Creation of the term Speed

When there is a translational motion, the object moves some amount of distance in some amount of time. The motion can be described by how fast its position changes. The change depends on the size of the path namely distance covered in the motion and the time taken for the object for this distance.    

Let’s say the relation between this distance and time is Speed. So, speed is the function of distance and time.

But can it be related with some mathematical operations?     

Let’s say speed as S and

            the distance covered in the motion as D and 
            the time taken for this distance as T.

It can be defined for unit of time as follows,

            To know what happen to the motion when one of these factors of variables change in the function of Speed, we should make one variable as a constant and change the other variable.

Making the time constant, we changed the distance. For a fixed time if the distance is too high it means the object moves very fast. If the distance is low, then it implies the object moves at a slow rate. Thus we found that the function Speed is directly proportional to the distance covered by the object in some amount of time.

Similarly, if you make the distance constant and changed the time taken for this distance, we can know that,

            If the time taken for some distance is high then it was understood that the motion happens at a slow rate and if the time taken for that distance is low then the motion happens quickly.

            Thus speed is indirectly proportional to the time taken for the distance in any motion.

            Hence, the Speed is directly proportional to the distance covered and indirectly proportional to the time taken and it can be simply written as

Speed  α  Distance and

Speed α   1/Time  [where “α” – “alpha” means “proportional to”].

Combining the above two, we can rewrite it as,

Speed α  Distance / Time

and let us take the proportionality constant as 1.

Finally we described the first mathematical term in motion as

Speed (s)= Distance (d) / Time (t) or s= d/t

We can get the meaning of this term d/t as follows,

“d” distance was covered in time “t”.

            consequently,

time “t”                        for        distance “d”               

[Note that d, t are the number values of distance and time]

            value of t*unit time      for        distance “d”

            unit time                       for        distance equal to the (value of d)/(value of t)

            unit time                       for        (d/t) distance

Then the length covered in unit time is

            Distance covered for Unit time = d/t

This is the same mathematical equation that we defined for Speed.

As a result finally speed “s” can be easily understood as the distance covered in unit time t and it is denoted as s = d/t.

To check whether the definition of speed fulfills our need to describe translational motions, we should try it with some real life problems, so that we can find its validity.

  

Uses:

As we have already seen, now we can compare the speeds of various runners of various ages using this definition of speed. The shape of the track is not a problem. We can make them run in a circular path and we can evaluate their speed by measuring the perimeter of the path distance “d” and time taken “t”.

Using this definition of speed, we calculated the various speeds of different animals, people, vehicles, and many other natural things.  

And another major use of “d/t” was the measurement of distances.

Using the relation “d/t” we can measure any distance between two places that lies very far away from each other. And we can also predict the time that will take for an object or animal or people having certain speed limits.  

These measurements are often used in travelling and to determine the borders of any kingdom or country.

The measurements were done using the values of Speed, Distance and Time by applying it in simple mathematical operations like multiplication and division.

Let’s start measuring,

We know that  speed = d/t      

Which implies that,     

value of distance d = value of speed * value of time t            

[*Provided that the value of t is not equal to zero as per the conditions of Divisions in Mathematics]

If we know speed “s” and time “t” then distance “d” can be measured.

But at each instant of time, speed can be calculated only if we know length and time.

Then how it can be used the above equation to find distance?  

This problem can be solved by making the speed constant over some time t.

[Note: Constant means nothing but remaining same without any change.  

In physics the changings are happening with respect to time. So if any quantity doesn’t change its value with respect to time then it is called constant with respect to time. In real, all the measurements are done with the help of constancy only. The time of period of this constancy can change but the constancy might happen.

For example we will say the speed of the vehicle is 10 meters per second. From this sentence we can know that the vehicle is achieving the constant speed of reaching 10 meters for one second at some instant. In that instant of small time the vehicle doesn’t change its value.

Though the vehicle changes its speed in the following instants of time, we can be sure that the speed is constant for that instant. Maybe the amount of time being constant can be 1 millisecond or 1 Micro second or 1 Nano second but the constancy happens.

Thus the notion of “being constancy for small intervals or instants of time” is the initialization for limits and it serves as the basic for differentiation and Integration.]

 If speed remains constant for a long time then we can find the distance “d” by using the above equation [d= s*t].

Here if the speed of an object remains constant for 5 seconds with the speed of 5meters per second then we can find the distance covered by that object in 5 seconds by multiplying 5 with the value of speed that is 5 m/s.

It equals to 5 seconds*5 meters/ seconds = 25 meters [using basic mathematics of multiplication and division]

The above calculation hold true only if the object moves in constant speed over time because, in constant speed, the vehicle will reach same amount of length in same amount of time. In the above case, in each second the object will move 5 meters. And for 5 seconds 25 meters.

Though there are no any perfect vehicles or animals that move at constant speed, we can estimate the near value.

Thus constancy helps us to solve many problems.

The simple real life of use of this constancy for a king on protecting his country is…

First we will calculate the speed of a horse or any other vehicle by making it run for some distance. Horse was specified here as just because it is the vehicle for ancient people.

Then it was made to run that horse of known speed constantly over some time t until it reaches the border of the country in the shortest path.

As we have already calculated the value of the speed of the horse, the distance covered by the horse in time t can be calculated as “speed s* time t”.

Thus we calculated the nearly distances of the border of the country from the palace or the capital of the kingdom using the animals like horses.  

So, when there happens a war, we can estimate the minimum value of the time that takes for the enemy troops to reach the palace of the kingdom.

Here we know that “The minimum time to reach the palace is the maximum time got by the king to ready his army”.     

So what is the minimum time?

Speed = Distance / Time

Time = Distance / Speed

If we want Minimum time then

condition 1: the distance (numerator) should be minimum and

condition 2: the speed (denominator) should be maximum as we have studied in mathematics.

[Note: In mathematics, when p/q=r , r is minimum only if p is minimum and q is maximum because p is directly proportional to r and q is indirectly proportional to r]

As because of we have done this experiment in the shortest path, the distance is the minimum one. Accordingly, the first condition is satisfied.  

            The maximum speed can be calculated by taking the fastest horse and making it to run at its maximum speed. According the second condition is also satisfied.

And so, now we can calculate the maximum time the King have to save his palace and his kingdom.   

In the same way, most of the things in transportations can be predicted by calculating the value of speed.

Thus, by calculating speed people solved many real life problems.  

But is it enough?

            Can we tell everything about a motion by just knowing the value of speed?

No.

The definition of motion was further improved by the need of “the direction of the position”.

Kinematics and Its assumption

The first branch of Mechanics called Kinematics was created to explain the motions of the object but without concerning the external cause on that object. It was just made to explain the motions of the objects. All other branches in mechanics were only started after this Kinematics.   

Thus Kinematics plays a main role in Mechanics. These kinds of branches are just made to understand Mechanics easily by piercing it to many various topics. It needs not to be confused with these different names of branches.  

Since we are interested in simple motions, the study of motion [Kinematics] had begun with translational motion and not with the Rotational as it is complicated for beginners.

Note:

            A body is said to be rigid if the distance between any two various particles of the body remains invariant under the action of any external force.

Translational Motion:

            A rigid body is said to undergo translational motion if it moves in such a way that it always remains parallel to itself. This means that a line connecting any two various particles of the rigid body always remains parallel to itself throughout the motion. All particles of the rigid body should have same speed, displacement, velocity and acceleration. It means that the rigid body should not rotate itself about any axis in that body. Hence the Size of the body is not important in Translational motions. It is as same as the object to be considered as a point object.

           

So the task for the Scientists was to represent “Translational Motion” using Mathematics. But they end with the Cartesian Co-ordinate system through a simple hypothesis.     

In Cartesian Co-ordinate system, the positions in space are specified using the points and the number lines of X and Y axis. The space itself is represented by full of these points and axis lines.

 So, any position can be referred uniquely to only one point in this system. The size and the shape of the object cannot be included.

As far as we concerned in translation motion, we don’t need to care about the size and the shape of the objects for we just want to calculate “the change in position” of that object.

Positions are very important than the size and the shape of the object while dealing with Translational motions.     

And so our ancient Scientists solved the problem of size and shape with a simple assumption that we have already discussed in translational motion.

Note: Assumptions are often made each and every time in Physics because these assumptions are the stepping stone for our understanding of the Physics. Assumptions are the one just made to describe the observations made in Nature. We need to be more careful about these assumptions and should not believe entirely in this.     

And the assumption made was,

“All objects should be considered as a point mass and point size” in space though it has real shape and size.

Note: Motion of objects with Unavoidable shapes and size will be studied in Rotational Mechanics.

With the point assumption, we connected the Mathematics of Cartesian Co-ordinate system with the Motions of the objects. Now the problem of positions is solved. 

The position of a moving object in space is specified in Cartesian System as,

But the motion is about the change in positions and for that, we need some mathematics of length, direction, types of measurements, units, functions and finally differentiation and integration with full history. 

Mathematical terms related with functions

After deriving functions using physics, it was used to represent all mathematical operations in a generalized, common and a simple way. Differentiation and integration were created only after these functions.

It has to be represented everything in a simplest way on dealing with physics and mathematics. 

As it have been studied in the functions, it was represented in the generalized version as y=f(x).

[Note: Symbols are not important. Don’t focus on the symbols and be not confused with them. e.g. y=f(x) is same as a=b(X)] 

Depending on the situation “x the input" can have many values. And those values are symbolized with the Number system.

 E.g. In speed(s) = distance (d) / time (t)

The distance (d) which is an input can have values from “zero” to “infinity”. But it cannot have negative values as the distance is always positive. Mathematically the distance (d) can be from zero to infinity.

We represent all these values in a single Notation called “Sets”.

       Sets are the representation of a group of all possible values of one variable (“x” or “y”) in a function.

       It was denoted using two brackets “{ }” and the “possible values” written inside the brackets. This notation is called the Set builder Notation.

       The possible values are called the “elements” of a set.

  E.g. Set of all possible values of distance (d) is denoted by “D = {x | x is from zero to infinity}”

where the possible values of x is called the elements of the set D.

       In mathematics we have already seen that the set of Whole numbers were denoted by,

“W= {0,1,2,3,4,….. up to the infinity}” where 0,1,2,3,4,…etc. are the elements of the set of W.

       Set of integers were denoted by,

“Z={negative infinity,…..-1000,…-100,…-4,-3,-2,-1,0,1,2,3,4,….positive infinity}”

       Set of Real numbers were denoted by,

“R={negative infinity,…..-0.11111,…-0.1,..-0.00001,…0,…0.1,..0.2345..,…positive infinity}”

      It contains every possible real values which includes rational and irrational numbers.

Also it can be seen that the “set D = {x | x is from zero to infinity}” is the same set that is, “the set of non- negative real numbers which includes the zero”.

       

Note: As the knowledge of Number system made us easy to understand the sets,Now it can be understood why the set of Natural Numbers, Whole Numbers and Real Numbers were already defined in our elementary mathematics.  

       Thus the function is y=f(x), and Y={set of all possible values of y}  and X= {set of all possible values of x}.

We can also say that “the function is from X to Y” because for each element in X there is an output element in Y. It means that the machines starts from the input and finally gives the result of output. 

Mathematically, the set X which is the set of inputs is called the Domain of the function f( ).

But what is set Y? How can it be determined the all possible values of “y” in a function?

What if “the number of elements in the set Y is greater than the number of elements in the set X?”

Is it possible to have a few elements in the set Y are present which are not the outputs of any element in set X? Does it have any confusion with the definition of the function?

Excess number of elements in the set Y that is not the outputs of the input set X doesn’t cause any confusion when we are dealing it with physics and mathematics problems as it always cannot be sure of the output values.

      

Hence the set Y can have excess values than the outputs f(x). It is like excess wastages coming out of the machine which is not the required output.

       Therefore the description of set Y becomes as “the set of all possible outputs and the excess elements other than outputs”.

       The set Y was named a new name called the Codomain of the function.

       The elements of the set Y are called the images of the input values of the set X.

       Each “y” value is called the image of “x” under the function “f” and each “x” is called the pre-image of “y”.  

And the set of all possible “outputs” or “images” are called the Range of the function.   

Sometimes it may happen that the set Y has less number of elements than the set X.

It is also possible to get the same output value for different input values. E.g. Constant function is the function where all the input values of the domain have unique output value that is a constant.

If the Range and Codomain is same in a function, then the function is called Onto function or Surjective function and if Codomain have excess elements than the Range then the function is Into function.

An illustration of Into function is given below   

Thus the conclusion of the definition is,

“A function from X to Y is a rule or correspondence that assigns to each element of set X, one and only one element of set Y”. Let the rule or correspondence be ‘f( )’, then the function from X to Y can be written mathematically as  f:X→Y    [where “→”denotes the meaning “to”]

where y=f(x), and  x €  X and y € Y  [“€” denotes that “subset of” or “the element of”]

and ‘y’ is the image of ‘x’ under ‘f( )’. 

X is the domain of the function,

Y is the codomain of the function,

and the set of output elements is the Range of the function.

My favourite pencil drawings

Mother Teresa 

and a painting of a thirsty butterfly,

Contemplation of the positive and the negative

Charge comes in two varieties, which we call “positive” and “negative”.

The reason we called it as “positive” and “negative” because their effect tends to cancel each other naturally. Initially there were no charges on the glass or ebonite. When we rubbed the glass with silk and ebonite with fur they get charged. And if you again touch the positive glass rod with the negative ebonite rod [Note that “positive” and “negative” is chosen by the humans and not by the nature], they cancel their effects and comes to neutral which is the initial condition. So, the fact is that positive and negative charges occur in exactly equal amounts in all matter, so that their effects are almost completely neutralized.

What if the two kinds of charge did not tend to cancel?

Were it not for this, we would be subjected to enormous electric shocks from all of the objects in Nature.    

Thus we assumed that the electric charges are there already in these objects (glass, ebonite, silk, fur, etc).

It shows their properties [effects] while rubbing with other objects.

Question and think:

Why did we choose the charge on the glass as “positive” and the charge on the ebonite as “negative”?

What will happen if I chose the charge on the glass as “negative” and the charge on the ebonite as “positive”?

Maybe in some other alien planet, people have been calling the charge on the glass is “negative” when rubbed with silk and ebonite is “positive” when rubbed with fur. 

Maybe they will be studying that “the protons in the nucleus of an atom have “negative” charge and the electrons surrounding the nucleus have “positive” charge.

But it will not make any problems in their physics. Physics holds true in every place in this universe.

No matter whether protons have positive charge or negative charge, it doesn’t cause any problem with physics. The most important thing is that protons should have the opposite charge of the electrons because these things are just the matter of sign. Signs are the matter of our choice. Nature doesn’t have any positive or negative. It has only the effect of “opposite”.

If you chose one as “positive” then the other is “negative” or if you chose one as “negative” then the other should be “positive” [It is what the effect of “opposite”].

It is important to be aware of this sign confusion because the same “positive” and the “negative” confusion will come, when you are studying about the direction of the

conventional current.  

Statement:

We observed,

 “Negative” ebonite rod repels another “Negative” ebonite rod.

            “Negative” ebonite rod repels the charge on the “amber” that is rubbed with fur.

So we said the charge on the “amber” is “negative” when rubbed with fur. Thus we choose “positive” and “negative”.

But why it should be like that?

Think:

            This may seem too obvious to the opposite comment of the statement of choosing “positive” and “negative”, but I want to contemplate other possibilities also.

What if there were 8 or 10 or infinite different species of charge?

                         

Instead of the above statement, we can also think it in another way,

Say the charge on the ebonite as “charge A” and the charge on the amber as “charge B”

and the statement of “positive” and “negative” changes to,

“Charge A” repels “charge A” and

“Charge A” repels “charge B”.

But now we don’t know whether the “charge A” and “charge B” is same. It can also be different type of charges.

So,

Why it should be only the positive and the negative electric charge? 

   

There are also the possibilities of 8 or 10 or 100 or 1000 or infinite types of different charges like charge A, charge B, charge C, charge D, charge α, charge β, charge 1, charge 2, charge 100, charge 1000, etc. 

         

Think about it.

Electricity - Electric charges

Physics is the detailed study of nature based on the observations from the nature.

In that way, a long time before 600 BC it was observed that certain objects such as rods of amber, on rubbing with cat's fur attracts light objects like feathers.

And the other famous observation which observed for long time from our birth is the lightning.

Many stories were told in various civilizations to explain this lightning.

But as a physicist, we should only concern about real experimental observations.

To get a clear vision of any observation, we are trying to make some experiments on that observation.

Similarly in the above case,

            We rubbed many things with one another and tested whether it gives shock or not.

And the experimental work was done by the great Thales of Miletus and later by William Gilbert.

After many experiments, it was observed the electric shock only when we rub two things such as rods of amber rubbed with cat’s fur, glass with silk, hard rubber rubbed with fur, and comb through hair, etc.

This type of contact electrification in which certain materials become electrically charged after they come into contact with another different material through friction is called as the triboelectric effect (also known as triboelectric charging).  They also noted that if they rubbed the amber for long enough, they could even get an electric spark to jump.

After rubbing when you take the two different rubbed objects near to each other, they attracted each other. Instead of two different objects, it you take the two parts of same object it repels each other.

It means that something is there inside these objects which make them to attract or repel. And that something else is called as Electric charges.

The continuous experiments showed that same objects repelled each other. e.g. Amber repelled amber, glass repelled glass and ebonite repelled ebonite. Due to symmetrical argument the charge on one amber piece is the same as the charge on the other amber piece. So we concluded that same charges (similar charges) repel each other.

It was also observed that different objects like glass and ebonite attracted each other. We know that the charge on the glass will not be there in ebonite as we already know that like charges repel each other. So it must be two different charges.

From careful experiments it was concluded that there are only two kinds of charges because all these charged objects showed only two qualities that is attracting or repelling. Same kind of charges repels each other and different kind of objects attracts each other.

E.g. When amber rubbed with cat’s fur,

Amber repels another amber piece – Same kind of charges repel each other  

Amber attracts fur – Different kind of charges attracts each other

similarly when Ebonite rubbed with fur,

Ebonite repels another ebonite piece - Same kind of charges repel each other  

Ebonite attracts fur - Different kind of charges attracts each other

and Glass with silk,

Glass repels another Glass piece - Same kind of charges repel each other 

Glass attracts silk - Different kind of charges attracts each other

but also Ebonite attracts Glass - Different kind of charges attracts each other

So it says that the charge on ebonite is different from the charge on the glass. And Ebonite repelled silk - Same kind of charges repel each other.

And so we concluded that the charge on ebonite is different from the charge on the glass and the charge on the ebonite is same as the charge on the silk.

First we named the charge on the glass as the positive charge. Being the same it implies that the charge on the fur is same as the glass that is positive.

It was named the charge on the ebonite as negative charge and also the charge on the silk. 
Only these two kinds of charges were found yet. When two objects rubbed with each other, the gaining of positive or negative charge is determined by humans and it was ordered in the following triboelectric series.

  
Triboelectric Series:

                    Order from  Most positively charged  {+}   to 
                                        Most Negatively Charged {-} 

Polyurethane foam {+}
Hair, oily skin
Nylon, dry skin
Glass
Acrylic, Lucite
Leather
Rabbit's fur
Quartz
Mica
Lead
Cat's fur
Silk
Aluminium
Paper (Small positive charge)
Cotton
Wool (No charge)

 Place where the change of sign happens with the materials {0}

Steel (No charge)
Wood (Small negative charge)
Amber
Sealing wax
Polystyrene
Rubber balloon
Resins
Hard rubber
Nickel, Copper
Sulfur
Brass, Silver
Gold, Platinum
Acetate, Rayon
Synthetic rubber
Polyester
Styrene and polystyrene
Orlon
Plastic wrap
Polyethylene (like Scotch tape)
Polypropylene
Vinyl (PVC)
Silicon
Teflon
Silicone rubber
Ebonite    {−}

Our final conclusions are,

•  There are two charges in nature. And it was called the positive and the negative electric charges.
•   Like charges repel each other and unlike charges attracts each other.
•   Positive repels positive.
•   Negative repels negative.
•   Positive attracts negative.
•   This classification of positive and negative charges was termed by American scientist, Benjamin Franklin who is the one of the Founding Fathers of the United States of America.
•   It was assumed that the charge on the Glass is positive when rubbed with silk. And obviously the charge on the silk is negative as they attracted each other.  

Thus we found two new electric charges which gave us a start to examine Electricity.  

Umbilicus sinus

I couldn’t talk to anyone as I have admitted in the hospital for one month. The disease is not infectious or some usual disease you could think of. Moreover it is not disease but some special of kind of thing.   Doctors called it as umbilical sinus. It is formed due to the non-stop growth of my umbilicus after the birth. To me, it was grown up to my bladder and the pelvis.

Thank god. He showed this thing just before it gets worse. Otherwise

 But in the mean time I studied a little about that disease. I will report my case.

I have a deep bellybutton (navel).

For last four weeks I happened to see some white liquid with yellowish colour discharged from my navel button (belly button). Scientifically it is called the umbilicus. So I searched it on the web and found that it was belly button discharge that caused by bacterial or fungus infection.

I applied natural remedies such as Neem tree paste. I drank neem juice and applied neem paste over my whole body. But the discharge never stopped. Instead it was increased. Finally it started to give pain that I realized that it was sinus which comes out from my navel.

Soon I concerned to local doctor. But he gave me the basic medicines like paracetamol  and amoxicillin.

And I put amoxicillin over the navel where discharge happens.

The pain was so pathetic that I couldn’t walk or sit or lie down. So I went to the nearby hospital.

Doctor said it was umbilical sinus and said me to take sinogram test.

I don’t know what is that sinogram.  It was said to take a 10 ml syringe, an yellow venflon, towel and an attender. I know about syringe, towel and attender (the person who should attend with the patient).

But I searched about the venflon and for why it needs.

Venflon -  In medicine, a peripheral venous catheter (PVC or peripheral venous line or peripheral venous access catheter) is a catheter (small, flexible tube) placed into a peripheral vein in order to administer medication or fluids. Upon insertion, the line can be used to draw blood.

The catheter is introduced into the vein by a needle (similar to blood drawing), which is subsequently removed while the small tube of the cannula remains in place. The catheter is then fixed by taping it to the patient's skin (unless there is allergy to adhesives). Newer catheters have been equipped with additional safety features to avoid needlestick injuries. Modern catheters consist of synthetic polymers such as teflon (hence the often used term 'Venflon' or 'Cathlon' for these venous catheters).

A peripheral venous catheter is the most commonly used vascular access in medicine. It is given to most emergency room and surgical patients, and before some radiological imaging techniques using radiocontrast, for example. In the United States, more than 25 million patients get a peripheral venous line each year.           

A peripheral venous catheter is usually placed in a vein on the hand or arm. It should be distinguished from a central venous catheter which is inserted in a central vein (usually in the internal jugular vein of the neck or the subclavian vein of the chest), or an arterial catheter which can be placed in a peripheral as well as a central artery. In children, a local anaesthetic gel (such as lidocaine) is applied to the insertion site to facilitate placement.

After two days, I went to that place to take sinogram test.

It was a dreadful day in my life. I understood about venflon but I never thought that it was going to be inserted straight through my navel (umbilicus). They inserted needle through my navel and cleaned the inner parts when I am awake. I am not given any anaesthesia. That is why it was the worst day in my life.  

They put some liquid through venflon to my navel using the 10 ml syringe. Now I understood about sinogram that it is similar to X-rays but it is used to take the clear vision of inner parts.

Blood came out from my navel on taking sinogram. My mom who is the attender cleaned those things. Finally they cleaned my navel and freed me to go out.  But I learned about a new thing called,

SINOGRAM

What is a Sinogram?

A sinogram is a way of outlining any small track or

wound, usually opening onto the skin, by injecting an

X-ray dye (contrast medium) through a fine tube

placed in the opening.

Are there any risks?

All X-ray procedures involve exposure to radiation in

varying amounts. The duration and level of exposure

to X-rays is strictly controlled and kept to the

minimum necessary.

The contrast medium we use is very safe and it is

extremely rare to have a serious reaction when having

a sinogram. Please inform a member of staff if you

suffer from any allergies.

Who will you see?

You will usually be cared for by a small team including

a radiologist and a radiographer. During the examination, they will be watching a television screen and taking separate X-ray films.

Later on the radiologist will review the X-ray images and issue a report.

what happens during the investigation?

You will be taken into the X-ray room and asked to lie on the table. The area of skin

involved will be exposed and cleaned well. The radiologist will then gently insert a fine

tube into the opening and inject a little clear dye through it. While the dye is going in

the doctor will be looking at the area on the camera and taking some pictures.

How long will it take?

Usually it should take no more than 30 minutes.

Are there any side effects?

Occasionally there may be a little discomfort but most people do not feel anything.

When will you get the results?

After the procedure, the images will be examined further by the radiologist, who will

then write a report on the findings. Your results will be available from the clinican

who sent you for the examination.

After my sinogram report..

When I went to consult my doctor, in my sinogram report it was said that,

• Patient was evaluated to sinogram and revealed a blind sinus tract and leakage of contrast from the same opening.

And from the CT scan it was found that,

  

• Umbilical granuloma with sinus and small inferior extension into the urachal remnant.
• No evidence of any urachal remnant cyst or diverticulum.
• No communication with the bladder or underlying bowel.
• Other organs are normal.

First in the operation, parts painted and draped. Elliptical incision made around the umbilicus. Sinus tract identified and isolated. There is extension of sinus tract into pelvis. Lower midline laparotomy incision made.

There were 2 sinus tract extents from the umbilicus to the wall of pelvis which was dissected up to lateral wall of pelvis, and trans fixation done.

Fortunately it was not too much connected with the bladder so they cut it out. But blood leakage was happened through my bladder. Urinal bag was attached with my bladder for 12 days. After 6 days blood was stopped and the urine started to come but with reddish colour. After 12 days it became normal.

That is how I am cured from umbilical sinus.