Air speed

Introduction :
It is the speed of an air related to the aircraft among them the qualifying airspeed are Calibrated airspeed, Indicated aircraft, Equivalent air speed, true airspeed and finally the density airspeed. This aircraft speed is measured by the airspeed indicator which is shortly and popularly known as ASI. These are connected to the pitot static system. Types of the airspeed are Indicated airspeed, Calibrated airspeed, Equivalent airspeed, True airspeed. In this article we will know types of articles and how to calculate the airspeed.

Air speed Types

Indicated airspeed is abbreviated as IAS. This indicator reads directly form the airspeed indicator by the pitot static system on the aircraft. This is the airspeed related to the CAS that is calibrated airspeed it is corrected for the installation errors and the instrument.

These IAS are very much important for the pilots for the various purposes like calculation of the limited speeds and so on. This plays an important role in the airspeed.

Calibrated air speed is for the instrument errors and position errors and the installation errors. This equation shows the installation and the minus position.
Where, Vc is the calibrated airspeed
qc is the impact pressure
Po is static air pressure. Measures 29.92126 inches Hg at sea level.
ao is speed of sound. Measures 661.4788 knots at standard sea level.

Equivalent & True airspeed

Equivalent airspeed: This produces dynamic pressure as the true speed at the altitude where the vehicle is flying. It is forward to the flight for the effects of compressibility. Compressible impact pressure makes a function of calibrated airspeed. At standard sea level equivalent airspeed and calibrated airspeed are equal.

True airspeed is also called as TAS, it is the physical speed of the aircraft. The relation between true airspped and speed is Vg.
Vt = Vg - Vw
Where Vw is the wind speed vector.
To compute true airspeed using a function of mach number
V_{t =} a_o.M`sqrt(T/(To))`
Where:
a_o= Speed of sound(661.4788 knots) at standard sea level
M = Mach number
T = Temperature in kelvins
T_o= (288.15 kelvins)Standard sea level temperature

Speed of Light and Sound

Introduction :

Light and sound are the essential part of our life and with an absence of one; we will not be able to communicate or to detect properly as we can do with help of these two. Light and sound both are the sensations produced by energetic particles with the help of which we will be able to see or listen. 

Difference between Speed of Light and Sound :

Regarding the speed of light and sound we can say the following points

1. Speed of light is much faster than the speed of sound in air.
2. Light do not require the medium to travel with its speed while the sound require medium to propagate.  
3. Speed of light is much less in transparent than what it had in vacuum.  While the speed of sound is much, fast in solid medium such as steel then in air.

Speed of light and sound : Conclusion

Why speed of sound Differ in different mediums means solid, liquid and air?

Explanation:
Since sound require medium particles to propagate properly, hence the medium having particles much closer will enhance the movement (speed) of sound wave rather than the medium which have a long gap between the particles. Since, the molecules spacing for solid, liquids, and gases are different in that gas molecules are more spread apart & free to move, liquids are a little more structured, and solids are very compact.             

The other reason for the different speed in different mediums is the elasticity of the medium. More the elasticity in the medium more will be the speeds of sound as we can understand with ball, more the elasticity of the ball more will it jump. Since steel is more elastic than air, so sound travels 19 times much faster in steel than its speed in air. E.g. if we put your ear on rail track we can hear the vibration of the train movement in the track much before than the whistle of the train which travels through air.

Aircraft speed of sound

Introduction :
Air crafts with propellers in the initial stages were not able to perform well when they approached the speed of sound. This problem resulted into deep research into jet engines conducted mainly by Frank White of England and Hans van Ohain of Germany. They carried out this research in their respective countries.

Breaking Sound Barriers

Various sources claimed to have broken the sound barriers. Claims were made that air crafts ran smoothly at the speed of sound without any turbulence but there were many disputes against these claims. These claims were made as early as 1945. Man has attempted to break the sound barriers since the time the first plane was invented by the Wright Brothers. Bell X-1 was the first flight to travel faster than the speed of sound and this happened on 14^th October, 1947 under Captain Charles Yeager.

Speed of Sound

The exact speed of sound is not known but it is considered that it varies according to the height above sea level or what we call as altitude. It is 761 mph at sea level and at 20000 feet above it is 660 mph.

Modern Aircrafts and their speed

Today there are several air crafts like fighter jets that travel at speeds faster than the speed of sound regularly. When the aircraft reaches close to the speed of sound what happens is quite interesting in respect of the movement of air around the wings of the plane. It is called the Prandtl-Glauert singularity and it is quite photogenic.

Conclusion to aircraft speed of sound

In two decades ranging from 1947 to 1967 there were appreciable efforts by man to reach the speed of sound and there are crafts that are unmanned and cross the speed of sound easily and that is quite a remarkable achievement. There will be further developments and we all have to wait and watch how fast air crafts will become.

Orbital Speed

The orbital speed of a celestial body measures its speed around another object’s center of gravity. This can be its speed at a given time and place in its path or may be its average speed. Depending upon the eccentricity of heavenly body's orbit the orbital speed changes as a satellite or moon gets closer to its center of gravity or further away. The two regions where speeds can change the most are pericenter and apocenter.

A satellite in orbit moves faster (pericenter) when it is close to the planet or other body that it orbits and slower (apocenter) when it is farther away. A satellite moving in a circular orbit has a constant speed which depends only on the mass of the planet and the distance between the satellite and the center of the planet.

Calculating the Orbital Speed

The speed (v) of a satellite in circular orbit is:

`v = sqrt((GM)/r)`

Where, `G` is the universal gravitational constant and the value is `6.6726 xx 10^-11 N m^2 kg^-2`,
`M`  is the mass of the combined planet-satellite system, in case Earth's mass is `5.972 xx 10^24 kg`, and we can ignore the satellite's mass, in case for smaller man made satellites.
and `r` is the radius of the orbit measured from the planet's center.
The period `P` of a satellite in circular orbit is the orbit's circumference divided by the satellite's speed:

`P = (2*pi*r)/v`

Kepler's Law for Orbital Speed:

Kepler's second law is illustrates that the line joining the Sun and planet sweeps out equal areas in equal times, this means the planet moves faster when it is nearer the Sun (perihelion). Henceforth, a planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. The point of nearest distance of the planet to the Sun is known as perihelion; the point of greatest separation is known as aphelion. Therefore, by Kepler's second law, the planet moves fastest when it is near perihelion and slowest when it is near aphelion.

Arrhenius theory acid

Introduction :
According to Arrhenius an acid  is any substance that dissociates   to give  a H+ ion  in aqueous solution.

Thus an aqueous solution of hydrochloric acid will  show the presence of H+ ions and Cl- ions.
 Later it was found that the H+ ions have no free existence in water or in aqueous solution but exist in the solvated state as hydronium ion as H₃O^+.

  Thus according to Arrhenius definition of an acid,  any substance that will increase the concentration of H+ ions in water is said to be an acid.

  General Representation:  An Arrhenius acid  is generally represented by the formula with a H in the begining as HCl , H₂SO4 , HNO_3. All  acids that can donate a proton in aqueous solution or  can increase the concentration of H₃O⁺ ions in solution  are called Arrhenius acids.The dissociation of an acid in water can be represented by the equation a follows:
 If HCl be the acid then the dissociation is given as
HCl((g)  +  H₂O(l)    ---> H₃O⁺  + Cl^-

The advantage of the Arrhenius definition of an acid.

1) All protic acids that can dissociate in aqueous solution to increase the H+ ione concentration show similar properties such as :

Reaction with bases result in neutralisation of the acid and formation of water and a salt
example: HCl + NaOH----------> NaCl + H₂O
                  HNO₃ + KOH --------> KNO₃ + H₂O      

2)  The basicity of the acids depends upon number of H+ ions, an acid can releas in aqueous solution

3) The pH of any substance depends upon the number of H+ ions the substance can release in solution

Limitation of Arrhenius definition of acid>

1) Arrhenius definition of acid holds good only for acids in aqueous solution. For example
HCl (aq) ----------> H⁺(aq)  + Cl^- (aq)
      H⁺ (aq) + H₂O (l) ---------> H₃O⁺ (aq)
    But HCl in gaseous state is neither acidic nor basic.

2) Acid not dissolved in (aq) solution cannot dissociate into H+ ions. For example
     HNO3 (l) + 2H2SO4 (l) -----------> NO⁺⁺ (l) + H₃O⁺ (l) + 2HSO₄^-   (l)
Here HNO3 acts as a base

3) Arrhenius definition of acid cannot account for the acidic character of AlCl₃

Learn definition of sec

Introduction :
Learn definition of Sec is defined as the function which is used to calculate the ratio of sides of the triangle. It is also known as inverse of cos function. Sec is a one kind of trigonometric functions. Sec of an angle is the ratio of hypotenuse and the length of the adjacent side. In other words, the learn definition of Sec is the reciprocal of cos.

In a right angle triangle,

                  Sec(A)=hypotenuse       
                              adjacent side        
               Here A is a angle, Sec (A) = 1/ (cos A)        

Learn definition of sec:

Learn properties of sec angle:
Learn definition of sect is intervallic and repeats itself every 2 radians. An essential property is sec(0)=1. Few other main properties are

By the definition of sec,
           sec x               = 1/cos x
           sec( x + 2 )   = sec (x) sec ( /2)    = ∞ (infinity)
           sec(-x)            = sec(x)
           sec(x)             = i sec h(ix)

Learn important calculus relations of sec:
             d/dx sec(x) = sec(x) tan(x)    (differentiation)
            ∫ sec(x) dx   = ln sec(x) + tan(x) = ln ( /4 + /2)  (integral)

Learn series expansion of the function of sec:
           sec(x)  = 1 + x²/2 + 5x⁴/24 + 61z⁶/ 720 + ..... + (-1)ⁿ E_2n/(2n)! X_2n + ......
Here the E's are the Euler numbers of secant.

Learn domain of sec:
          Every numbers are real except /2 + k , k is an integer.

Learn range of sec:
           (-∞ , -1] U [1 , +∞)

Learn Period of sec:
                 2 π

Learn y intercepts of sec:
           y = 1

Learn of sec symmetry:
           sec(-x) = sec (x).   Because sec (x) is an even function and graph is symmetric.

Learn of sec intervals of increase/decrease:
From 0 to 2, sec (x) is increasing on (0 to /2) U ( /2  to  ) and decreasing on ( to 3 /2) U (3 /2 to 2 ).

Learn vertical asymptotes of sec:
           Vertical asymptote = /2 + k π , where k is an integer.

Learn co function for sec : 
           sec x  = cosec (90^o - x).

Practice problem for learn definition of sec:

Practice problems using learn of secant function:
1. Find the function value of sec 45^o.

Solution:
         Use the Sec's co task identity to solve the problem.
By the definition of sec,
        function for sec is  sec x   = cosec (90^o - x)
                                         sec 30^o= cosec (90^o – 30^o )
                                                      = cosec (60^o)
                                          sec 30^o = 0.866
         The solution of sec of 30^o is 0.866.

2. Find the angle of a right triangle where hypotenuse = 2, length of the adjacent side = 1 using secant function?

  Given:
         In a right angle triangle length of the hypotenuse = 2, length of the adjacent side = 1

  Solution:         
By the definition of sec,
           Sec x  =  hypotenuse/adjacent side
                      = 2 / 1
                   x = sec^-1 (2)
                   x = 60^o 
The secant angle of triangle is 60 degrees.

Electricity sources

Introduction :

Electricity is the main branch of physics, which deals with the motion of the charges. The device which produce electricity or which can convert one form of energy into another form is called the sources of electricity.The sources of elecricity can be had from nuclear plant,  fossil fuels like coal, natural gas etc. Even the solar radiation can be used to obtain electricity.Here we discuss the sources of electricity.

About Electricity sources

Electricity is the very important form of energy, which we use, in our daily life. Now these days we even do not imagine the life in the absence of electricity. The sources of electricity are cells, which are very common and very convenient in use. There are two types of the cells one are called the primary cells and t0he other are called the secondary cells. The primary cells are those, which cannot be recharged, and the secondary cells are recharged several times up to some limit. Voltaic cell is the most important type of the source of electricity.

It is the simplest form of the electrochemical cell. It consists of a glass vessel containing dil. sulphuric acid. Copper and the zinc rod are dipped in the dil. Sulphuric acid. These copper and zinc rods are called the electrodes. When the bulb of a torch is connected across the electrodes through a conducting wire, it glows that means the electricity is produced due to some chemical reaction. When sulphuric acid dissolved in water, it decomposes into ions as shown in the reaction given below

H2SO4       `->`         2H+ + SO4 2-

Zinc atoms from zinc plate begin to dissolve slowly in H2SO4 in form of Zn2+. Each zinc atom dissolved in H2SO4 from the Zn plates leaves two electrons on the Zn plate. This zinc plate becomes negatively charged.

Zn (in solution)        `->`        Zn 2+   + 2e- (on Zn plate)

The potential acquired by the Zn plate is – 0.62 Volt. When Zn ions enter the solution from the Zn plate, an equal number of H+ leaves the solution and deposit on the copper plate. The hydrogen ions get electrons from the copper plate to become neutral hydrogen atoms.

H+ + e -    `->`            H

A pair of hydrogen atom combines to form the hydrogen molecule and the bubbles of the hydrogen gas are formed. Copper plate becomes positively charged and the potential is 0.46 Volt. So the potential difference of the voltaic cell is 0.46 – (-0.62) = 1.08 Volts.

Conclusion of the electricity sources

Thus, we observed that the same potential difference is developed across the plates of the cell. That means there are some free charges, which are in motion. As we connect a resistance in the path of the free charges, it will move and the electricity is produced so that the current flows through the bulb and it will glow.