This is Mechanical Engineering

      Mohr's Circle

Introduced by Otto Mohr in 1882, Mohr's Circle illustrates principal stresses and stress transformations via a graphical format,

                

The two principal stresses are shown in red, and the maximum shear stress is shown in orange. Recall that the normal stresses equal the principal stresses when the stress element is aligned with the principal directions, and the shear stress equals the maximum shear stress when the stress element is rotated 45° away from the principal directions.

As the stress element is rotated away from the principal (or maximum shear) directions, the normal and shear stress components will always lie on Mohr's Circle.

Mohr's Circle was the leading tool used to visualize relationships between normal and shear stresses, and to estimate the maximum stresses, before hand-held calculators became popular. Even today, Mohr's Circle is still widely used by engineers all over the world.

    Derivation of Mohr's Circle:

To establish Mohr's Circle, we first recall the stress transformation formulas for plane stress at a given location,

             

Using a basic trigonometric relation (cos²2q + sin²2q = 1) to combine the two above equations we have,

               

This is the equation of a circle, plotted on a graph where the abscissa is the normal stress and the ordinate is the shear stress. This is easier to see if we interpret s_x and s_y as being the two principal stresses, and t_xy as being the maximum shear stress. Then we can define the average stress, s_avg, and a "radius" R (which is just equal to the maximum shear stress),

                                    

 

The circle equation above now takes on a more familiar form,

                 

The circle is centered at the average stress value, and has a radius R equal to the maximum shear stress, as shown in the figure below,

                      

Working of a Rotary Engine

Working of a Rotary Engine

A rotary engine is an internal combustion engine, like the engine in your car,but it works in a completely different way than the conventional piston engine.In a piston engine, the same volume of space (the cylinder) alternately does four different jobs -- intake, compression, combustion and exhaust. A rotary engine does these sam­e four jobs, but each one happens in its own part of the housing. It's kind of like having a dedicated cylinder for each of the four jobs, with the piston moving continually from one to the next.
The rotary engine (originally conceived and developed by Dr. Felix Wankel) is sometimes called a Wankel engine, or Wankel rotary engine.

Principles of a Rotary Engine

Like a piston engine, the rotary engine uses the pressure created when a combination of air and fuel is burned. In a piston engine, that pressure is contained in the cylinders and forces pistons to move back and forth. The connecting rods and crankshaft convert the reciprocating motion of the pistons into rotational motion that can be used to power a car.
In a rotary engine, the pressure of combustion is contained in a chamber formed by part of the housing and sealed in by one face of the triangular rotor, which is what the engine uses instead of pistons.

The rotor and housing of a rotary engine from a Mazda RX-7: These parts replace the pistons, cylinders, valves, connecting rods and camshafts found in piston engines.

The rotor follows a path that looks like something you'd create with a Spirograph. This path keeps each of the three peaks of the rotor in contact with the housing, creating three separate volumes of gas. As the rotor moves around the chamber, each of the three volumes of gas alternately expands and contracts. It is this expansion and contraction that draws air and fuel into the engine, compresses it and makes useful power as the gases expand, and then expels the exhaust.

We'll be taking a look inside a rotary engine to check out the parts, but first let's take a look at a new model car with an all-new rotary engine.

­Mazda RX-8
­Mazda has been a pioneer in developing production cars that use rotary engines. The RX-7, which went on sale in 1978, was probably the most successful rotary-engine-powered car. But it was preceded by a series of rotary-engine cars, trucks and even buses, starting with the 1967 Cosmo Sport. The last year the RX-7 was sold in the United States was 1995, but the rotary engine is set to make a comeback in the near future.

The Mazda RX-8 , a new car from Mazda, has a new, award winning rotary engine called the RENESIS. Named International Engine of the Year 2003, this naturally aspirated two-rotor engine will produce about 250 horsepower. For more information, visit Mazda's RX-8 Web site.

Disadvantages of the Two-stroke

Disadvantages of the Two-stroke

You can now see that two-stroke engines have two important advantages over four-stroke engines: They are simpler and lighter, and they produce about twice as much power. So why do cars and trucks use four-stroke engines? There are four main reasons:

• Two-stroke engines don't last nearly as long as four-stroke engines. The lack of a dedicated lubrication system means that the parts of a two-stroke engine wear a lot faster.
• Two-stroke oil is expensive, and you need about 4 ounces of it per gallon of gas. You would burn about a gallon of oil every 1,000 miles if you used a two-stroke engine in a car.
• Two-stroke engines do not use fuel efficiently, so you would get fewer miles per gallon.
• Two-stroke engines produce a lot of pollution -- so much, in fact, that it is likely that you won't see them around too much longer. The pollution comes from two sources. The first is the combustion of the oil. The oil makes all two-stroke engines smoky to some extent, and a badly worn two-stroke engine can emit huge clouds of oily smoke. The second reason is less obvious but can be seen in the following figure:
  

Each time a new charge of air/fuel is loaded into the combustion chamber, part of it leaks out through the exhaust port. That's why you see a sheen of oil around any two-stroke boat motor. The leaking hydrocarbons from the fresh fuel combined with the leaking oil is a real mess for the environment.
These disadvantages mean that two-stroke engines are used only in applications where the motor is not used very often and a fantastic power-to-weight ratio is important.

Pipe Line Design Handbook

Pipe Line Design Handbook  

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