
suitable method consists of applying alternate layers of bituminous enamels
and paper, or burlap wrapping, for a total of three to five layers. P. D.
M illons (11) describes such a method in his recent paper. This method has
been used on many pipe lines. Machines have been developed for applying
this protection after the pipes are assembled in the field. These machines
will coat and wrap ten miles of pipe line a day with three layers of the
protective material. It must be remembered, however, that, although it is
only semi-permanent, the method is one of the best protective systems
CHEMICAL. The chemical methods usually employed are divided into
two classes-chemical environment and surface conversion. The first of
these consists of the addition of chemicals to water or other liquid so as to
create conditions which will make the metal resist corrosion. These chemicals
are known as inhibitors. An example of an inhibitor is sodium dichromate.
which is often added to the salt brines in the refrigeration industry. The
second method, ihat of surface conversion, depends for its effectiveness on
changing the metal surface to a more resistant compound, such as a dense
oxide or phosphate film. These surface films are very thin and mechanical
abrasion will destiny them. They find wide industrial use but provide only
temporary protection by themselves in most cases.
ELC'RRtCAL. The electrical method of corrosion control consists of
forcing the metal to he protected by functioning as the cathode of the system.
To date, two methods are in general use. They are galvanic and cathodic
protection. These methods have been used with good success.
Fig. 2-Galhanic protection installed in water tank and on pipe line.
With galvanic protection voltaic cells are made with the metal to be
protected and some other metal that is higher in the galvanic series. The two
metals most commonly used for protecting iron are zinc and magnesium.
Of these, magnesium appears to be more promising and should find wider
use inl the future since it is now being produced at a reasonable cost. An
Example of the theory behind such a system is provided by the common dry
cell which is simply a carbon rod located in a zinc case containing a
corrosive paste. When on short circuit- a current flows, the zine corrodes,
and the carbon rod is unaffected although hydrogen is liberated from it.*
When iron is coupled with zinc or magnesium, a similar process takes place.
In this case the iron assuming the role of the carbon rod in the drt cell.
The advantage of this system lies in the fact that as long as current is flowing
the iron is protected. A further advantage is that the system requires no
external source of current and it can be located any place where the
structure to be protected is surrounded by water or moist soil. Fig. 2 shows
a typical application and the method of installation. When galvanic protec-
tion is used the zinc or magnesium anodes must be replaced after certain
intervals of time, since they are destroyed in the protecting process.
Cathodic protection consists of applying an external electric current
in such a manner that the metal to be protected mill function as a cathode.
To accomplish this a metal electrode is located in the corroding medium and
connected to the positive terminal of a direct current source. The metal to
be protected is then connected to the negative side of the power supply. The
completed circuit is of such a nature that the current flow"* is always into
the surface of the metal to be protected. Fig. 3 illustrates the application of
the cathodic method,
Fig. 3-Cathodic system on water tank and pipe line.
*In the dry cell special chemicals are added to remove the hydrogen as it forns,
'*By present conventions, clrrrnt flow is always oppose electron flow.
The cathodic method has some advantages over the galvanic method
since there are no replaceable anodes and the system can be controlled more
carefully, thereby adding to the economy. Its chief disadvantage is that it
must he located near a power source to supply electrical energy for operating
the rectifier units or motor generator sets. In some services wind generators
and gasoline engine generator sets have been used. but they require constant
maintenance and attention.
It should be noted that in the electrical method for protection the com-
ponents are divided into anodic and cathodic areas. For protection the iron
structure is made cathodic, while external anodes are added to the system.
Once this process is set in operation the system proceeds as described under
In some cases of corrosion mitigation, a combination of two or more
methods is used. In the case of zinc chromate pigmented paints, chemical and
mechanical methods are used together. The paint film protects the metal
until a small amount of moisture penetrates the film. Then the moisture
dissolves the slightly soluble zinc chromate pigment, which is a corrosion
inhibitor, and slows the destruction of the iron to a very small rate.
In long pipe lines it is sometimes more economical to use a combination
of both electrical and mechanical protection (11). While the paint film is
intact, very little current will flow since the coating offers high resistance
to the flow of electricity. Age and nature gradually destroy the protective
film on the surface of the pipe, but the current concentrates at the area
of exposed metal giving added protection.
Every year millions of dollars worth of structures, pipe lines and
chemical equipment are destroyed or rendered useless by corrosion. The
preceding methods, although suitable for retarding corrosive action, do
not completely eliminate it. Research on corrosion continues in the hope
that more and better methods of protection can be found.
A Area to be protected, sq. It.
Ai Cross sectional area perpendicular to the path of current. sq. ft.
A. Anode area. sq. ft.
Ab Tank bottom area. sq. ft.
A, Tank side wall area. sq. ft.
C Electric power cost. dollars per 'ear.
c Power cost, cents per kw-hr.
(id Tank diameter, ft.
d.. Electrode diameter (anode), ft.
d,, Diameter of each electrode in the multiple anode system. ft.
E,, Back voltage due to polarization, volts. ISee footnote on Page 21.)
E, Required potential difference between the anode and cathode, volts.
E, Rectifier voltage Ivoltsl.
e Efficiency of rectifier unitl.
f, Radius factor. (Used in multiple electrode systems.)
It Length of current path. (Used in resistance derivations. ft.
I Current required for cathodic protection famnps).
i Current density (inilliamps-l /1000 amperel.
1i Total height of tank. ft.
1 Length of anode, ft.
l1 Distance of anode from bottom of lank. ft.
R Resistance. ohms.
Rb Electrical resistance of the water to the flow of current from anode to
R, Electrical resistance of the water to the flow of current floni anode to
tank side wall.
R, Total electrical resistance of water in the tank. ohms.
ri Tank radius, ft.
r: Electrode radius, ft.
r,, Equivalent radius of multiple anode system. ft.
'r, Radius of multiple electrode assembly, ft.
,, Mathematical constant (3.1416).
A Specific conductance of the electrolyte.
p Specific resistance of the electrolyte.
MA Millamps or 1/1000 ampere.
Letters for designating sides in similar triangles. (Used in derivations.)
ENGINEERING DATA RELATIVE TO THE INSTALLATION OF
CATHODIC PROTECTION SYSTEMS IN WATER TANKS
The cathodic system offers to the engineer one of the best methods for
corrosion control. Thioreticallv. with the properly applied power, it is
possible to eliminate corrosion completely. In most cases, however, this
would not be economical. Therefore- the engineer is usually interested in
an economic balance between the prolonged life of the equipment and
the cost of the protection.
hI is the purpose of this section of the bulletin to present to the engineer
a mathematical tool that can be used to design, install and specify the
necessary pieces of equipment required for an effective cathodic system.
Tie cathodic system for corrosion mitigation is one in which a current
is made to flow front. an electrode (anodel. through the solution, into the
gnetal to be protected (cathode). As long as this condition exists, the
chemical action of the water is decreased and galvanic currents due to
non-u iformities in the iron surla-es are suppressed.
There are certain fundamental facts known about cathodic protection.
These. coupled with a few simple electrucleminial principles. can be used
to dicgn a ,temn whli h will effectively, miligte c'orosion.
I. When a metal is freely corroding in any liquid medium. it will
have a definite solution potential.
2. If the corroding metal is made the cathode of a cathodic system,
its single electrode potential with respect to the corroding medium
will be decreased. The amount of depression will depend on the
current applied per unit area and the solution properties. A
cathode potential drop about two tenths of a volt from the normal
solution potential is usually adequate for protection.
.. The resistance offered by the solution to the flow of the electric
current depends on the areas of the anode and calhode. and the
conductivity of the solution.
The above information was summarized from the published results of
many experimenters and text books dealing with electiochemistrv (3, 5,
The engineer. when designing a cathodic system, is interested in two
things-first, the power rating of the rectifier unit. and second, the size and
placement of the andes. in order to oblain this information, the data in
the following outline must be obtained:
1. Current requirements.
2. Anode Isize. placement and area).
3. \oltage requirements.
4. Rectifier specification.
5. Cost of operation.
of the outline, as listed, represents the steps in the
Method and Equations
CURnnRE REQUlRNI:MENTS. In the State of Florida, the types of water
dealt fith in c, rrosion work vary from highly pure spring water to sea
water. All have different chemical and electrical properties; therefore each
presents a different problem. The current density requirement for cathodic
protection in the various waters may be found by the methods of Britton.
Evans, and Bannister I ). The curves they prepared indicate the change
of cathode potential with increases or decreases in the current density.
Fig. 4 is an illustration of their curves, and Fig. 5 is a layout diagram of an
apparatus which may be used for preparing them.
MA/ SQ- FT.
Fig. 4. Typical Britton Curve
When preparing current density curves with the apparatus illustrated in
Fig. 5. the following procedure is recommended:
1. About 3,000 cc. of water are placed in the glass vessel containing
the anode and the iron cathode. The saturated calomel cell is then
located witlh it. tip as close as possible to the iron surface. (The.
cathode surface away from the anode is coated with a water
resistant varnish so that only one surface is affected by the
2. The current flowing between the anode and cathode is varied in
steps of 0.5 amps. from 0 to full batter) capacity. The cathode
potential is tIeaburcd by means of varuunm tube voltmeter for
each current increase. (A good potentiometer would be much
better than the vacumn tube voltmeter. I
3. The two sets of curves Fig. 6 and Fig. 7 prepared by this method,
serve to illustrate Ihow salL concentration and pIH affect the current
density requirements. Fig. 6 is a comparison of fresh water,
brackish coastal water and sea water. while Fig. 7 is a family of
curves for waters uf varying pH values. 'ig. 5 shows the apparatus
used in this lahnratorv for preparing these curves.
Fig 5.- Appalrats for preparing TBrion curves.
Where it is impossible to prepare actual curves for the type water
present in the equipment to he cathodicalli protected, the curves of Fig. 6
and 7 will give a go. ro approxt mtiou
I I I I _-__ _ 0
---- ---- --- ---- ----______ _______ 0
_ _ _ _ _ _ _ _ - -------_ _ _ _
____ _______- 0\___ __
x - 4
---------- I '.g--------
Fig. 6.-Britton curves for three types of waters common in Florida.
After the current density-cathode potential curve is prepared for the
given water it is possible to predict what current density is required to
give the necessary cathode potential for protecting the iron surface. As
the current density (i) is given in rnillamps/sq. ft., the total current output
1I in amperes required from the D.C. power can he obtained by multiply-
ing this value by the total area ( A in square feet) to be proteLted. divided by
one thousand. Expressed in equation form:
1) IA :1
ANotES. The anode of a cathodic system is the origin of the protective
currents. It is at all times subject to severe corrosive forces, and therefore,
in the design of the central electrodes, the material of construction is very
important. The metals most commonly used, listed in their order of
importance are. stainless steel, carbon. monel. iron. aluminum and platinum.
Of these carbon and platinum are the only ones which do not dissolve at
the high anode current densities in use. Stainless steel, when used at low
densities, is nio destroyed and finds wide application in fresh water installa-
tions. Table -I lists the electrode materials and other information concerning
their use t61.
ELECTRODE MATERIALS AND CURRENT DENSITIES
Metal Useful Current Range Remarks
Carbon All Does not dissolve in use, but will
crack and distort.
Platinum All Can be used under all conditions.
Stainless Steel Up to 4 amps./sq. ft. Should be used in fresh water only.
Monel Below 1 amp./sq. ft Dissolves in use at rate of 2.1bs. per
1.000 amp. hrs.
Aluminum Below 1 amp./sq. ft. Dissolves in use at rate of 0.73 lbs.
per 1.000 amp. lrs.
Iron Below 1 amp./sq. ft. Dissolves in use at rate of 1.53 lbs.
per 1,000 amp. hrs.
In the design of cathodic system it has been found that whenever
possible the anode current density should not exceed one ampere per
The method of suspending the electrodes in a tank will be left to the
engineer since the construction of the tank is the controlling factor. A good
rule is to locate the electrode or electrodes in the center. or symetrically
about the center, of the tank. This is desirable in order to obtain a uniform
current distribution on the cathode surface. In all cases the electrode
should extend to within one foot of the bottom of the tank (referred to as
1n in calculations) for bottom surface protection.
With the anode area (Aï¿½ sq. ft.) known (calculated from the current
CATHODE POTENTIAL VOLTS
I__ __ __ __ __
Fig. 7- Brllon curves for walers of different pH values.
requirements), it is possible to calculate the electrode diameter (d2 in feet)
from the following equation for the area of a cylinder:
2 1 A, = w da ie
3, da _As
The term (I.) is the submerged length of the anode. All values are
in terms of feet.
When a multiple electrode system i- sed a change is made in the
frmila and the results are:
4) de :
Where X is the number of electrodes. and d,. is the diameter of each
.f the anodes in feet.
VOLTAGE IEtQUilREMENTS. The voltage required from the rectifier unit
(Eri is composed of two parts. The first is the voltage necessary for
cathodic protection E)j, and second E,)1" the voltage necessary to over-
come polarization effects.
6) Er z Ep + Ec
According to Ohms Law
7) Ec: I Rt
Where R1 is the total resistance of the wteh I1 solution in the tank.
Combining equations (6) and (7) then:
) Er dRI +EP
The resistance offered to the flow of the electric current by the fluid
in the tank will depend on the specific resistance of the liquid (p), the
length of the current path (h), and the reciprocal of the cross sectional
area fl/A,) perpendicular to the path of the current (6).
"Note. The termn E repremrntb a combination of clkctrical effects produced by
the potential meal in the electrolite. It is the single electrode potential of that metal
when coated by gases (hydrogen, etc.) evolved and solids precipitated, during the
Starting with this fundamental equation (9), and using methods of
integral calculus, equations (10) and ill) are obtained. These two equa-
tions are then combined by means of equation (12) to give the total
resistance of the liquid. The terms R. and Rb represent the resistance of
the fluid between the central electrode and the side and bottom of the tank
10) R ,-2. a _ g I lo
b so.5rr Ir
Where r, and r, are the radius of the tank and the central electrode
respectively. The total resistance (Rj) will then be:
12) Rt: Rb R
These equations (10), I11. and (12) are correct for all cylindrical flat
Empirical data. taken on a large number of installations, has indicated
that in cases where the diameter of the tank is less than the height, a
simplified equation may be used. Equation (13) is less than 5% in error
for most installations of this type. See Appendix 11 for the derivation and
13) t- s ~ I tr2
The above equation is of sufficient accuracy for use on tanks which have
conical or round bottoms, so long as they meet the diameter height
When multiple electrodes, located symetrically about the center of
the tank. are used they may be considered equal to an equivalent central
electrode of radius r,. This equivalent radius is obtained by selecting a
radius factor (f,) from the curve Fig. 8, and using the following equation:
14) re z f rh
The term r, is the distance of each electrode from the center of the tank.
The value of r, is then substituted for r2 in equations (10) and (11) or
(13). When r, is greater than 8, four electrodes are used. For values less
than 8, more are necessary. This radius factor curve was derived from
experimental data taken from laboratory and field data. It has proved very
- - =-
7- -------- ^^ -- - - -
Zl0 OF E1hEECTIOBES
4 5 6 7
8 9 10 II 12
Fig. 8.--LIeclrode (actor curve four multiple elctrode systems.
useful for predetermining operational characteristics of many test
The specific resistance (p) of the electrolyte used in equations (10),
Il). and (13) depends entirely on the water. It will he different in every
case. Therefore. it will be necessary to measure it for every installation.
The methods used for determining the specific resistance may be found in
any good book of electrochemistry. A number of these will be found listed
under the references in the bibliography (5, 6, 13).
The galhanic effects caused by the dissimilar metals used in the anode
and cathode will produce an opposing voltage. Under polarizing conditions.
as are present ini cathodic protection, this voltage difference does not depend
,an the metals. but on the pH of the water. The curve. Fig. 9, was prepared
for numerous experiments with a varielv of different metals-as anodes and
iron cathodes in water a pH from 2 to 8. The polarization potential for any
pH proved constant regardless of the electrode metals at the protective
RECTIFIER SPECIrFlt VTIONS. The values calculated for the voltage (E, i
and current I I I are the minimum required for the cathodic unit. In order
that additional control be possible in the system, the current and voltage
specified for the rectifier unit should he increased about five and ten per
COST oF OPERATION. The cost of operation of a cathodic system >will
depend on dthe power Lost in that area tc). usually in terms of cenLs/kilowatt
hr. In .ider to find the yearly operation expenses (C) the following
formula is used:
158766 I-Erc = c
where (e) is the efficiency of the rectifier unit.
It is desired to cathodically protect a water tank of 1100 gal. capacity,
20.5 ft. wall height, and 17.25 ft. in diameter. The overflow pipe is 6
inches fromthe top rim of the tank. This tank holds a natural spring water
with a pH of 6.8. The tank is so constructed that either a central or multiple
electrode assembly may be used. It is required to specify the size and area
of the electrode, and a rectifier unit of suitable capacity for protecting
From a sample of the water submitted a current density cathode
potential curve is prepared. (See Fig 10) In order to obtain a cathode
potential in the range necessary to protect iron under these conditions, a
current density of 4.5 milliamps per sq. ft.. is required. The dotted lines on
the graph indicate the method.
The total area to be protected is obtained from the dimensions of
POLF.ARIAThl FpOTMETIAL VOLTI
Fig. 9.--Polaritation potential curve.
E -- - I
05 --------_- - - -------- -____
Fi. 10 -Brilttn
CUfWtlNTt DitTy MA/so FT
curve Io, water used in illustrative example.
Side wall area:
A -Td h = 3.1418 6 1725 X 20 1083.3 sq.ft.
Area of bottom:
S= ,2 =31416 x 8a625) =233.6 sq ft.
(A)=- As t Ab = ioa3.3+233.6 13le.9 sq.ft
The total current from equation (1)
A - I - 131.9 x .0045 - 5.92 aps- I
This is the minimum current requirement for the rectifier.
The electrode, or the multiple electrodes, will be made from stainless
steel for illustrative purposes. Referring to Table VIII of electrode
materials, it is noted that the anode current density should not exceed one
amp per sq. ft. With an electrode that has a submerged length of 19 ft. since
it is located 1 ft. from the bottom, the diameter may be calculated from
A2 d- d 92- - .090eoft.
2 - - 3.1416 X 19 -
or .0980 x 12 x 1.185 inches.
As the nearest commercial size stainless steel rod obtainable is 11/,",
this size will be used in the calculations.
If a multiple electrode system is desired, the procedure is as follows:
(For this illustration a four electrode system will be assigned.) The
current requirement of the system is constant, therefore, the electrode area
is fixed. Equation (4) can be used to calculate the diameter of each
A2 = de 5.92 - 0245 ft.
47,l2 4 X 3.1416 X I
or .0245 x 12=0.294 inches.
The nearer suitable diameter obtainable in stainless steel rods would
be %, in.
Thevoltage requirements for the system is calculated from equation (8).
Er=IRt vEp = EP Ec
The resistance using the single central electrode obtained from
equation (13) will he:
R - 2 2.303 log 1
am 1, r,
The conductivity as measured by the conductivity apparatus was
.0001085 mhos and the specific resistance (p) is obtained by the following
-=- -0- .50 =9200 Chlrs
R- 92oo00 2303of lo ..t - 2.2 ohms
61 AX31416 X20 1.25
using equation (8)
Er I Rt = 5 92 X 12.2 72 3 volts
if the multiple electrode system is used. and it is to be the four electrode
,sstem as shown in Fig. 9. the procedure is as follows: (Since the electrode
placement can depend on st many factors, as stated before. It will be assumed
Ihal the ratio r, will equal 10.)
86 - P - .6 ft
equals maxiunim distance allowable from the center. For convenience of
design r, will be made % ft.
I - .6 - 11.-45
The radius factor obtained from the cuive Fig. 9. will be 0.835. The
effective electrode radius (rc) is then:
S- x f X = 0.75 X o.8 5- 0o.62
R- 9200 2.o03 log o.6 - e.as ohms
61X 3,1416 X 20 0.626
Er,= I Rt= 5-92 A 6.25= 37 VOLTS
For the specification the current is increased 10%:
foao x 5.92 + s.: .51si amlps
and the voltage increased 5%:
10.05 x 371 + 37 = n.5 vo0lt
Sinte the commercial unils on the market have ratings in even num-
bers a rectifier suitable for this purpose would deliver 40 volts at 8 amps.
If it is desirable to calculate the cost of operation, equation (15) is
used. Assuming a rectifier efficiency of 95%', and power at $0.03 per kwh.
8766 X 5.2 X 37 X0.03 = #00.00 - cOSt/Or
1000 X 0. 95
A Area to be protected. sq. ft.
A, Cross sectional area perpe,idii,ldar In lie path of current. sq. ft.
\2 Atnode area. sq. ft.
A,. Tank bottom area. sq. ft.
A. Tank side wall area. sq. ft.
C Electric power cost. dollars per year.
c Power cost. cents per kw.-I.
d, Tank diameter, ft.
d2 Electrode diameter lanilode. ft.
d., Diameter of each electrode in the multiple anode system. ft.
E, Back voltage due to polariation. volts. i Set footnote on Page 21.1
E... Required potential difference helween the anode and cathode, volts.
E. Rectifier voltage (volts).
c Efficien-yv of rectifier tnil.
f, Radflu fa'oir. i 'sed in multiple ehletrode s stems.)
hI Length of current path. IUscd in resistance derivations.) ft.
I Curient required for 'atlholdi protection lamps).
i Current density, (imilliamps-1 1000 ampere).
1, Total height of tank. ft.
1t Lrength of anode. ft.
1.1 Distance of anode from bottom of tank. ft.
I Resistance, ohms.
Ri, Electrwal resistance of the water to the flow of current from anode to
R. Electrical resistance of the water to liht flow of current froit anode to
tank side wall.
R, Total electrical resistance of water in the tank. ohms.
S Ta t nk radius, ft.
r. EIlectrode radius. flt.
r,. Equivalent radius of multiple anode system. t.
ri, Radius of multiple electrode assembly. It.
r Mathematir'al constant 13.1-116 .
A Specific conductance of the electtrolyte,
t Specific resistance of the elertrolte.
MA oiillitamnp or I 10U0 ampere.
[Attlrs for designating sides in sinilar triangles, tscd in derivations.)
Single Electrode Potentials
When studying cell reactions, the determination of the potential exist-
ing at each electrode of the system is necessary. It is impossible to measure
a single potential, but the potential difference between any two electrodes
of a system can be obtained. However, if a half cell is assigned an arbitrary
potential, relative potentials for all other half cel:s may be obtained. This
is done, by arbitrarily assigning to the standard hydrogen half cell a
potential of zero. This is now the accepted standard for all potential
The standard hydrogen half cell is somewhat cumbersome to use in
routine laboratory investigations, therefore, some more convenient half
cell is employed. The table below lists a few of these commonly used half
cells, with their potentials.
Potential based on the
Half cell standard hydrogen half cell
Hydrogen - 0.0000
Calomel (Saturated) +0.2479 (12)
Calomel 11.0 Normal) +0.2800 17)
Calomel (0.1 Normal +- 0.3338 (7)
Copper. Copper sulfate + 0.3475 (8)
Silver, Silver Chloride + 0.2224 14)
When potentials. measured with any of the half cells are to be converted
to the basis of the standard hydrogen electrode, the measured potential is
added algebraically to the potential of the half cell used. Examples:
(1) Potential of unknown electrode (measured with a saturated
calomel half cell) - 1.2379 volts
Potential of saturated calomel cell + 0.2479 volts
Unknown -- - 1.2379 - 0.2479 = - 0.9900 volts
(2) Potential of unknown electrode (Vs Copper Sulfate electrode)
+ 0.1364 Potential of Copper, Copper Sulfate half cell + 0.3475
Unknown = + 0.1364 + 0.3475 = + 0.4839 volts
Derivation of Equations 10 and 11
It is desied to find the resistance offered to the flow of an electric
current by the water contained in a flat bottomed tank, and with an
electrode located concentrically in the center, 1 ft. from the bottom.
(See Fig. lA.)
Fig. A.-Watr h.pe n tank.
It is known that the resistance of any uniform conductor is propor-
tional to the length of current path, and the reciprocal of the cross sectional
area through which it flows.
Where p is the specific resistance.
The source of the current is the central anode. Since the cross sectional
areas, perpendicular to the path of current- are different for the current
flow to the bottom and the sidewalk it will be necessary to separate the
fluid shape into two parts. (See Fig. 2A.)
PART I - . '
:'- .-- -
Fig. 2A.-Component parts of water shape.
Taking the section through which the current flows
first (see hig. 3A), by methods of similar triangles and
the mathematical derivation is as follows:
to the side walls
As the path of current (h) varies from rT to r, the length of the fluid
section varies from 1 to 11. .
Fig. 3A.-Water shape for calculating R,.
4- xh -X
eliminating the term x, then:
a_= hla- r213 h3 - r2 13
a -r 2 r,-r12 1 -r2
The cross sectional area at any time, as h varies from r2 to r1 in terms
of h. will be:
A= 2Thh (6
r -I2 , -r2
Placing the fundamental equation in the form of a differential, and
using the area as obtained, then:
Integrating the above equation between the limits of r2 and rx:
R3 - 10 + rin/ I
In order to put the equation in such a form that the length units will
be feet. and to change the naperian logarithms to logarithms of the base
ten, two conversion factors are added. This then puts equation (10) in its
P - 1 3 [otB' -log J- la'
Equation 11 is derived in the same manner. (See Fig. 4A.)
xt r2 - k h
Substituting values of x for k
X..- = e
Fig. 4 A.-Watr 4 iap.' fr cafc. uling itR
The cross Peltional area (A) at any time. a Ih maics from 0 to 1,
Using the fundamental equation as a differential and using the area
as derived above.
Integralting this equation between the limitsof 0 and I .andsimrnplifying
, --r, re
Correcting for units:
This is eqn tlm . io ) in its final form.
In connection with above equations, it is apparent, that the two values
for the resistances as obtained are in parallel. Therefore, they must be
added according to the following method.
The derivation of equation (13), is based on the following facts:
1. In dealing with resistances added in parallel. the lowest value
2. In water tanks where the diameter is equal to or less than the
height, the value of Rb is large as compared to RL.
Therefore. in deriving this equation, the fluid shape handled is as
shown in Fig. 5A. the assumption made is that the central anode extends
the entire length of the tank, and that in this condition the bottom resistance
Fig. 5A.-Water shape for calculating R, by equation (13).
The fundamental equation is the same as before,
The area (A) in this case would be:
Arranged as a differential
Integrating between the limits of r_ and ra.
Rl = ï¿½ n ,
Correcting for units, equation (13) is obtained in the final form.
= -Mo I|o-"
t ** ag~ '*f
1. Evants. . R., Bannister. L. C. and Britton. S. C.,
Proe. Roy. Soc. A. 131,1931.
2. Foster. Inorganic Chemistry for Cclleges. D. Van
Nostrand Co. Inc.. Second Edition. 1936.
3. Gaily and Spooner, Electrode Potential Behavior
of Corroding Metals in Aqueous Solution. Oxford
at the Clarendon Press. 1938.
4. Gelnan. F. H.. Jour. Phys. and Chem.. 34. 1454.
5. Glaston's. Introduction to Electrochemistry. D.
Van Nostrand Co.. Inc. 1942.
6. Handbook of Physics and Chemistry. Chem.
Rubber Pub. Co.. 23rd Edition. 1895. 1939.
7. Homer. Trans. Electrochem. Soc., 72. 45, 1937.
8. Harned, H. S. and Ehlers. R. W.. Jour. Arer.
Chem. Soc.. 5-t. 1350. 1932.
9. Kohthoff and Laitinen. pH and Electro Titrations,
John Wiley and Sons. Second Edition. 1941.
10. McKay and Worthington. Corrosion Resistance of
Metals and Alloys. Reinhold Publishing Co.,
Second Printing., 1937.
11. Millions. Corrosion. Vol. II, No. 2. 1946.
12. Riem. H., Z. Physik. Chem., A160, 1, 1932,
13. Thompson. Theoretical and Applied Electro-
chemistry. The Macmillan Co.. 1939.
FLORIDA ENGINEERING AND INDUSTRIAL
As long as the supply is adequate, copies of available publications are
free for general distribution. Address all requests to: The Director, Florida
Engineering and Industrial Experiment Station, University of Florida,
No. I "The Mapping Situation in Florida." by William L. Sawyer.
No. 2 "The Eletriial industry in Florida," by John W. Wilson.
No. 3 "The Locating of Tropical Storms by Means of Associated Static,"
by Joseph Weil and Wayne Mason.
No. 4 "Study of Beach Conditions at Daytona Beach. Florida, and
Vicinity," by W. W. Fineren.
No. 5 "Climatic Data for the Design and Operation of Air Conditioning
Systems in Florida," by N. C. Ebaugh and S. P. Goethe.
No. 6 "On Static Emanating from Six Tropical Storms and its use in
Locating the Position of the Disturbance." by S. P. Sashoff and
No. 7 "Lime Rock Concrete-Part I," by Harry H. Houston and Ralph
No. 8 "An Industrial Survey of Hides and Skins in Florida," by William
No. 9 "Studies on Intermittent Sand Filtration-Part I," by D. L.
No. 10 "Florida Spray Gun for Pine Tree Gum Flow Stimulation," by
Norman Bourke and Keith W. Dorman.
No. 11 "Developments of Ceramic Compositions Suitable for the Produc-
tion of Porcelain Type Artware." by B, W. Thorngate.
No. 12 "Mold and Mildew Control for Industry and the Home." by S. S.
No. 13 "Engineering and Industrial Research at the University of
No. 14 "Reverse Cycle Refrigeration for Heating in the South," by S. P.
No. 15 "Analysis of the Two Span Rigid Frame Highway Bridge," by
C. D. Williams.
No. 16 "Beach Erosion Studies in Florida," by Howard J. Hansen.
No. 17 "Corrosion Studies." by Albert L. Kimmel.
Technical Paper Series
No. 1 Heats of Solution of the System Sulfur Trioxide and Water, by
Ralph A. Morgen.
No. 2 The Useful Life of Pyro-Meta and Tetraphosphate, by Ralph A.
Morgen and Robert L. Swoope.
No. 3 Florida Lime Rock as an Admixture in Mortar and Concrete. by
Harry H. Houston and Ralph A. Morgan.
No. 4 Country Hides and Skins, by William D. May.
No. 5 Empirical Correction and Compressibility Factor and Activity
Coefficient Cures, by R. A. Morgen and J. H. Childs.
No. 6 Crate Closing Device, by William T. Tiffin.
No. 7 The System Sodium Acetate-Sodium Hydroxide-Water. by R. A.
Morgen and R. D. Walker, Jr.
No. 8 Patent Policies for Sponsored Research, by Ralph A. Morgen.
No. 9 Conservation of Municipal Water Supplies in Air-Conditioning
Systems, by N. C. Ebaugh.
No. 10 Florida Scrub Oak-New Source of Vegetable Tannin, by H. N.
Calderwood and W, D. May.
No. 11 Protein Feed from Sulfite Waste Liquor, by Ralph A. Morgan and
Robert D. Walker. Jr.
No. 12 Effect of Moisture on Thermal Conductivity of Limerock Concrete,
by Mack Tyner.
No. 13 Insect Tests of Wire Screening Effectiveness, by S. S. Block.
No. 14 Properties of Limerock Concrete, by Mack Tyner.
No. 15 Scrub Oak as a Potential Replacement for Chestnut, by H. N.
Calderwood and W. D. May.
No. 16 Yeast from Sulfite Waste Liquor, by Robert D. Walker. Jr.