Solidification of metals animation

Solidification of pure metals take place animation:-


                Solidification is the transformation of materials from the liquid the solid crystalline state on cooling.During solidification, the disordered structure of the liquid transforms to the orderly arrangement characteristic of the crystal. This process of solidification does not occur instantaneously. The process is characterized by the formation of numerous small particles of the new phase (s), which increase in size until the transformation completes. The process of solidification may be broken down into two stages-nucleation and grain growth. Nucleation involves the appearance of very small particles called nuclei, these nuclei then grow in size, untill the phase transformation is complete.

solidification of metals animation

            All solid metals are crystalline and crystals or grains are made up of several atoms. These individual crystals or grains are aggregated to form a visible mass of solid metal. These grains are formed when liquid metal solidifies. The process of solidification starts when liquid metal cooled below the equilibrium temperature (the temperature at which given metal exist simultaneously solid and liquid phase).
 Solidification starts when two or more atoms associate themselves to form very small crystal called nuclei. This may happen simultaneously at a Number of locations throughout the liquid metal. At these points a few atoms assume an orderly arrangement to give the unit cubic structure and growth takes place in three dimensional as shown in fig. As a result of this growth tree like crystals known as dendrites  [arise from Greek word dendrom  meaning tree ] are formed. A dendrite consists of unit cell, which are exceedingly small, first form in a straight line.




Slow rate of cooling promotes crystallization while a faster cooling rate of cooling rate may prevent crystallization. 

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Types of SAND in civil Engineering

Types of sand according to size:-

GREEN SAND

DRY SAND

LOAM SAND

FACING SAND

BACKING SAND

SYSTEM SAND

PARTING SAND

CORE SAND


Define all types SAND:_-

          GREEN SAND- It is a mixture of silica sand with 18 to 30 percent clay, having a total water content 6 to 8 percent. The clay and water furnish the bond for green sand. It is fine, soft, light, and porous. Being damp when squeezed in the hand, it retains the shape, the impression given to it under pressure. Moulds prepared in this sand are known as green sand moulds.


           DRY SAND- Green sand that has been dried or baked after the mould is made is called dry sand. They are suitable for larger castings. Moulds prepared in this sand are known as dry sand.


            LOAM SAND- Loam Sand is high in clay, as much as 50 percent  or so, and dries hard. This is particularly employed for laom moulding usually for large castings.


            FACING SAND- Facing sand forms the face of the mould. It is used directly next to the surface of the pattern and it comes into contact with the molten metal when the mould is poured. Consequently, it is subjected to the the severest conditions and therefore, must possess, high strength and ls with refractoriness. It is made of silica sand and clay, without the addition of used sand. Different forms of carbon are uscd to prevent the metal from burning into the sand. They are sometimes mixed with 6 to 15 times as much fine moulding sand to make facings.


          BACKING SAND- Backing sand or floor sand or floor sand is used to back up the facing sand and to fill the whole volume of the flask. Old, repeatedly used moulding sand is mainly employed for this purpose.
     The backing sand is sometimes called black sand because of the fact that old, repeatedly used moulding sand is black in colour due to the addition of coal dust and burning on coming in contact with molten metal.


           SYSTEM SAND-In mechanical preparation and handling unit, no facing sand is used. The used sand is cleaned and reactivated by the addition binder in of water binders and special additives. This is known as system sand, In etimes mechanical foundries, where machine moulding is employed so called system sand is used to fill the whole flask. Since the whole mould is made of this system sand therefore, strength, permeability and refractoriness of this sand must be higher than those of backing sand.


              PARTING SAND-Parting sand is used to prevent the green sand from sticking to the pattern and also to allow the sand on the parting surface of the cope and drag to separate without clinging. This is clean clay-free silica sand which serves the same purpose as parting dust


              CORE SAND- Sand used for making cores is called core sand sometimes called oil sand. This is silica oil sand. This is silica sand mixed with core oil which is composed of linseed oil, resin, light mineral oil and other binding materials. Pitch or flours and water may be used in larger cores for the sake of economy.

Types of SAND in civil Engineering

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Stress and strain. Hook's Law

DEFINE STRESS AND STRAIN:-

Stress-
             When some external forces are applied to a body, it offers resistance to these forces. The magnitude of this resisting force is numerically equal to the applied forces. This internal resisting force per unit area is called stress. Therefore, stress can be defined as the intensity of internal forces resisting change in the shape of the body. It is calculated by simply dividing on an area divided by the a: ea. It is measured in N/m2 o: kg the force acting cm2. There are three types of stresses namely, tension, compression and shear. Mathematically,
                                                               Stress, a = P/A
                                   where,             P= Force applied
                                                          A=Cross-sectional area.
[जब कुछ बाहरी बलों को एक निकाय पर लागू किया जाता है, तो यह इन बलों के लिए प्रतिरोध प्रदान करता है। इस प्रतिरोध बल का परिमाण संख्यात्मक रूप से लागू बलों के बराबर होता है। प्रति इकाई क्षेत्र के इस आंतरिक प्रतिरोध बल को तनाव कहा जाता है। इसलिए, तनाव को शरीर के आकार में परिवर्तन का विरोध करने वाली आंतरिक शक्तियों की तीव्रता के रूप में परिभाषित किया जा सकता है। इसकी गणना केवल a: ea द्वारा विभाजित क्षेत्र पर विभाजित करके की जाती है। यह एन / एम 2 ओ में मापा जाता है: बल एक्टिंग सेमी 2 किग्रा। तनाव, संपीड़न और कतरनी जैसे तीन प्रकार के तनाव हैं.]


Types of Stresses;-
                                 The various types of stresses may be classified as follows-

(1) Simple or direct stress 
(a) Tension               (b) Compression         (3) shear

(2) Indirect stress
(a) Bending              (2) Torsion

(3) Combined stress



Strain-
              Strain is defined as the deformation or change produced in the dimensions of a body due to the effect of stress on it. It is a ratio of the change in dimension to the original dimension. Mathematically
                                   
                               
                                             Strain,                                                                                                                                         

                where, 


 

  


          Strain is a dimensionless quantity. Depending upon the type of stress, it where, can be of three types, namely tensile, compressive and shearing strain.



Types of Strain ;-
                           The various types of strains may be classified as follows-

(1) Tensile strain
(2) Compressive strain
(3) Shear strain
(4) Volumetric strain.


Hook's Law;-

Define:

                      According to Hook's law, when a material is loaded within its elastic limit, the stress is proportional to strain, or in other words, within elastic limits the ratio of stress in a material to the strain produced remains. Mathematical


                                                           

                                                                     


                 Where,
                               E is a constant of proportionality, which is called as a modulus of elasticity, or young's modulus. It has unit as the stress, i. e. or






Poisson's ratio;-
                                       Whenever body is stressed within elastic limits, it is subjected to both longitudinal and lateral deformation. The ratio of the lateral strain to longitudinal strain is a constant quantity for a material and this ratio is known as Poisson's ratio. This ratio is designated by 1/m or u. Mathematically,

Poisson's ratio, 1/m or





Thus,  
           

The limitation of Poisson's ratio is that it can be applied only when material is stressed within the elastic limits

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Casting process steps

CASTING PROCESS


Define ;-(casting)

          [ In casting, the molten metal is poured into a refractory mould with a cavity of the shape to be made, and allowed to solidify.After solidification, the desired metal object is taken out from the mould. The solidified object is known as casting. Sand moulds are generally used for casting, however, they cannot maintain better tolerances and smooth surface finish. Thus, now-a- 104days metallic moulds are more common.]

[कास्टिंग में, पिघली हुई धातु को एक आग रोक साँचे में डाला जाता है, जिसे आकार की एक गुहा के साथ बनाया जाता है, और जमने दिया जाता है। जमने के बाद, वांछित धातु की वस्तु को साँचे से बाहर निकाल लिया जाता है। जमना वस्तु कास्टिंग के रूप में जाना जाता है। आम तौर पर कास्टिंग के लिए सैंड मोल्ड का उपयोग किया जाता है, हालांकि, वे बेहतर सहनशीलता और चिकनी सतह खत्म नहीं कर सकते हैं। इस प्रकार, अब- a- 104days धातु के सांचे अधिक आम हैं।]

            Various casting processes are as follows- 

(i)        Sand casting 
(ii)       Plaster mould casting
(iii)      Vacuum casting
(iv)      Investment casting
(v)       Slush casting
(vi)      Pressure casting
(vii)     Centrifugal casting
(viii)    Continuous casting
(ix)      Squeeze casting
(x)       Shell mould casting
(xi)      Die casting


Applications of Casting-

(i) Automobile parts such as engine blocks, cylinder blocks, pistons, piston rings, etc
(ii) Machine tool structures, e.g. planar beds.
(iii) Wheels and housings of steam and hydraulic turbines, turbine vanes and aircraft jet engine blades.
(iv) Railway crossings (Mn-steel cast section)
(v) Supercharger casing
(vi) Water supply and sewer pipes
(vii) Sanitary fittings
(ix) Agriculture part
(x) Communication,

Define;-(Moulding)

      Moulding can be defined as a process of making sound mould of sand by using pattern and cores, so that the metal can be poured into the moulds to produce casting.


MOULDING & CASTING PROCESS_

         (I) Expendables mould casting -
                       In this type of casting processes, the mould cavity is obtained by consolidating a moulding material around a pattern. The commonly used moulding material for these processes is sand or some other refractory material. Because of the sand moulding the dimensions accuracy and surface finish of the casting are not up to the requirements of modern  Industries.

NATURAL SEE

(II) Permanent Mould Casting;- 
                    In type of casting processes, the mould is not destroyed after the solidification of the casting and can be used repeatedly. These moulds are adaptable to the production of tens and thousands of castings. The products of this process have smooth surface and better dimensional accuracy. Due to the high cost of permanent moulds their use is limited to mass production of small and medium sized parts of light non- ferrous alloys

(iii) Semi-permanent Mould Casting;-
                 In this type of casting processes, moulds are prepared from high refractory materials like graphite These moulds are less durable as compared to permanent moulds and can only be used for few tens of castings.

Properties of sand in construction

(1) Porosity
(2) Flowability
(3) Collapsibility
(4) Adhesiveness
(5) Cohesiveness or Strength
(6) Refractoriness
(7) Chemical Resistivity

casting process download pdf

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Fourier Transform

The Fourier Transform 


1.1 Fourier transforms as integrals 
      There are several ways to define the Fourier transform of a function f : R → C. In this section, we define it using an integral representation and state some basic uniqueness and inversion properties, without proof. Thereafter, we will consider the transform as being defined as a suitable limit of Fourier series, and will prove the results stated here.

 The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations:

Yikes. Rather than jumping into the symbols, let's experience the key idea firsthand. Here's a plain-English metaphor:

• What does the Fourier Transform do? _Given a smoothie, it finds the recipe.
• How? _Run the smoothie through filters to extract each ingredient.
• Why? _Recipes are easier to analyze, compare, and modify than the smoothie itself.
• How do we get the smoothie back? _Blend the ingredients.

Here's the "math English" version of the above:The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall "cycle recipe" (the amplitude, offset, & rotation speed for every cycle that was found).

Time for the equations? No! _Let's get our hands dirty and experience how any pattern can be built with cycles, with live simulations.

If all goes well, we'll have an aha!_moment and intuitively realize why the Fourier Transform is possible. We'll save the detailed math analysis for the follow-up.

This isn't a force-march through the equations, it's the casual stroll I wish I had. Onward!

function
Fourier transform--1	1
Fourier transform--cosine
Fourier transform--delta function
Fourier transform--exponential function
Fourier transform--Gaussian
Fourier transform--Heaviside step function
Fourier transform--inverse function
Fourier transform--Lorentzian function
Fourier transform--ramp function
Fourier transform--sine

Fourier transform formula PDF 

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Laws of Thermodynamics Equilibrium

THERMODYNAMIC EQUILIBRIUM (थायरोडायनामिक एक्विलिब्रियम)

Equilibrium Expressions

Equilibrium Constant Expressions	Rules for Writing Equilibrium Constant Expressions	Altering or Combining Equilibrium Reactions
Reaction Quotients: A Way to Decide Whether a Reaction is at Equilibrium	Changes in Concentration that Occur as a Reaction Comes to Equilibrium	Hidden Assumptions that Make Equilibrium Calculations Easier
A Rule of Thumb for Testing the Validity of Assumptions	What Do We Do When the Approximation Fails?	Equilibria Expressed in Partial Pressures
The Effect of Temperature on a Chemical Reaction

            A system is said to exist in a state of thermodynamic equilibrium when no change in any macroscopic property is registered, if the system is isolated from its surroundings
         
            An isolated system always reaches in course of time a state of thermodynamic equilibrium and can never depart from it spontaneously .
            Therefore, there can be no spontaneous change in any macroscopic property if the system exists in an properties of physical systems that are found in equilibrium states .
            A system will be in a state of thermodynamic equilibrium, if the conditions for the following three types of equilibrium are satisfied:

(a) Mechanical equilibrium
(b) Chemical equilibrium
(c) Thermal equilibrium

(ए) मैकेनिकल संतुलन

(b) रासायनिक संतुलन

(c) थर्मल संतुलन


           In the absence of any unbalanced force within the system itself and also between the system and the surroundings, the system is said to be in a state of mechanical equilibrium. If an unbalanced force exists, either the system alone or both the system and the surroundings will undergo a change of state till mechanical equilibrium is attained.
👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇👇
(सिस्टम के भीतर और सिस्टम और परिवेश के बीच किसी भी असंतुलित बल की अनुपस्थिति में, सिस्टम को यांत्रिक संतुलन की स्थिति में कहा जाता है। यदि कोई असंतुलित बल मौजूद है, तो या तो प्रणाली या दोनों प्रणाली और परिवेश यांत्रिक संतुलन प्राप्त होने तक राज्य के परिवर्तन से गुजरेंगे।)

           If there is no chemical reaction or transfer of matter from one part of the system to another, such as diffusion or solution, the system is said to exist in a state of chemical equilibrium equilibrium state. Thermodynamics studies mainly the

           When a system existing in mechanical and chemical equilibrium is separated from its surroundings by a diathermic wall (diathermic means 'which allows heat to flow') and if there is no spontaneous change in any property of the system, the system is said to exist in a state of thermal equilibrium. When this is not satisfied, the system will undergo a change of state till thermal equilibrium is restored
           When the conditions for any one of the three types of equilibrium are not satisfied, a system is said to be in a nonequilibrium state. If the nonequilibrium of the is due to an unbalanced force in the interior of a system or between the system and the surroundings, the pressure varies from one part of the system to another. There is no single pressure that refers to the system as a whole. Similarly if the nonequilibrium is because of the temperature of the system being different from that of its surroundings, there is a nonuniform temperature distribution set up within the system and there is no single temperature that stands for the system as a whole. It can thus be inferred that when the conditions for thermodynamic equilibrium are not satisfied, the states passed through by a system cannot be described by thermodynamic properties which represent the system as a whole.
             Thermodynamic properties are the macroscopic coordinates defined for, and significant to, only thermodynamic equilibrium states. Both classical and statistical thermodynamics study mainly the equilibrium states of a system.
(थर्मोडायनामिक गुण स्थैतिक निर्देशांक हैं, और केवल थर्मोडायनामिक संतुलन राज्यों के लिए महत्वपूर्ण हैं। शास्त्रीय और सांख्यिकीय दोनों थर्मोडायनामिक्स मुख्य रूप से एक प्रणाली के संतुलन राज्यों का अध्ययन करते हैं।)





           In a balanced chemical equation, the total number of atoms of each element present is the same on both sides of the equation. Stoichiometric coefficients are the coefficients required to balance a chemical equation. These are important because they relate the amounts of reactants used and products formed. The coefficients relate to the equilibrium constants because they are used to calculate them. For this reason, it is important to understand how to balance an equation before using the equation to calculate equilibrium constants.

Introduction

There are several important rules for balancing an equation:

1. An equation can be balanced only by adjusting the coefficients.
2. The equation must include only the reactants and products that participate in the reaction.
3. Never change the equation in order to balance it.
4. If an element occurs in only one compound on each side of the equation, try balancing this element first.
5. When one element exists as a free element, balance this element last.

Example 1:

H2(g)+O2(g)⇌H2O(l)$$H_2(g)+O_2(g)\rightleftharpoons H_{2}O(l)$$

Because both reactants are in their elemental forms, they can be balanced in either order. Consider oxygen first. There are two atoms on the left and one on the right. Multiply the right by 2	H2(g)+O2(g)⇌2H2O(l)$$H_2(g)+O_2(g)\rightleftharpoons 2H_{2}O(l)$$
Next, balance hydrogen. There are 4 atoms on the right, and only 2 atoms on the left. Multiply the hydrogen on left by 2	2H2(g)+O2(g)⇌2H2O(l)$$2H_2(g)+O_2(g)\rightleftharpoons 2H_{2}O(l)$$
Check the stoichiometry. Hydrogen: on the left, 2 x 2 = 4; on right 2 x 2= 4. Oxygen: on the left: 1 x 2 = 2; on the right 2 x 1 = 2 . All atoms balance, so the equation is properly balanced.	2H2(g)+O2(g)⇌2H2O(l)$$2H_2(g)+O_2(g)\rightleftharpoons 2H_{2}O(l)$$

Example 
$2$:

Al(s)+MnSO4(aq)⇌Al2(SO4)3+Mn;(s)$$Al(s)+MnS{O}_4(aq)\rightleftharpoons A{l}_2(S{O}_4{)}_3+Mn;(s)$$

First, consider the SO42- ions. There is one on the left side of the equation, and three on the right side. Add a coefficient of three to the left side.	Al(s)+3MnSO4(aq)⇌Al2(SO4)3+Mn(s)$$Al(s)+3MnS{O}_4(aq)\rightleftharpoons A{l}_2(S{O}_4{)}_3+Mn(s)$$
Next, check the Mn atoms. There is one on the right side, but now there are three on the left side from the previous adjustment. Add a coefficient of three on the right side.	Al(s)+3MnSO4(aq)⇌Al2(SO4)3+3Mn(s)$$Al(s)+3MnS{O}_4(aq)\rightleftharpoons A{l}_2(S{O}_4{)}_3+3Mn(s)$$
Consider Al. There is one atom on the left side and two on the right side. Add a coefficient of two on the left side. Make sure there are equal numbers of each atom on each side.	2Al(s)+3MnSO4(aq)⇌Al2(SO4)3+3Mn(s)$$2Al(s)+3MnS{O}_4(aq)\rightleftharpoons A{l}_2(S{O}_4{)}_3+3Mn(s)$$

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