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March 03, 2020
Understanding the difference between watts and volts, as well as amperes (amps) and ohms, is crucial when working with any type of electrical system. Repairing household wiring requires a solid understanding of electrical terms, and it is even a helpful knowledge base to have for everyday living. How many times have you seen a lightbulb printed with "100W/120V" and wondered how the two units of electricity relate? Can the two be used interchangeably? Before looking at differences, it helps to start with basic definitions.
Watts, Volts, Amps, and Ohms Defined
Electrical terms and definitions such as watts and volts are set by a system called SI (International System of Units). An intergovernmental, international agency called BIPM (Bureau International des Poids et Mesures) sets terms and definitions for weights and measures under this system. Over a hundred countries are members or associates of BIPM.
The hydraulic (water) analogy is a common method of explaining electrical terms. Water flow within a closed-system pipe, or circuit, is compared to electrical flow. As with the closed-system pipes, electricity must move in a continuous circuit (or circular fashion) to work.
Volts
A volt represents the "potential difference between two points of a conducting wire carrying a constant current of 1 ampere when the power dissipated between these points is equal to 1 watt." The symbol for volt is "V."
Simplified, this means that voltage, compared to water pressure through pipes, is the speed of the electrons as they pass a point within the circuit.
Amps
With amps (short for amperes), the SI official definition is not only unwieldy but ever-changing. Its general thrust, though, never changes. Amps are the base unit that measure the volume of the electrons in the electrical circuit. The letter "A" capitalized is the symbol for amperes or amps.
With the hydraulic comparison, amps would be a unit of measure indicating the volume of water moving past a certain point. Volume is quantity, not speed. A lightning strike is about 20,000 amps. A watch may draw one-millionth of an amp. Household electrical cables typically are rated for 15 amps or 20 amps.
Watts
A watt expresses the rate of power flow. When one amp flows through an electrical difference of one volt, its result is expressed in terms of watts. "W" is the symbol for watt or watts.
Watts are derived from the formula V x A = W.
Ohms
The base unit ohm is the SI term indicating electrical resistance. Ohm is a measurement of the resistance that a device or material placed within the electrical circuit resists or reduces the electrical flow. The Greek symbol for omega, resembling a downward horseshoe, is also the symbol that denotes ohms.
The Difference Between Watts and Volts

Watts and volts are not independent of each other. Watts cannot exist without volts since they are the product of a combination of volts and amps. In basic terms and using the hydraulic analogy, volts are similar to pressure and watts are similar to rate.
Understanding the concept of rate is key to understanding watts vs. volts. When traveling in a car, it is possible to say that the vehicle covered 65 miles. While this is useful information, it doesn't give us a good picture of exactly what just happened. Did the car do those 65 miles in one hour, as one might reasonably expect, or did it take three months to cover that distance?
Or if you were to tell a friend that you drove for ten hours, she might follow up by asking where you drove or how far you drove. Discussing the length of a car trip is far less meaningful than if you said that you covered 800 miles during those ten hours.
One set of data deals with distance in the physical world; another set deals with time. Instead of juggling two sets of data back and forth, it is much more helpful and convenient to come up with a single number that combines the two. That number is rate.
So, the formula V x A = W is similar to the car trip example; both indicate rate. With the car, that rate is the familiar designation MPH (miles per hour): rate is equal to distance divided by time.
In electrical systems, amperage and voltage are useful sets of information. But wattage is an additional usual body of data because it combines the two to produce an indicator similar to rate or speed.

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February 12, 2020

Spark Ignition Engines (S.I. Engine)
It works on Otto cycle. In Otto cycle, the energy supply and rejection occur at constant volume process and the compression and expansion occur isentropically. The engines working on Otto cycle use petrol as the fuel and incorporate a carburettor for the preparation of mixture of air fuel vapour in correct proportions for rapid combustion and a spark plug for the ignition of the mixture at the end of compression. The compression ratio is kept 5 to 10.5. Engine has generally high speed as compared to C.I. engine. Low maintenance cost but high running cost. These engines are also called spark ignition engines or simply S.I. Engine.
SI engine P-V and T-S Diagram

Compression Ignition Engines (C.I. Engine)
It works on diesel cycle. In diesel engines, the energy addition occurs at constant pressure but energy rejection at constant volume. Here spark plug is replaced by fuel injector. The compression ratio is from 12 to 25. Engine has generally low speed as compared to S.I. engine. High maintenance cost but low running cost. These are known as compression ignition engines, (C.I) as the ignition is accomplished by heat of compression.
CI Engine P-V and T-S Diagram
The upper limit of compression ratio in S.I. Engine is fixed by anti knock quality of fuel. While in C.I. Engine upper limit of compression ratio is limited by thermal and mechanical stresses of cylinder material. That’s way the compression ratio of S.I. engine has more compression ratio as compared to S.I. Engine.

Dual cycle is a combination of the above two cycles, where part or the energy is given a constant volume and rest at constant pressure.

The following are the main differences between SI and CI Engines:

Spark Ignition Engine (S.I Engine)
Compression Ignition Engine(C.I Engine)
Spark plug required
No spark plug required
The mixture of air and fuel is introduced into the cylinder from carburettor.
Only air is introduced into the cylinder.
These type of engines compresses air and fuel together in the cylinder
In these engines air is only compressed in the cylinder.
No fuel pump is used.
Fuel pump is used to inject fuel.
Fuel is mixed with air before compression starts.
Fuel is mixed with air once compression is complete.
Compression ratio is low.
Compression ratio is high.
This type of engine makes use of highly volatile liquid fuel.
This type of engine makes use of less volatile liquid fuel.
Less efficient.
More efficient.
Fuel used in this engine is expensive.
Cheaper fuels are used in these engines.
Higher fuel consumption in these engines for same power.
These engines have lesser fuel consumption for same power.
Engines are more compact and light.
Heavier and strong engines due to higher pressure involved
Initial cost is less
Initial Cost is high.
These engines have a smooth operation
Roughness in engine operation encountered, especially when the engine runs at high speed and low loads.





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January 03, 2020
The differences in mechanics may be defined as ,



Theoretical Mechanics


This is a term used to differentiate between experimental mechanics (bouncing little balls off each other) and theoretical mechanics (trying to derive equations how little balls bounce off each other). As such, it encompasses classical mechanics, analytical mechanics and rational mechanics.

Classical Mechanics

Classical Mechanics is used in two different contexts: First, it is the antonym to Quantum Mechanics. As such, we usually assume a strictly deterministic world ruled by certain differential equations, as opposed to a quantum mechanical view where probability densities evolve according to the Schrödinger/Heisenberg equation (iℏ∂tΨ=HΨiℏ∂tΨ=HΨ or A˙=iℏ[H,A]+∂tAA˙=iℏ[H,A]+∂tA).
On the other hand, the term ‘classical mechanics‘ is sometimes used to describe Newtonian Mechanics as opposed to the later developments by Euler, Lagrange, Hamilton and Jacobi. Newtonian mechanics rely on the equation F=p˙=maF=p˙=ma (assuming m˙=0m˙=0) to describe the movement of a point particle of mass m. Since a=x¨a=x¨, they usually require two integrations to solve for the trajectory of the particle.


Analytical Mechanics

Analytical Mechanics form the ‘other’ branch of classical mechanics and build upon Newtonian mechanics. It can be divided into three major steps: Lagrangian Mechanics, Hamiltonian Mechanics and mechanics based on the Hamilton-Jacobi equation.


Lagrangian Mechanics

Lagrangian Mechanics starts off with the definition of the Lagrangian LL which acts as a measure for the difference between kinetic and potential energy. It is a function of the coordinates and velocities of all particles:
L(q1,q2,…,qN,q˙1,q˙2,…,q˙N,t)=T−UL(q1,q2,…,qN,q˙1,q˙2,…,q˙N,t)=T−U
Lagrange then postulated that the actual trajectories of the particles between time t1t1 and time t2t2 are these that minimise the action SS as defined by
S=∫t2t1LdtS=∫t1t2Ldt
which leads to a variation problem: Find {qi,q˙i}{qi,q˙i} such that
δS=∫t2t1δLdt=0δS=∫t1t2δLdt=0
where δXδX describes the variation of XX by its arguments (coordinates and velocities, in our case). As it happens, there is an equation that describes when a given quantity fulfills this requirement, namely the Euler-Lagrange equations. These are:
∂qiL−ddt∂q˙iL=0∂qiL−ddt∂q˙iL=0
where ∂x=∂∂x∂x=∂∂x and I dropped the argumets of LL. Note that these equations are of first order in {qi,q˙i}{qi,q˙i}, as opposed to Newton’s F=p¨F=p¨. Furthermore, note that I used qiqi to denote the coordinate(s) of the ii-th particle rather than xixi: This is because Lagrangian mechanics makes it very easy to implement generalised coordinates. This is best shown by example:
Assume (in two dimensions) that you have a bolt of length ll fixed at the origin (0,0)(0,0) and a mass mm at the other end of the string. Furthermore assume that the bolt has always the same length. To then describe the movement of the mass using the standard coordinates, we need to introduce yy and xx and integrate each of them and do all sorts of ugly things and, most importantly, always have to take care that y2+x2=l2y2+x2=l2. However, we notice that there is only one degree of freedom: the angle. By then introducing a generalised coordinate qq, we can implement the requirement y2+x2=l2y2+x2=l2 by simply not admitting any other coordinates. We set
x=lcos(q)y=lsin(q)x=lcos⁡(q)y=lsin⁡(q)
and can be sure that the bolt always has the same length. Assuming a constant gravitational potential (i.e. potential energy m⋅g⋅xm⋅g⋅x), we can write
L(q,q˙,t)=12mlq˙2−m⋅g⋅lcos(q)L(q,q˙,t)=12mlq˙2−m⋅g⋅lcos⁡(q)
and hence
m⋅g⋅lsin(q)−ddt1mlq˙=0.m⋅g⋅lsin⁡(q)−ddt1mlq˙=0.
You might notice that there’s still a q¨q¨ hidden there. That’s where Hamiltonian Mechanics comes in.


Hamiltonian Mechanics

Hamilton noticed that Lagrangian mechanics is still basically Newtonian mechanics with a nicer dress, but by applying a Legendre transformation to LL, we can actually get rid off q˙q˙ (and therefore q¨q¨).
To this end, we introduce the ‘canonically conjugated momentum‘ pj=∂q˙jLpj=∂q˙jL and the Hamiltonian HH which is a function of qq, pp (and, rarely, tt), defined by:
H(q1,q2,…,qN,p1,p2,…,pN,t)=∑iq˙ipi−L=T+U.H(q1,q2,…,qN,p1,p2,…,pN,t)=∑iq˙ipi−L=T+U.
You might want to verify that HH does not depend on q˙iq˙i, but only on the canonically conjugated coordinates and their momentums {qi,pi}{qi,pi}. We can then rewrite the Euler-Lagrange equations as follows:
q˙i=∂piH;p˙i=−∂qiH.q˙i=∂piH;p˙i=−∂qiH.
You can memorise these by setting H(q,p,t)=T(p)+U(q)H(q,p,t)=T(p)+U(q), the second term then becomes ‘something like’ ∇U=−F=−p˙i∇U=−F=−p˙i.
These equations are still asymmetric (hence the rule above), but by introducing Poisson brackets:
{A,B}=∑i[∂qiA∂piB−∂piA∂qiB]{A,B}=∑i[∂qiA∂piB−∂piA∂qiB]
we can actually fix that. Observe:
q˙i={qi,H};p˙i={pi,H}q˙i={qi,H};p˙i={pi,H}
since ∂qipj=0∀i,j∂qipj=0∀i,j.
Furthermore, we can now leap to quantum mechanics with relative ease: Simply add a ‘hat’ to HH and replace {⋅,⋅}{⋅,⋅} by −iℏ[⋅,⋅]−iℏ[⋅,⋅], where [A,B]=AB−BA[A,B]=AB−BA denotes the commutator :)
If you feel particularly nasty, look up the Hamilton-Jacobi equation, it is really not nice (or the most beautiful thing ever seen, depending on your POV).
Analytical mechanics is a branch of classical mechanics that is not vectorial mechanics . Analytical mechanics uses two scalar properties of motion, the kinetic and potential energies, instead of vector forces, to analyse the motion. Analytical mechanics includes Lagrangian mechanics, Hamiltonian mechanics, Routhian mechanics...

Theoretical mechanics is a branch of mechanics which employs mathematical models and abstractions of physics to rationalize, explain and predict mechanical phenomena. This is in contrast to experimental mechanics, which uses experimental tools to probe these phenomena.
Rational mechanics is a branch of theoretical mechanics characterized by a purely axiomatic approach, where some few axioms are selected and then the rest of the theory logically derived as theorems and corollaries. This branch is usually more mathematically oriented than others.
Classical mechanics is that branch of mechanics that ignores quantum effects. Classical mechanics can be either relativistic or non-relativistic, although in older literature classical mechanics often means pre-relativistic classical mechanics.
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