Unit 1 Tutorial 1 What is Physics?

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Human beings have always felt the nature as a wonder and wanted to know the secret behind it. Gravitational pull, flow of fluids, storms, planets, stars, kinematics etcetera. This curiosity was not only for the wonder but also to interact with the nature for his comfort. This led to many inventions and thus the science was created which in turn created physics.

What is science?

The word science comes from the Latin word “Scientia” which means “to know” or “knowledge”. Science is a method or systematic approach to understand the principles or the wonder behind the nature in as much as detail or depth possible using observations and experiments.

There are many persons who contributed for the science and its growth. Some of them are Newton who suggested the gravity, Albert Einstein who found the famous Mass-Energy equation, Neil’s Bohr who suggested the quantum theory using hydrogen atom and many others whom we will see in the upcoming tutorials.

What is physics?

Physics is a derived from a Greek word which means the “knowledge of the nature”. Thus physics can be defined as the branch which deals which the study of matter and its motions in the space and time along with the related concepts like energy and force. In a simple way it can be said that physics is the branch of science which deals about the matter interacting with the nature.

In physics we try to explain nature with regard to some of the universal laws. For example gravitational theory can be used to explain the famous Newton’s falling of an apple and also the rotation of the moon around the earth. In the similar way we can explain all the concepts of nature with respect to the universal laws stated in the physics which we will see in the further tutorials.

Physics is subdivided further into two branches. They are MacroscopicPhysics and Microscopic Physics. Macroscopic physics deals with the nature and its particles which are visible directly to the human eye, while microscopic physics deals with the nature and its particles which are in microscopic size. It can be said that physics is further divided into many braches while we will cover them in the upcoming tutorials.

Finally to conclude physics is a vast subject and it has a large scope which does not have any end. There is not end for physics and every day there is an invention coming under physics out of many a few are making the human life easier.   

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Why I have started tutorials for JEE Mains and Unit 1 syllabus

When I have started this blog I thought of writing about fluid Mechanics but I have seen that there is a need for starting from basics so that if anyone gets doubt in basics then you guys can search about it and get the results. First I will start with the physics and continue to the other subjects so that this blog of mine will serve you very well. You can find our objectives of the first unit and the topics which will be covered in for the first unit here:

This is the unit 1 of the JEE mains and also the basics in physics. Let us have an approach which is different for learning and also useful for JEE mains.

Unit 1 – Physics and Measurement
Tutorial 1: What is Physics?
Tutorial 2: Technology and Society
Tutorial 3: SI Units
Tutorial 4: Fundamental and derived units
Tutorial 5: Least count
Tutorial 6: Accuracy and precision of measuring instruments
Tutorial 7: Errors in measurement
Tutorial 8: Dimensions of physical quantities
Tutorial 9: Dimensional analysis and its applications

Find the PDF of this unit here:

http://www.docdroid.net/file/view/xfty/unit-1.pdf

1.9 Bulk Modulus and Compressibility

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Bulk modulus:

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It is defined as the ratio of change in pressure to the volumetric strain of the fluid.
It should be noted that the volumetric strain is the ratio of change in volume to its original volume.
 Bulk modulus is represented by B and by some authors as K.

This mathematically bulk modulus can be given as

where dp is the change in pressure.
 dV  is the change in volume.
V is the original volume.

It should be noted that here a negative sign is added to the bulk modulus mathematical relation(formula) because the stain is considered to be compressive strain. If the strain is tensile then the negative should not be considered. 

In SI units its dimensional formula can be given as M¹L⁻¹T⁻².

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Compressibility:

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It is defined as the inverse of the bulk modulus. Thus it can be defined as the ratio of the volumetric strain to the change in pressure. Thus mathematically it can be given as

Compressibility = 1/K or 1/B

In SI units its dimensional formula can be given as M^-1L¹T².

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References:
http://en.wikipedia.org/wiki/Bulk_modulus
http://www.britannica.com/EBchecked/topic/84278/bulk-modulus
http://dictionary.reference.com/browse/bulk+modulus
Img Credits: http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/bulk3.gif

1.8 Types of fluids based on viscosity

There are five types of fluids in fluids mechanics

1. Ideal Fluid
2. Real Fluid
3. Ideal Plastic Fluid
4. Newtonian Fluid
5. Non-Newtonian Fluid

1.Ideal Fluid

A Fluid which has an ideal flow and which is incompressible is called as ideal fluid. Ideal fluids are assumed to have zero viscosity.
It should be noted that in practice there is no ideal fluid. 

2. Real Fluid

A fluid which doesn't have ideal flow and which is compressible is called as real fluid. Real Fluids have viscosity and they face friction while they are flowing. 
All the fluids in real practice are Real Fluids

3. Ideal Plastic Fluid

A fluid in which shear stress is more than the yield value and the shear stress is directly proportional to the shear strain(du/dy) is called as Ideal Plastic Fluid.
 One of the example of the Ideal Plastic Fluid is Bingham Plastic. 

4. Newtonian Fluid

The Fluid which obeys the newtons law of viscosity is called as Newtonian Fluid. It should be remembered that the Newtons law o viscosity can be given as

And thus the fluid which obeys this law is called as Newtonian fluid.

5. Non Newtonian Fluid

A Fluid which does not obey the above equation(Newtons law of viscosity) is called as Non-Newtonian Fluid. Thus Non Newtonian fluids deviate from the above equation.

References:
http://en.wikipedia.org/wiki/Bingham_plastic
http://www.definition-of.com/Ideal+Plastic+fluid 
http://encyclopedia2.thefreedictionary.com/Ideal+Fluid  
http://mechteacher.com/fluid/

1.7 Newtons law of viscosity.

It states that the shear stress of  a fluid element in a fluid layer which is flowing with some velocity is directly proportional to the rate of shear strain. The equation we have already seen in viscosity concept is the one proposed by newton. It is given as

And if the constant of proportionality is introduced then the equation becomes

Where, μ is the constant of proportionality and is called as the coefficient of dynamic viscosity or viscosity.
τ is the shear stress and
du/dy is the rate of shear strain 

Types of fluids based on newtons law

1. Newtonian Fluids
2. Non-Newtonian Fluids

1.Newtonian Fluids

Fluids which behave according to the equation of Newtons law of viscosity are called as Newtonian Fluids. 

2. Non Newtonian Fluids

Fluids which do not satisfy the newtons law of viscosity or the newtons equation on viscosity are called as non-newtonian fluids.

Note:

1. All real fluids are Non Newtonian Fluids.
2. All ideal fluids accept the Newtons law of viscosity and are called as Newtonian fluids.
3. Water, thin motor oil are considered to be partially Newtonain Fluids.

Example Problem:
This is an example problem and remember that the values in the real life will be in the order of exponential. All the values given here are for the sake of beginners.
Consider a fluid flowing in a river. If the shear stress is  equal to 10N/m² distance between the fluid layers is 2m. Fluid is flowing with a velocity of 5m/s. 

1. Find whether the fluid is Newtoinain Fluid or non Newtonian fluid if the coefficient of dynamic viscosity is 40N.s/m².
2. Find the viscosity of the fluid if it were a Newtonian fluid.

Sol: 

1.We know from the equation that   

Therefore we can observe that

 10 ≠ 40x5/2

Therefore the given fluid is not a Newtonian Fluid.

2.If it was a Newtonian Fluid then from the above equation it can be found that 

μ = 4N.s/m².

References:

http://en.wikipedia.org/wiki/Non-Newtonian_fluid

http://en.wikipedia.org/wiki/Newtonian_fluid

http://www.enchantedlearning.com/math/symbols/

 

1.6 Kinematic Viscosity

Kinematic viscosity is defined as the ratio of the dynamic viscosity to the density of the given fluid. It is denoted by the symbol v(nu).

v = Viscosity/Density

v = μ/ρ

Video:
It should be noted that the video here also contains about the what is viscosity. I suggest you to watch about the viscosity, to refresh about the viscosity as kinematic viscosity is dependent on viscosity.
 

It's units in SI and MKS system are given by m²/s. In CGS system its units are given by cm²/s.
It should be noted that cm²/s is also called as stoke and 
stoke = 10^-4 m²/s.

Note:

1. 1Stoke = 100 Centistoke

1.5 Viscosity

Viscosity is the measure of the fluid resistance to flow.

Video:
This video also contains about the kinematic viscosity which we are going to cover in the next post. If you want to watch it you can watch it.


It can be said that the resistance is due to the intermolecular forces between the fluid layers. Thus in the figure the top fluid layer only has force on it by the fluid layer under it. But for the fluid layer under it has forces above it and layer under it.


To understand this properly let us consider an example.

Let us consider a fluid moving in x direction as shown in the figure. 

Let us assume that the lines represents the fluid layers and they are dy distance apart. And also assume that the top layer of the fluid is moving at a velocity of u. Now the viscosity is that the layer 2 pulls back the layer 1 for its movement. Thus the velocity of the second layer will be u-du. Therefore the shear stress on the first layer will be towards the left hand side and on the second layer will be towards the right hand side for this example. And we know that the shear stress is defined as the force acting on the given object per unit area. Therefore shear stress can be given as 

Here the proportionality constant becomes the coefficient of viscosity. and is denoted by μ.

Thus the equation can be represented as 

where,

τ is the shear stress 

μ is the coefficient of dynamic viscosity or viscosity.

and du/dy is the rate of shear strain or velocity gradient.

Thus we can write the equation of viscosity can be given as 

Units of viscosity can be given as

and in CGS system can be given as

Where 1 Newton is equal to 100000 dynes and it should be noted that dyne.s/cm² is also called as poise

in MKS system the units can be given as 

and the relation between the MKS system and the SI system can be given as 

Note:

1. All Real fluids have viscosity.
2. Only in ideal fluids viscosity is assumed to be zero.
3. Viscosity is also called as dynamic viscosity. 
4. The More the viscosity the slower the motion of the liquid.