Mathematical Model for Chlorine Concentration Decay in a Pipe


Chapter 1-Introduction

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Chapter 2- Mathematical Model for Chlorine Concentration Decay in a Pipe.

( I ) Unsteady State in One Dimensional Flow.

( two ) Steady State in Two Dimensional Flow.

Chapter 3- Unsteady State Two Dimensional Model in a Channel Flow and in Pipe for Chlorine Concentration Decay.

Chapter 4- Chlorine Concentration Decay in a Bulk Water Reservoir.

Chapter 5-Mathematical Model for Water Hammer in a Rigid Pipe.

Chapter 6-

Chapter 7-


On history of the exponential growing of scientific discipline and engineering and the exponential growing of complexness of the jobs originating in industry and engineering, it is need of the twenty-four hours that mathematician, scientists and applied scientists to interact with technocrats and executives to work out complex jobs and to assist industry in accomplishing edification efficiency and economic system. As we know that H2O is highly indispensable for human existences, animate beings, other populating things and workss, so a proper direction of H2O is need of the twenty-four hours to halt the wastage of even a individual bead of H2O. Not merely to salvage H2O but it is besides of import that the H2O required for human existences must be of good criterion means it should non incorporate any harmful bacteriums or chemical compounds or any other unwanted drosss. Chiefly there are three parts of H2O distribution systems ( I ) storage of H2O ( two ) purification and disinfection of H2O and ( three ) supply of H2O.


Water intervention methods such as boiling of H2O, sand and gravel filtration and straining are really old procedure found in ancient Sanskrit ( India ) and Greek about 4000 BC old the mohenjodaro and harappan ruins dating back 5000years have thrown visible radiation on the fact that people had given importance to proper H2O supply for domestic intents, irrigation and other public public-service corporation in that early period. Deposit was the chief drive force between those H2O interventions. They were non much aware about bacterial micro being and other chemical contaminations. After 1500 BC, the Egyptian foremost discovered the principal of Sedimentation. Some chemical compound and alum were used by them for colonies of partials. Some groundss for this are the images of this purification technique, which were found on the wall of the grave of Amenophis II and ramses II. After 500 BC Hippocrates discovered the mending power of H2O. He invented the pattern of filteration of H2O and obtained the first bag filter. The chief intent of the bag was to pin down deposits and that caused bad gustatory sensations or smells. After 300 BC and before 200BC, Rome built its first aqueduets. During this period Archimedies discovered his H2O prison guard. Between five 100s AD to fifteen 100s AD no attending was paid earnestly on H2O distribution system and disinfection of imbibing H2O due to less scientific research. After 16 hundred 20 seven AD some experiments were carried out on the sea H2O purification. Sir Francis Bacon was one of the active scientist at that clip. He manfully used sand filtration technique but this was non appreciated more. During the twelvemonth 17 hundred the H2O filters which were made by some waste stuff like wood coal, wool, sponge, rocks etc. were used domestic H2O supply. Approximately after 1803 AD the chief focal point was given to the H2O intervention workss for imbibing H2O by the Robert thom, Scoteland. The chief technique for H2O filtration was based on slow sand filtration. After five decennary some scientist and research worker of medical field that were chiefly H2O born disease such as cholera, icterus etc. So lone filtration of H2O is non sufficient extra intervention should given to disinfect the H2O and for this purpose Cl was used. From the clip the authorities of some states have started to build large H2O filters for populace sector which were based on sand filtrations and chlorination. America took enterprise in this respect for building immense H2O armored combat vehicle about around 18 1890ss. It is found that H2O born disease such as enteric fever and cholera etc were reduced after utilizing treated municipal H2O. But some negative side consequence of chlorinated H2O were brought in the cognition of scientist and it was due to inordinate sum of Cl in the H2O which caused respiratory job. Some alternate compound like Ca hypochloride and ferrous chloride were used together for disinfecting and deposit of imbibing H2O in some states like Belgium. After that ozone was besides used to disinfect the imbibing H2O supply in some states e.g. France. To get away from chemicals some people started to utilize place filters for imbibing H2O. After some decennary the clean H2O ACT in united provinces was passed and which came into consequence 18 October 1972.

Different method for disinfecting the H2O: There are many method for disinfecting the H2O and some of them are given below.

  1. Disinfecting the H2O by boiling: This is one of the oldest method for disinfecting the H2O if the H2O is boiled for long clip but this method can non be apply for municipal H2O supply because a big sum of H2O is non practically to boil.
  2. Disinfecting the H2O by inordinate line: In some H2O workss line is used for diminishing hardness of H2O by adding inordinate line to the H2O bacterium can be killed from 90 % -99 % .But it besides increase the PH value of H2O and which makes the H2O extremely alkalic. Therefore before providing the H2O to the imbibing H2O pipe line inordinate H2O should take.
  3. Disinfecting the H2O by ozone: Ozone is extremely effectual to disinfect H2O. Which can be produced by a high tenseness electromotive force current through is watercourse of air in a closed chamber. The chemical reaction of ozone formation from oxizone is as follows.

  1. Disinfecting the H2O with Iodine and Bromine: To kill the infective bacteriums mixture of Bromine and Iodine is used for intervention of H2O. But this procedure is non suited for handling immense sum of H2O for public supply.
  2. Disinfecting the H2O by potesssium parmeganate: Potessium parmeganate putting to deaths bacteria up-to 98 % in the H2O and take about all orginzium. Which are responsible for cholera. But the chief draw back of this intervention is that it is found that dark brown precipitate is formed as a coaling on Bessels. Which is hard to take and therefore this method is non used by the municipality for public H2O supply.
  3. Disinfecting the H2O by intervention by ultraviolet fury: Ultraviolet fury are found in some light but these fury can besides be produced by go throughing electric current through quicksilver in a quartz tubing or bulb. Ultraviolet fury are really much effectual for killing the bacterium of sorts and so we get strictly safe H2O. This procedure is chiefly used in aqua guard and RO system for domestic, infirmary, in establishment. This intervention is really dearly-won therefore it is non in municipal H2O supply.
  4. Disinfecting the H2O by chlorination: Chlorination of H2O is wildly used all over the universe as Cl kills about all bacteriums of the H2O. Besides it is cost effectual ( inexpensive ) easy to manage and reliable. The inordinate usage of Cl converts the H2O to bitter and bad gustatory sensation. On the other manus really little sum of Cl or no Cl is non effectual to kill the bacteriums wholly.

Mathematicss is playing an of import function in work outing the flow jobs non merely in a H2O industry but besides in other Fieldss like flow jobs in biological system ( blood flow in arterias etc. ) , flow jobs oil pipe lines etc. Our chief involvement is to utilize mathematics in patterning to disinfect or kill the bacteriums by chlorination in imbibing H2O pipe line systems. In 2nd portion of the thesis we have made an effort to cipher the rush force per unit area and fluid speed caused by transient flow ( H2O cock jobs ) in stiff and viscoelastic pipes of H2O distribution systems.

In our work our chief concern is to happen how the Cl concentration decreases with clip and infinite in imbibing H2O pipe line system, H2O reservoir and overhead armored combat vehicles.

The basic mathematical equations of fluid kineticss such as equation of continuity equation of gesture and mass transportation equation used in the thesis are given below.

Equation of continuity in Cartesian co-ordinates system ( x, y, omega ) :

Where U, V, w are velocity constituents along x, Y, omega axes

Equation of continuity in cylindrical co-ordinates system ( R,, omega ) :

Equation of gesture in rectangular co-ordinates system ( x, y, omega ) :

Since the H2O is treated as a Newtonian fluid with changeless denseness and viscousness so the Equation of gesture are

Ten constituent:

y constituent:

z constituent:


Equation of gesture in cylindrical co-ordinates system ( R,, omega ) :


z constituent:


Mass transportation:

The motion of chemical species from a part of high concentration to a part of low concentration can be observed with the bare oculus by dropping a little crystal of K permagnate into a beaker of H2O. The K permagnate begins to fade out in the H2O, and really near crystal there is a dark purple concentrated solution of K permagnate off from the crystal. The advancement of the diffusion can so be followed by detecting the growing of violet part – dark purple where K permagnate of mass is written in the signifier.

The preservation statement may, or class besides be expressed in footings of moles. The chemical species a may come in or go forth the system by agencies of diffusion and by virtuousness of the over all gesture of the fluid. Besides species A may be produced or destroyed by homogenous chemical reactions.

A Typical Water Treatment Plant


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