Category: Physics Notes PPT

Specific gravity is one of the properties of any fluid. The specific gravity is having much application even in our everyday life. In order to understand fluid dynamics, we must understand what is the specific gravity and the specific gravity formula as a priority. The specific gravity often is even referred to as the relative density and it is a dimensionless entity. The density of the object majorly determines this factor. In this topic, we will discuss what is specific gravity, what is specific gravity formula and a small derivation of specific gravity formula along with solved examples.

Specific Gravity of Liquid

The specific gravity of liquid refers to the ratio of the density of an object or the fluid and the reference material, usually, water is considered as reference material for fluids and air for gases. Furthermore, the specific gravity of a liquid or an object can tell us if the object will sink or float in reference material. Besides, the reference material for liquids is water that always has a density of either 1 gram per cubic centimetre or 1000 kg/m³ and the specific gravity of water is always one.

In general, we can say the specific gravity defines whether an object will sink or float in water. Anyways, there are many other factors that determine whether an object will float or sink, such as density, specific weight, etc. The specific gravity of the object is always denoted by the letter S.

Application of Specific Gravity

The main application of specific gravity is that it lets us decide whether the given object is denser than the water or not. If the specific gravity of the object is less than the specific gravity of water i.e., S ＜ 1 then the object will float on the water. At the same time if the specific gravity of the object is found to be greater than the specific gravity of water i.e., S > 1 then the object will sink in the water. For example, we can think of a plastic ball floating on water. 

If we know the specific gravity of any material then we can easily determine the density of the material. Let us have a look at the specific gravities of a few familiar objects:

• The specific gravity of water = 1

• The specific gravity of mercury = 13 . 6

• The specific gravity of aluminium = 2.72

• Specific gravity of gold = 19.3

What Is Specific Gravity Formula?

Let us have a look at the specific gravity of liquid derivation to understand what is specific gravity formula. According to the definition of specific gravity, we can formulate the same mathematically as follows:

⇒ S = [frac{rho_{object}}{rho_{water}}]

Where,

[rho][_{object}] – The density of the object or the material under consideration

[rho][_{water}] – The density of the water (or the reference material depending upon the material used)

Since both the numerator and the denominator have the same units (i.e., both are densities), hence they cancel out each other, thus the specific gravity is a dimensionless physical quantity. From the specific gravity formula, it is clear that the specific gravity is directly proportional to the density of the materials. In order to calculate the specific gravity, we must first know how to calculate the density of the materials.

The density of the materials can be calculated by using the formula:

⇒ [rho] = [frac{mass}{volume}] = [frac{m}{v}] Kg/m[^{3}]

We know that the mass of an object can be in grams, kilograms, and pounds, irrespective of the unit of measurement the density of the object can be determined. At the same time, the density directly relates to the mass of the object. So, we can also rewrite the specific gravity by dividing the mass of an object with the mass of the water without violating the laws of physics. Thus, the specific gravity formula in terms of mass is given by:

⇒ S = [frac{text{mass of the object}}{text{mass of the water}}] 

And from the theories of physics, we have seen that the mass of the object is also directly related to density. Also, from Newton’s law, we know that the mass is measured in Newtons. Hence, we can also calculate the specific gravity of an object with the help of the weight of the object and water, and it is given by the formula:

⇒ S = [frac{text{Weight of the object}}{text{Weight of the water}}] 

One of the important points to note down here is that in all these formulas of specific gravity all the units are the same and they cancel each other out.

Solved Examples:

1. A liquid has a mass of 45 grams and the volume of the water (reference material) is 5 ml. Then calculate the specific gravity of the object? Also, specify whether the object will sink or float in the water? 

(Note: Consider the density of the water is 1 gm/ml) 

Sol:

Given,

The mass of the object = m = 45 grams

The volume of the water = V = 5 ml

The density of water = [rho][_{water}] = 1gm/ml

We are asked to determine the specific gravity of the given object. Before we start calculating the specific gravity, we must determine the density of the given object.

Thus, the density of the given object is given by:

⇒ [rho][_{object}] = [frac{mass}{volume}] = [frac{45}{5}] = 9 gm/ml…..(1)

Therefore, the specific gravity formula is given by:

⇒ S = [frac{rho_{object}}{rho_{water}}] …..(2)

Where,

[rho][_{object}] – The density of the object or the material under consideration

[rho][_{water}] – The density of the water 

Substituting all the values in equation (2) and simplify. We get:

⇒ S = [frac{9}{1}] = 9

Thus, the specific gravity of a given object is 9. Since the specific gravity of the object is more than 1 i.e., S > 1, the object will sink in the water.

2. A liquid has a mass of 10 grams and the volume of the water (reference material) is 12 ml. Then calculate the specific gravity of the object? Also, specify whether the object will sink or float in the water? 

(Note: Consider the density of the water is 1 gm/ml) 

Sol:

Given,

The mass of the object = m = 10 grams

The volume of the water = V = 12 ml

The density of water = [rho][_{water}] = 1gm/ml 

We are asked to determine the specific gravity of the given object. Before we start calculating the specific gravity, we must determine the density of the given object.

Thus, the density of the given object is given by:

⇒ [rho][_{object}] = [frac{mass}{volume}] = [frac{10}{12}] = 0.8 gm/ml …..(1)

Therefore, the specific gravity formula is given by:

⇒ S = [frac{rho_{object}}{rho_{water}}] …..(2)

Where,

[rho][_{object}] – The density of the object or the material under consideration

[rho][_{water}]  – The density of the water 

Substituting all the values in equation (2) and simplify. We get:

⇒ S = [frac{0.8}{1}] 

Thus, the specific gravity of given objec
t is 0.8. Since the specific gravity of the object is less than 1 i.e., S < 1, the object will float in the water.

The force of attraction is a force that draws the body close to it due to an attraction. In nature, several attraction forces exist. These are the electric force, magnetic force, electrostatic force, gravitational force, and electromagnetic force. Gravitational force is a well-recognized force that attracts the body towards it despite the distance. Through Newton’s Gravitational force we get a lot of clarification regarding this force and how it operates. It states that the mass existing in the Universe attracts some or other mass prevalent in the universe. It validates that anything that is thrown up eventually comes down. The formula of the force of attraction is based on this theory. 

Representation of Force of Attraction Equation

Suppose there are two masses denoted by ma and mb separated by a space. Then the force of attraction formula is stated by 

 

F_g = [frac {(G m_a m_b)} {d^2}]

 

Where, 

 

F= force of attraction

 

G= gravitational constant

 

m_a= mass of the first object a

 

m_b= mass of second object b

 

d = distance between two objects d

 

This force of attraction formula helps in the calculation of any two bodies having a greater mass as the smaller mass is insignificant. 

 

Even when things are not in close proximity, the force of attraction draws them together. Learn about the three forces of gravitational, electrical, and magnetic attraction, as well as their formulae and concepts.

What is meant by Gravity?

Gravity is probably the most well-known force of all. We people on Earth imagine gravity as an apple landing on Isaac Newton’s head. It is only due to the gravity that we observe things falling to the ground. Similar instances occur throughout the universe as well. However, this is merely our perception of gravity. In reality, just as the earth pulls the apple towards it owing to gravity, the apple also pulls the earth. The problem is that the earth is so enormous that the gravitational interactions of every other item on the globe are overwhelmed. 

Every item with mass has a gravitational pull on everything else. This force explains why the planets orbit, among other reasons. Furthermore, everything, including you, pulls every other object in the cosmos, which is known as Newton’s Universal Law of Gravitation. The acceleration of the moon as compared to the acceleration of things on Earth by Issac Newton. Newton was able to derive an important conclusion regarding the dependency of gravity on distance by believing that gravitational forces were responsible for each. He came to the conclusion that the gravitational pull between the Earth and other things is inversely proportional to the distance between the Earth’s center and the object’s center based on this comparison. However, distance isn’t the only factor that influences the amplitude of gravitational forces.

What Do You Mean by Electric Force?

The electric force, also known as the electrostatic force, is the second force that may induce attraction. While gravity affects mass things, electrostatic forces impact charge objects. The quantity of electrons and protons in a thing determines its charge. Most items are electrically neutral, which means they contain an equal number of electrons (which have a negative charge) and protons (which have a positive charge). Objects can, however, lose electrons and become positively charged, or absorb electrons and become negatively charged. As a result, positive and negative charges will attract one another. As a result, the adage “opposites attract” is true.

What is Magnetic Force?

The magnetic force is the third force that may produce attraction. Objects with magnetic characteristics are attracted by the magnetic force. A magnet attracts iron-rich metals, such as steel, as well as nickel and cobalt. When a north magnetic pole is placed close to a south magnetic pole when an object is magnetized, the magnetic force is attracted. Electric currents are the primary source of magnetism. There is an electric current when charges move. The electric force affects charges that do not move, while the magnetic force affects charges that move. The proverb ‘Opposites attract’ may also be explained by magnetic attraction.

Factors affecting the Three Forces of Gravitational, Electrical, and Magnetic Attraction

The gravitational force is equal to the product of the masses, m1 and m2, and inversely proportional to the square of the distance between the two masses, denoted by r. The attraction is inversely proportional, which implies that it is strong when the masses are near to each other and weak when they are far apart.

The force of electrical attraction is proportional to the product of the charges, and it is inversely proportional to the square of the distance between the charges, exactly like gravitation. There exists an attraction between a positive and a negative charge separated by r.

The force is stronger when the charges are near to one another, and weaker when the charges are further apart, just as the gravitational force.

Metal atoms contribute electrons to nonmetal atoms when metals and nonmetals combine to create compounds. Because of the loss of negatively charged electrons, metal atoms become positive ions, whereas nonmetal atoms become negative ions. Ions display attraction forces toward ions with opposite charge, giving rise to the saying “opposites attract.” Coulomb’s law governs the force of attraction between oppositely charged ions: F = k * q1 * q2 / d2, where F is the force of attraction in Newtons, q1 and q2 are the charges of the two ions in coulombs, d is the distance between the nuclei of the two ions in meters, and k is a proportionality constant of 8.99 x 109 Newton square meters per square coulomb.

Conclusion 

The formula of force of attraction is important to understand the concept of gravity that works on the earth. Moreover, when we calculate force of attraction it also explains the gravitational phenomenon that happens in space. 

This article gives a clear knowledge of the AC Voltage and Inductor when an AC voltage is applied to the inductor. But first thing is first. We need to know about an inductor. In the presence of the electric current, an inductor works as most of the power electronic circuit that stores energy in the form of magnetic energy.

 

An Inductor is a coil of wire that sets an altering magnetic field around it when an altering current flows through it. Due to this inductance,a coil is subjected to an alternating current and a back emf is induced in the coil. The current across the inductor changes to equalize the current passing through it. The other names of inductors are choke, reactor, or just coil.

The inductor voltage can measure the amount of electromotive force (voltage) generated for a given rate of change of current.  Consider that an inductor produces an EMF of 1 volt when current passes through the inductor. This inductor possesses an inductance of 1 Henry and changes at the rate of 1 ampere per second.

These are the symbols used for the inductor:

 

(Uploaded soon)

 

AC Voltage Applied to an Inductor

An inductor can oppose or block the passage of current through it. There are two cases to do so. One case is for the DC circuit, and another is for the AC circuit. The first inductor is connected to a DC supply, and the second one is connected to the AC supply. In the DC circuit, a constant current flows through this inductor, and the bulb connected to it glows brightly. But in the AC circuit, the bulb does not lighten up as brightly as the first one; this happens because the inductor opposes the flow of alternating current.

 

(Uploaded soon)

 

AC Voltage Applied to an Inductor Derivation 

Here is a derivation of AC Voltage Applied to an Inductor Class 12:By using Lenz’s law, the flow of AC current through an indicator can be examined. We know that alternating current changes with magnitude and direction. When the current rises from zero to top value, then the magnetic field, as well as the current of the coil, increases. That is why we find an induced EMF and its direction as stated by the Lenz’s Law:

 

[E = – frac{dphi}{dt} ]

 

In certain cases, when the current declines from peak value to zero, the magnetic field of the coil also becomes zero. Therefore, the relation of the induced EMF is:

 

[E = -L frac{di}{dt} ]

 

Supplied voltage must be equal to the reverse Emf to maintain the current.We know that 

[phi  = L times i ]

The amount of voltage that the AC source requires is given by:

[V = L times frac{di}{dt}]

 

Across the coil, the relation between current and voltage is:

 

[V = L times frac{di}{dt}]

[frac{di}{dt} = frac{V}{L} ]

[frac{di}{dt} = frac{V_m Sin omega t}{L}]……….. 1

 

Here, 

Vm = Maximum voltage

ω = Angular frequency.

After integrating equation 1

 

[i = int frac{V_m sin omega t}{L} dt]

 

[i = frac{-V_m cos omega t}{omega L} dt]

 

[i = frac{V_m sin (omega t – frac{pi}{2})}{L} dt]

 

[i = i_m sin (omega t – frac{pi}{2})]

 

Here, im = Maximum value of current 

So, the relation for inductive reactance V = Vmsin⁡ωt

 

[V = V_m sin omega t]

 

[V = i_m sin omega t]

 

[V = i_m sin (omega t – frac{pi}{2})]

 

[i = -i_m cos omega t]

 

[i_m = frac{V_m}{omega L}]

 

[i_m = frac{V_m}{X_L}]

 

In the above expression, Inductive reactance = XL

 

AC Voltage Applied to an Inductor Derivation with Graph 

 

()

 

AC Voltage Applied to an Inductor and Power Consumed

An AC voltage is applied to the inductor to know its function in an electric circuit. The circuit diagram given in Fig.1 shows the presence of an inductor and an A Voltage V, which is represented by the symbol “~.”

 

The expression for the AC voltage, V = Vmsin⁡ωt

 

The expression for the amplitude of the current [i_m = frac{V_m}{L omega} ] 

 

As we know, the symbol for inductive resistance is XL.  XL = ωL

 

Hence, the amplitude of the current in this circuit can be written as:

[i_m = frac{V_m}{X_L} ]  

 

The above equation’s dimensional formula for inductance signifies the same dimensional formula for resistance. Ohm is the SI unit of capacitance. The purpose of the capacitive resistance is to block the current flow in a purely inductive circuit. This exactly happens when resistance delays the current flow in a purely resistive circuit.After knowing this, we can clearly infer that the inductive resistance is directly proportional to the frequency and the inductance. A conclusion is found from the above expressions that the current in an inductive circuit is π/2 behind the voltage across the capacitor.

 

Do you know?

Inductors work on the principle of magnetism that stores the energy from the current in the form of a magnetic field. A magnetic field is developed in the inductor when a voltage is applied across the terminals of an inductor.We can determine the value of the current inductor flow by its own self-induced EMF or back EMF value because the progress of the current passing through an inductor is not on the spot.

 

When current is at its peak value, a steady-state current is flowing through the coil, and there is no back EMF induced to block the current passage. That is why the coil behaves as a short circuit, which allows maximum current passage through it in the case of a DC circuit. 

 

Conclusion:

This article focuses on Inductor Voltage and its application. You can go through the article for a better understanding of the topic. 

The study of how gases interact with moving bodies is known as aerodynamics. Aerodynamics is mainly concerned with the forces of drag and lift induced by air flowing over and through solid bodies since air is the most common gas we experience.

Engineers use aerodynamic concepts in the design of a wide range of objects, including houses, bridges, and even soccer balls; however, the aerodynamics of a plane and automobiles are of primary concern.

Aerodynamics is used in the study of flight and aeronautics, which is the science of constructing and operating aircraft. Aeronautical engineers design aircraft that navigate through the Earth’s atmosphere using aerodynamic principles.

History of Aerodynamics

• Modern aerodynamics only dates from the seventeenth century, but humans have been harnessing aerodynamic forces in sailboats and windmills for thousands of years, and pictures and stories of flight exist in recorded history, such as the Ancient Greek legend of Icarus and Daedalus.

• Aristotle and Archimedes both used the terms continuum, drag, and pressure gradients in their writings.

• Sir Isaac Newton, one of the first aerodynamicists, was the first person to establish a theory of air resistance in 1726.

• Daniel Bernoulli, a Dutch-Swiss mathematician, published Hydrodynamica in 1738, in which he defined a fundamental relationship between friction, density, and flow velocity for incompressible flow that is now known as Bernoulli’s theory, which is used to calculate aerodynamic lift.

• The more general Euler equations, which could be applied to both compressible and incompressible flows, were published by Leonhard Euler in 1757.

• In the first half of the 1800s, the Euler equations were expanded to include the consequences of viscosity, resulting in the Navier–Stokes equations. The Navier-Stokes equations are the most general governing equations of fluid flow, but they are difficult to solve for all but the most basic shapes.

• Sir George Cayley was the first to recognise the four aerodynamic forces of flight weight, lift, drag, and thrust, as well as their interrelationships, in 1799.

• Francis Herbert Wenham built the first wind tunnel in 1871, which enabled precise measurements of aerodynamic forces. 

• Charles Renard, a French aeronautical engineer, was the first to predict the power needed for sustained flight in 1889.

• Otto Lilienthal, who was the first to achieve great success with glider flights, was also the first to propose small, curved airfoils with high lift and low drag.

• The Wright brothers flew the first powered aeroplane on December 17, 1903, based on the inventions and experiments conducted in their own wind tunnel.

• The theory for flow properties before and after a shock wave was independently developed by Macquorn Rankine and Pierre Henri Hugoniot, while Jakob Ackeret led the initial work on calculating the lift and drag of supersonic airfoils.

• Computational fluid dynamics began as an effort to solve for flow properties around complex objects and has quickly progressed to the point where entire aircraft can be designed using computer software, with wind tunnel and flight tests to confirm the computer predictions.

• Designing aircraft for supersonic and hypersonic flight, as well as the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continue to drive new aerodynamics research, while work on important problems in basic aerodynamic theory such as flow turbulence and the existence and uniqueness of analytical solutions to the Navier-Stokes equation continues.

Define Aerodynamic Principles 

Weight, lift, thrust, and drag are the four principles of aerodynamics. These physics of flight and aircraft structures forces cause an object to travel upwards and downwards, as well as faster and slower.

Weight

There is a weight to all on Earth. Gravity pulls things down, which causes this force. A plane must be propelled in the opposite direction of gravity in order to travel. The force needed to push an object is determined by its weight. In comparison to a jumbo plane, a kite needs much less upward thrust.

Lift

A lift is a force that causes something to rise. It’s the force that’s the exact opposite of gravity. Anything that flies needs to be able to fly. An aircraft’s lift must be greater than its weight in order for it to climb. Since the hot air inside a hot air balloon is lighter than the air above it, it will provide a lift. The balloon is carried by hot air as it rises. A helicopter’s lift is provided by the rotor blades at the helicopter’s tip. The helicopter rises as a result of their movement through the air. 

The wings of an aeroplane provide lift. It is the shape of an aeroplane’s wings that allows it to fly. The top of an aeroplane’s wing is curved, while the bottom is flat. Because of the form, air flows faster over the top than under the bottom. As a result, there is less air pressure on top of the wing. The wing, as well as the aeroplane to which it is connected, moves up as a result of this situation. Many aircraft employ the use of curves to adjust air pressure. This is how helicopter rotor blades work. A curved form also provides a lift for kites. This principle is used on sailboats as well. The sail of a boat is similar to a wing. That is what propels the sailboat forward.

Drag

A force that seeks to slow something down is called drag. It makes moving an object difficult. Walking or running through water is more difficult than walking or running through the air. This is due to the fact that water has a higher drag coefficient than air. The amount of drag is often affected by the shape of an object. When compared to flat surfaces, most round surfaces have less drag. Surfaces that are narrow have less drag than those that are wide. The more air that comes into contact with a surface, the more drag it produces.

Thrust

The power of thrust is the exact opposite of drag. Thrust is the forward movement of something. An aircraft must have more thrust than drag to keep going forward. A propeller could provide thrust to a small plane. Jet engines could provide propulsion to a larger plane. There is no thrust in a glider. It can only fly until the drag slows it down and forces it to land.

Law of Aerodynamics

< span>Problems in aerodynamics can be solved using fluid dynamics conservation laws according to the assumption of a fluid continuum. The three conservation law of aerodynamics are:

The law of conservation of mass or principle of mass conservation specifies that the mass of the system has to remain constant over time for every system closed to any transfer of matter and energy, as the mass of that system cannot change, so no additional quantity or removal can be made. The amount of mass is therefore maintained over time. The law imposes, though the mass may be rearranged within space or the associated entities may change in form, that mass can be neither created nor destroyed.

In a closed system where no matter is exchanged and external forces do not act, the total momentum is constant. Newton’s laws of motion imply that fact, known as the law for the conservation of momentum. Newton’s Second Law can be considered to apply the mathematical formulation of this principle. Only external forces, such as viscous forces and weight, can change the momentum in a flow. This can include both surface forces. The principle of momentum conservation can be expressed as a vector equation or divided into three scalar equations (x,y,z components).

The law of conservation of energy states that the total energy of an isolated system remains constant over time. Energy is neither produced nor lost within a flow, according to the energy conservation equation, and any addition or subtraction of energy to a volume in the flow is induced by heat transfer or work into and out of the region of interest. The law of conservation of energy states that a perpetual motion machine of the first kind cannot exist; no device can provide an infinite amount of energy to its surroundings without an external energy supply.

Together, these three laws are the known basis for Navier-Stokes equations. The Navier-Stokes equations have no proven analytical solution and are solved using computational techniques in modern aerodynamics. Since high-speed computing methods were not previously available, and because the computational cost of solving these complex equations is high now that they are, simplifications of the Navier-Stokes equations have been and continue to be used. The Euler equations are a series of related conservation equations that ignore viscosity and can be used in situations where viscosity is assumed to have a minor impact. Bernoulli’s equation is also a one-dimensional approach of both momentum and energy conservation equations.

Branches of Aerodynamics

Classification of Aerodynamics Based on the Flow Environment or Properties of the Flow:

• A flow is said to be compressible if its density varies along a streamline, according to aerodynamic theory. This implies that, unlike incompressible flow, density variations are taken into account. 

• In general, when the Mach number in part or all of the flow reaches 0.3, this is the case where compressible flow occurs. 

• Although the Mach 0.3 value is arbitrary, it is used since gas flows with a Mach number less than that show density changes of less than 5%. 

• Furthermore, the overall density shift of 5% occurs at the object’s stagnation point, while density changes across the rest of the object would be much smaller.

• The density of an incompressible flow is constant in both time and space. Although all real fluids are compressible, a flow is often approximated as incompressible if the impact of density changes on the measured results is minimal. 

• When the flow rates are slightly smaller than the speed of sound, this is more likely to be the case of incompressible flow. 

• At speeds equal to or above the speed of sound, compressibility has a greater impact. 

• The Mach number is used to determine whether incompressibility can be assumed otherwise, compressibility effects must be taken into account.

Classification of Aerodynamics Based on the Flow Speed Is Below, Near or Above the Speed of Sound.

1. Subsonic Flow

• Subsonic or low-speed aerodynamics is the study of fluid motion in flow with speeds much lower than the speed of sound in the flow. 

• There are many types of subsonic flow, but when the flow is inviscid, incompressible, and irrotational, a unique case occurs. This is known as potential flow, and it allows the differential equations that describe the flow to be a simpler version of the fluid dynamics equations, allowing the aerodynamicist to choose from a variety of fast and simple solutions. 

• One of the decisions an aerodynamicist must make when solving a subsonic problem is whether or not to have compressibility effects.

• The amount of change in density in a flow is referred to as compressibility. When the effects of compressibility on the solution are minor, it is possible to make the statement that density is constant. 

• The issue then becomes one of incompressible low-speed aerodynamics. The flow is said to be compressible when the density is allowed to vary. 

• When the Mach number in the flow is less than 0.3, compressibility effects are generally overlooked. The problem flow should be defined using compressible aerodynamics above Mach 0.3.

2. Transonic Flow

• The word “transonic” refers to a range of flow velocities just below and above the Mach 0.8–1.2 local speed of sound. 

• It is defined as the speed range between the critical Mach number, at which some parts of the airflow over an aircraft become supersonic, and a higher speed, typically near Mach 1.2, at which the entire airflow becomes supersonic. 

3. Supersonic Flow

• Flow speeds higher than the speed of sound are referred to as supersonic flow. 

• Subsonic and supersonic flow behave very differently. Pressure changes are how a fluid is told to respond to its environment. 

• As a result, since sound is an infinitesimal pressure difference propagating through a fluid, the speed of sound in that fluid can be considered the fastest rate at which information can propagate through the flow.

• The fluid builds up a stagnation pressure in front of the object as it collides with it, bringing the moving fluid to a halt. < /span>

• This pressure disruption will spread upstream in a subsonic fluid, altering the flow pattern ahead of the object and giving the impression that the fluid is aware of its presence by shifting its movement and flowing around it. 

• However, in a supersonic flow, the pressure disturbance cannot travel upstream. As a result, when the fluid approaches the object, it collides with it, forcing the fluid to change its properties such as temperature, density, pressure, and Mach number in a violent and irreversible manner known as a shock wave.

• The central difference between the supersonic and subsonic aerodynamics regimes is the presence of shock waves, as well as the compressibility effects of high-flow velocity fluids.

4. Hypersonic Flow

• Hypersonic speeds are extremely supersonic speeds in aerodynamics. 

• The term came to be used to describe speeds of Mach 5 and higher, which are 5 times the speed of sound. 

• A subset of the supersonic regime is the hypersonic regime. 

• High-temperature flow behind a shock wave, viscous interaction, and chemical dissociation of gas defines the hypersonic flow.

In this article, we have discussed what is aerodynamics, the history of aerodynamics, principles of aerodynamics, the law of aerodynamics and branches of aerodynamics.

Conclusion

Aerodynamics is a branch of physics that studies the motion of air and other gaseous fluids, as well as the forces that act on objects moving through them. Aerodynamics aims to clarify the concepts that control the flight of aircraft, rockets, and missiles in particular. It also involves the design of cars, high-speed trains, and ships, as well as the construction of structures such as bridges and tall buildings to assess their wind resistance.

In Physics, the angle of incidence can be depicted as the angle formed in between a ray propagated on a surface and the line normal to the point of occurrence on the same surface. When a ray of light falls upon the surface of a mirror, it reflects in return. A ray of light strikes a surface at a specific point. The line straight up from that point, at 90 degrees to the surface, is known as the normal. The angle of incidence is the angle formed by the normal and the light ray.

 

We need to study in detail the concept of reflection of light to understand the angle of incidence. This article will deliver you information about the angle of incidence along with some important concepts related to this topic. 

 

Here are some key points regarding the angle of incidence:

1. The incident ray is the ray that strikes first upon the smooth surface of the mirror.

2. The reflected ray is the ray that drives away from the point of an incident of the ray.

3. The point of incidence is the place where the ray of light is propagated.

4. A normal is known as a perpendicular line that is drawn from the same point.

 

 

Concept of Light 

The behavior of sunshine is well-known to be fairly predictable. If a ray of light were to approach and reflect off of a flat mirror, the light’s behavior because it reflected would follow a predictable law called the law of reflection. The incident ray is the ray of light that approaches the mirror. The reflected ray is the ray of sunshine that leaves the mirror. A line perpendicular to the mirror’s surface may be drawn at the purpose of incidence where the ray impacts the mirror. An everyday line is what this line is named. The angle formed by the incident and reflected rays is split into two equal angles by the traditional line. The angle of incidence is the angle formed by the incident beam and also the normal.

This law is usually observed when adding a research lab. you need to sight along a line at the image position to work out a picture of a pencil in a mirror. The light that travels along the road of sight to your eye happens to obey the law of reflection. it’d be impossible for a beam of sunshine to come back from the item, reflect off the mirror in keeping with the law of reflection, so travel your eye if you were to sight along a line at a special place than the image location. Only when you examine the image does light from the thing reflect off the mirror and move to your eye in step with the rule of reflection.

The eye, for instance, is sighting along a line above the particular image location. The light from the item must reflect off the mirror in such the simplest way that the angle of incidence is a smaller amount than the angle of reflection for it to succeed in the attention. the attention during this situation, light from the item would reflect in such a way that the angle of incidence is larger than the angle of reflection so as for it to achieve the attention. Neither of those situations would be in line with the law of reflection. Beyond doubt, while sighting along the suggested line of sight, the image isn’t visible in each case. To look at the image of an object in a mirror, an eye fixed must sight at the image position because of the law of reflection.

When managing a beam that’s roughly parallel to a surface, the angle between the beam and also the surface tangent, instead of the angle between the beam and also the surface normal, is typically more relevant. The grazing angle, also referred to as the glancing angle, is the 90-degree complement to the angle of incidence. The term “grazing incidence” refers to the speed of occurrence at tiny grazing angles.

In X-ray spectroscopy and atom optics, where considerable reflection can only be achieved at small values of the grazing angle, grazing incidence diffraction is employed. Ridged mirrors are made to reflect atoms approaching from a narrow grazing angle. In most cases, this angle is expressed in milliradians. Lloyd’s mirror may be a concept in optics.

Law of Reflection

When we look within the mirror, it’s like our image is truly on the opposite side of the mirror. The rule of reflection tells us that the light is coming from a selected direction. Our image is precisely the identical distance behind the mirror as we stand removed from the mirror thanks to the angles. When a mirror is mounted on a room’s wall, all of the photographs in it are hidden behind the mirror, making the space appear larger. The visuals aren’t figments of our imagination, even after they make items appear to be where they can not be (such as behind a solid wall). Instruments can capture and videotape mirror images, which appear as clones of what we see with our eyes (optical instruments themselves).

Law of Refraction 

The angle that is  formed at the point of refraction by a refracted ray and a line drawn between two mediums

The bending of light when it passes from air to liquid is the commonest example of refraction, which causes submerged objects to seem displaced from their actual placements. Prisms split white lightweight into its constituent colors as a result of refraction. The wave theory of light is widely accustomed to justify refraction, which is predicated on the fact that lightweight travels quicker in some media than it will in others.

 

The Angle of Incidence Formula

We can find the angle of incidence by using Snell’s Law.

 

According to this law, 

 

[frac{text{sin i}}{text{sin r}}= frac{n_{r}}{n_{i}}]

 

Here, i = the angle of incidence

r = the angle of refraction

ni = the index in the incident medium

nr = the index in the refracting medium

 

 

The Angle of Incidence and Angle of Reflection 

 

From the above figure, we can infer the following three things, such as:

1. A ray of light falls on the point P of the smooth surface of a mirror.

2. The same ray gets reflected from the point of incident P.

3. After detailed observations, scientists have concluded that the angle of incidence is equal to the angle of reflection. A perpendicular is drawn to point P, which divides both angles. The normal drawn on the point P of a plane mirror helps to relate the angle of the incident ray and the angle of the reflected ray.

 

This means, i = r

 

The Angle of Incidence and Angle of Refraction

The Angle of Incidence 

It is the angle that covers between the normal and the incident ray. It is made when the ray of light touches the surface of the glass bar.

 

The Angle of Refraction

It is the angle that covers between the normal and the refracted ray. It is formed when the ray of light makes its way out of the glass bar.

 

As we know, the angle of incidence
is equal to the angle of refraction; they remain in a constant relation for this type of behavior. 

 

Relation between Angle of Incidence and Angle of Refraction

Scientists have named the refraction of light when the path of light passes through one medium to another as the refraction of light. There are multiple factors in the refraction process, such as incident ray, refracted ray, normal (perpendicular to the point of the incident), and point of incidence.

 

There are two mediums where the ray of light makes contact. The first name is a rarer medium and the second one is a denser medium.

 

The speed of light in the rarer medium is more as compared to the speed of light in the denser medium. 

 

In the angle of incidence and angle of refraction, the medium has a huge impact.

 

An example of a rarer medium is air or any kind of gas. Glass, diamonds, and kerosene are the denser medium. The speed of light is blocked inside the denser medium whereas there is no opposition from any rarer medium to the speed of light. 

 

Difference between Angle of Incidence and Angle of Refraction

Most importantly, the difference between the angle of refraction and the angle of incidence is the sequential order of the two angles. The incident angle and refracted angle are unequal.  

 

Firstly, it is created by a wave due to the different mediums.

 

When the beam of light gets refracted from a rarer to a denser medium, the angle of incidence lies between 0 to 900.

 

Nevertheless, we can’t be sure about the angle of refraction when the light ray comes from the rarer medium.

 

The above explanation does not apply to a condition where the ray of light travels from a denser medium.

 

If we do some modifications when the incident angle is inclined progressively, a change can be seen to the angle of refraction. 

 

The angle of refraction changes, which means it inclines rapidly when a certain value of the incident angle is not reached.

 

The refracted ray of light reaches its maximum point (900  where the refracted ray drives along with the border) at this critical angle of the incident ray.

 

Do You know? 

These are the main points that students must know about:

1. We use the unit of the degree to measure the angle of the incidence as well as the angle of refraction.

2. All the rays such as refracted ray, incident ray lie on the same interface along with the normal at the point of incident.

As the advancements taking place in physics have been getting better and more interesting to know about the universe. We know that atoms are made up of protons, neutrons and electrons. These were assumed to be extremely small and massless particles. After a period of time scientists were able to discover particles that are also constituents of the atom and categorized them as elementary particles. The group of elementary particles have particles and their antiparticles. 

Now, what are the antiparticles? We know that the universe is made up of several particles such as electrons, protons, neutrinos, etc… all these particles are having their corresponding antiparticles associated with them, such that the interaction of these particles will destroy each other and hence it will lead to extreme energy release in the form of photons or sometimes in the form a new particle. These antiparticles will be having the same mass as the particle but different physical and quantum properties.

Antiparticle of Electron:

So, whenever we speak about particles, the most basic and important particle is an electron. The electron is also having its corresponding antiparticle known as the anti-electron or the positron. According to the antiparticle definition, we know that it is such a particle when it reacts with its corresponding particle will lead to annihilation resulting in a large energy release. 

Therefore, the antiparticle of the electron is a positron, such that when an electron interacts with the positron both will get destroyed resulting in extreme energy release in the form of a photon. The positron is denoted by e+. An electron is negatively charged and the antiparticle of the electron is positively charged.

Now, let us have a look at what actually happens when an electron is interacting with the positron. So, when an electron interacts with the positron the energy will be released in the form of two gamma photons that will be carrying the rest mass energy of these particles to conserve the linear momentum.

⇒ e⁻ + e⁺ → γ + γ …….(1)

Both the gamma photons will be having excess energy of 0.511 MeV (which is nothing but the rest mass of the electron and the positron) and also if both the particles have some initial kinetic energy that will also be carried forward by these two. These pair annihilation will correspond to various conservations, such as during these reactions total charge of the system will be conserved, the total energy is conserved, total linear momentum is conserved, etc… 

Let us have a look at some properties of the electron and antiparticle of electron:

1. Both electrons and the positron are having the same rest mass energy given by 0.511 MeV.

2. The antiparticle of an electron is having an opposite charge, i.e., it is positively charged whereas the electron is a negatively charged particle. This is because to conserve the charge. 

3. The electron and its antiparticle are having the same spin. The electrons are the fermions and hence it is having a half-integral spin and hence the antiparticle of the electron is also having a half-integral spin.

4. The electron and its antiparticle are having an opposite magnetic moment. The electron is having a negative magnetic moment whereas the positron is having a positive magnetic moment. The magnetic moment is the property of elementary particles that describes how the particles interact with the external magnetic fields. 

5. Electrons and the antiparticle of electrons are having opposite lepton number. The lepton number of the electron is 1 and the lepton number of the positron is -1. 

These are some important properties that elaborate the relation between the electron and antiparticle of an electron.

Antiparticle of Proton:

Just like the electron had its own antiparticle, the proton is also having an antiparticle associated with it. The antiparticle of proton is known as the antiproton and it is denoted by p̅. Unlike electrons, protons are not elementary particles, protons are composite particles made up of elementary particles known as the quarks and hence the annihilation of these particles will be quite difficult in comparison with the annihilation of other elementary particles. 

So, as mentioned the protons are not the actual elementary particles, but they are the composite particles made up of further elementary particles known as the quarks. Protons are made up of the composition of two up quarks and one down quark, at the same time antiproton is made up of two anti up quark and one anti down quark. I.e., we write:

⇒ Proton = u u d

⇒ Antiproton = u̅ u̅ d̅

Now, when the proton interacts with the antiproton the annihilation of the quarks takes place. Thus the annihilation or the interaction of proton with its antiparticle is considered to be one of the complicated reactions. 

Let us have a look at some properties of the proton and antiparticle of proton:

1. Both proton and the antiparticle of the proton are having the same mass.

2. The antiparticle of the proton is having an opposite charge, i.e., it is negatively charged whereas the proton is a positively charged particle, without violating the law of conservation of charges. 

3. The proton and its antiparticle are having the same spin. The protons are the fermions and hence it is having a half-integral spin and hence the antiparticle of the proton is also having a half-integral spin.

4. The proton and its antiparticle are having an opposite magnetic moment. The proton is having a positive magnetic moment whereas the antiproton is having a negative magnetic moment. The magnetic moment is the property of elementary particles that describes how the particles interact with the external magnetic fields and the direction of alignment of the particle. 

5. The proton and the antiparticle of the proton are having opposite baryon number. The baryon number of the proton is 1 and the lepton number of the antiproton is -1. 

These are some important properties of the proton and the antiproton. This explains how the particle and antiparticles are associated with each other. Similarly, all other elementary particles are having their corresponding antiparticles such as the neutrino is having antineutrino, i.e., the neutrino antiparticle is antineutrino denoted by [bar{v_{0}}]. Basically, the antiparticle theory explains the interaction between the elementary particles and the conservation of laws.

Did You Know:

In recent times we have discovered a new elementary particle known as the Higgs boson. According to antiparticle theory, all the elementary particles are having their corresponding antiparticle, then what is Higgs boson antiparticle, it is not possible. Higgs boson will not have an antiparticle even though it is an elementary particle. Higgs boson is considered to be a god particle and all
other elementary particles are its constituents.