The Archimedes Estimation

The Archimedes Estimation of π

C = 2rπ = πD where C is the circumference, r is the radius and D is the diameter of a circle. Using
geometric construction we can calculate the perimeter for the inscribed hexagon (Pi) and the perimeter
for the circumscribed hexagon (Pc) in units of the radius. Pi
 = 6.00r and Pc
 = 6.93r. Therefore, 6.00r <
C < 6.93r and since C = 2rπ, 3.00 < π < 3.46. By using a 96-gon, Archimedes determined: 3.1409 < π <
3.14292, thereby establishing 3.14 for the first three significant figures of π. (Archimedes numbers are
estimates because he had to estimate the square roots involved in determining the perimeters. The local
book store was not selling pocket calculators in Syracuse in 250 BCE!)
Archimedes could also determine the area within irregular shapes by drawing ever smaller triangles in
the shape and adding up the areas of the triangles. This approach, much like the estimation of π, borders
on calculus and solves problems like Zeno’s paradoxes. Had the ancient Greeks discovered algebra, it is
possible that Archimedes would have invented calculus almost 2000 years before Newton!
When the Romans conquered Syracuse a soldier killed Archimedes. The soldier did not realize who he
had captured. The Roman General, Marcellus, had wanted to use Archimedes’s knowledge and, finding
he had been killed, had the tomb built for Archimedes with the marble monument of the sphere in the
cylinder that he had requested.
Archimedes lived about 100 years after Aristotle and, of course, had the advantage of the scientific and
mathematical knowledge of his time. Archimedes had the cumulative knowledge of the Pythagoreans,
Euclid, and others. It is a great misfortune that the cosmology and physics of Aristotle became dominant.
Clearly Archimedes’s physics was much more modern and would have been a much better foundation
for science. The advancement of science might have been more rapid if Archimedes, instead of Aristotle,
had become the standard.

The Greek astronomer, geographer, and mathematician, Claudius Ptolemy lived in Roman Egypt from
about 85 to 165 CE. Ptolemy set out to correct the problems of Aristotle’s astronomy but wanted to
maintain the principle of circular movement in the heavens. As we mentioned before, the planets were
often observed to reverse their directions, something that was not possible if they were moving in circular
orbits around the Earth. However, Ptolemy found that he could correct these motions by using epicycles
that were themselves combinations of circles upon circles.

Distillation | Types of distillation trays

The main requirement of a tray is that it should provide intimate mixing between the liquid and vapour streams, that it should be suitable for handling the desired rates of vapour and liquid without excessive entrainment for flooding, that it should be stable in operation and it should be reasonably easy to erect and maintain. In many cases, particularly with vacuum distillation, it is essential that the drop in pressure over the tray should be a minimum.
 The arrangements for the liquid flow over the tray depend largely on the ratio of liquid to vapour flow.


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Crushing & Grinding | Types of Fine Grinders | Roller Mill's

The roller mill is at present used exclusively for the grinding of grain in the manufacture of flour. It is, however, also suitable for grinding any moderately tough material that must be reduced to a very fine powder. Since this mill has a shearing action rather than crushing by direct pressure or having a rubbing action, it may be used where material is to be reduced to a moderately fine size but with the minimum of fines. See the picture above and below.

vertical Roller Mill

Construction & Working Process:

 It contains two pairs of rolls, and the rolls in each pair rotate toward each other. The rolls are corrugated, and one roll of each pair turns faster than the other one. This results in a shearing action instead of the direct pressure that is brought about in the ordinary crushing rolls. The drive side of the mill, half in elevation and half in section. Shaft pulleys are attached to the fast roll of either pair. The driving belt takes a turn around these pulleys and around the idler pulley. This pulley drives an idler shaft which passes through to the opposite side of the roll stand. From the other end of his idler shaft, belts go to the slow roll of each pair. Above the rolls proper is an oscillating feeder that delivers the material to be crushed equally to both pairs of rolls.

 
One roll of each pair runs in fixed bearings. The other roll of each pair runs in bearings that are mounted on adjustable bell cranks. These bell cranks are pivoted at the bottom and are adjustable by a hand-wheel and screw at the top. In this way, the distance between the rolls, and therefore the amount of reduction accomplished in each pass, may be regulated.

Crushing & Grinding | Intermediate Crushers | Hammer Mill and Single-Roll Crusher

The general name covers a wide variety of crushing and shredding devices that operates rather by impact than by positive pressure.

One type of such device is shown in above picture.In this machine a number of discs are assembled on a central shaft.Between these discs are hinged hammers, in the form of plain rectangular steel bars, which may be from 1/8 to 1/2 in. in thick. On one side of the casing are breaker plates of white cast iron or manganese steel, and around the bottom is a cage containing hundred screen bars. The shaft is rotated at a high speed, and centrifugal force causes the hammers to swing out radially. Brittle or friable material like coal, pitch, limestone or similar substances is beaten around inside the mill and by impact against the breaker plates or against the screen bars is crushed until it falls through the screen. By using hammers of different weights and screen bars of different cross sections, the machine can be adapted to materials ranging from brittle materials like coal on the one hand to fibrous materials like tanbark on the other hand.

The construction is such that hammers can be easily replaced when they have worn. You have see the picture of hammer mill, part of the screen cage is hinged so it can be lowered to remove from the mill any hard material that cannot be pulverized. For brittle materials like coal or limestone the cross section of the screen bars is usually rectangular as shown in above pictures. There are many types of these mills, differing in the details of construction and in the shape of the hammer bars, but the action of all the mills of this type is essentially the same.

There are a number of modifications of this type in which the beaters are smaller and only a single ring of them is used. In such cases both the screen bars and the sides of the housing act as attrition surfaces. Such mills are used for grinding resin, pitch, drugs, cork, and similar soft or fibrous materials.

Single-Roll Crusher:

Another type of machine that falls in this class because it depends mainly on impact, but which is not ordinarily classed as a hammer mill is the single-roll crusher. Such a mill is shown in the picture below.

 

The single-roll is usually provided with corrugations or teeth of different sizes and rotate at a relatively high speed. Its action is similar to the hammer mill in that it crushing effect is produced by the teeth driving the material to be crushed against the breaker plate, thus crushing it by impact rather than by positive pressure. These machines are made in a variety of designs and are quite generally used for crushing coal..

 

 

 

Crushing and Grinding | Classification of Crushing and Grinding Machinery or Equipments

The general terms used to describe the operations that subdivide solids mechanically are seldom used with any very definite significance. The terms crushing and grinding are usually associated in this phrase to signify subdividing to greater or less extent, neither of the terms is used alone with any precise meaning, although, in general, grinding means subdividing to a finer product than crushing.

Crushing & Grinding Equipments

In spite of the wide use of crushing machinery in hard-rock practice in the mining industry, little is really known of the basic theory that underlies processes for the mechanical subdivision of solids. As in certain other fields, this lack of theory and total reliance on empirical observation have led to an especially wide variety of types of equipment. By a process of a natural selection rather than analysis, certain devices have become preeminent for hard-rock crushing, and as a result, the mining industry in recent years has practically standardized on certain types of machines for specific ranges of crushing.

In the fields in which the chemical engineer is interested outside hard-rock practice, there is absolutely no standardization. Consequently we shall be largely a description of types of crushing machinery with an indication of the uses to which such apparatus is suited, although such usage arises more often from tradition and custom than from rational comparisons.

Classification of Crushing and Grinding Machinery:

Because of wide variety of devices used, it is extremely difficult to make a rigid classification of crushing machinery. The only classification in which definite limitations of the groups can be established is the division into coarse crushers, intermediate crushers, and fine grinders. Coarse crushers are defined as those types of machinery that can be developed to take, as feed, lumps as large as may be desired. Fine grinders are defined as those machines that can be made to give a product that will pass a 200-mesh screen. Intermediate crushers are those machines that ordinary do not take indefinitely large feed, nor will they make a product that will pass a 200-mesh screen.

The different devices may be classified under these heads as follows:

1.Coarse Crushers

(a) Jaw Crusher
(i) Blake Jaw Crushers
(ii) Dodge Jaw Crusher
(b) Gyratory Crusher

2.Intermediate Crushers

(a) Rolls
(b) Disc Crushers
(c) Edge Runners
(d) Disintegrators (cage)
(e) Hammer Mill

3.Fine Grinders

(a) Centrifugal
(i) Raymond
(b) Buhrstones
(c) Roller Mills
(d) Ball Mills and Tube Mills
(e) Ultra-fine Grinders

Machines in the coarse crusher class are ordinary employed where the feed is from 1 1/2 to 2 in. in diameter and larger. The largest devices of this class that have been made will take rocks up to 60 in. in diameter. No type of crusher except those listed in this class can be built in sizes that will take these very large pieces of feed.  

Liquid Filtration | Types of Filters | Vertical-jet or Pressure Leaf Filter

Pressure leaf filters are designed for final discharge of solids in either a dry or wet state, under totally enclosed conditions with fully automatic operation.
Each type of pressure leaf filter features a pressure vessel in which are located one or more filter elements or leaves of circular of rectangular construction.The filter media may be in the form of a synthetic fiber or other fabrics, or metallic mesh. Support and intermediate drainage members are in coarse mesh with all components held together by edge binding. Leaf outlets are connected individually to an outlet manifold which passes through the wall of pressure vessel.

Working Process:

The material to be filtered is fed into the vessel under pressure, and separation takes place with the solids being deposited on the leaf surface, and the liquid passing through the drainage system and out of the filter. Cycle times are determined by pressure, cake capacity or batch quantity. Where particularly fine solids must be removed, a layer of precoat material may be deposited on the leaves prior to filtration, using diatomaceous earth, Perlite or other suitable precoat materials.

Cake washing, for the recovery of mother liquor or for removal of solubles, may be carried out before discharging of the solids as a slurry or a dry cake.

Pressure leaf filters are supplied in a wide range of size and materials of construction. One typical design is the "verti-jet" unit with a vertical leaf filter, as shown in the figure below with rectangular leaves mounted individually but connected to a common outlet manifold.

For sluice cleaning either a stationary or oscillating jet system using high efficiency spray nozzles is fitted so as to give complete cake removal. For recovery for dry solids, vibration of the leaves allows automatic discharge of the solids though a bottom discharge port provided with a quick opening door.

In the "Auto jet" design, circular leaves are mounted a horizontal shaft which serves as a filtrate outlet manifold. The leaves are rotated during the cleaning cycle although, in addition, extra low speed continuous rotation during operation ensures uniform cake build up in difficult applications. The leaves are of metallic or plastics construction covered with fabric or wire cloth for direct or precoat operation, and rotation of the leaves during cleaning promotes fast efficient sluice discharge with minimum power consumption. As an alternative, the leaves may be rotated over knife blades which remove the cake in a dry state. Units of this type are used for handling foodstuffs and also for the processing of minerals and effluents.




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Liquid Filtration | Blocking Filtration

It is assumed that there is a well-defined boundary between the filter cake and the filter cloth. The initial stages in the build-up of the filter cake are important, however, because these may have a large effect on the flow resistance and may seriously affect the useful life of the cloth.

The blocking of the pores of the filter medium by particle is a complex phenomenon, partly because of the complicated nature of the surface structure of the usual types of filter media , and partly because the lines of movement of the particles are not well defined. At the start of filtration , the manner in which the cake forms will lie between two extremes-the penetration of the pores by particles and the shielding of the entry to the pores by the particles forming bridges. HEERTJES considered a number of idealised cases in which suspensions of specified pore size distributions were filtered on a cloth with a regular pore distribution. First, it was assumed that an individual particle was capable on its own of blocking a single pore, then, as filtration proceeded, successive pores would be blocked. So that the apparent value of the specific resistance of the filter cake would depend on the amount of solids deposited.

The pore and particle size distributions might, however, be such that more than one article could enter a particular pore. In this case, the resistance of the pore increases in stages as successive particles are trapped until the pore is completely blocked. In practice, however, it is much more likely that many of the pores will never become completely blocked and a cake of relatively low resistance will form over the entry to the partially blocked pore.

One of the most important variables affecting the tendency for blocking is the concentration of particles. The greater the concentration, the smaller will be the average distance between the particles, and the smaller will be the tendency for the particle to be drawn in to the streamlines directed towards the open pores. Instead, the particles in the concentrated suspension tend to distribute themselves fairly evenly over the filter surface and form bridges. As a result, suspensions of high concentration generally give rise to cakes of lower resistance than those formed from dilute suspensions. 

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Adsorption | Rotary-bed Adsorber

Because of difficulty of ensuring that the solid moves steadily and at a controlled rate with respect to containing vessel. Other equipment has been developed in which solid and vessel move together, relative to a fixed inlet for the feed and fixed outlet for the product.Following below picture shows the principle of operation of a rotary-bed adsorber used.

 Construction Parts:

Following are the construction parts of the rotary-bed adsorber

1. Steam

2. Solvent

3. Rotor drive

4. Air filter

5. Solvent laden air

6. Motor

7. Water

8. Solvent vapour

9. Fan

10. Air cooler

11. Storage drain

Working Principle:

For example, for solvent recovery from air on to activated-carbon. The activated-carbon is contained in a thick annular layer, divided into cells by radial partitions. Air can enter trough most of the drum circumference and passes though the carbon layer to emerge free of solvent. The clean air leaves the equipment through a duct connected along the axis of rotation. As the drum rotates the carbon enters a section in which it is exposed to the steam.Steam flows from the inside to the outside of the annulus so that the inner layer of carbon. Which determines the solvent content of effluent air, is regenerated as thoroughly as possible. Steam and solvent pass to the condensers and the solvent recovered, either by decanting or by a process such as distillation. In the particular equipment shown, there is no separate provision for cooling the regenerated adsorbent, instead it is allowed to cool in contact with vapour-laden air and the adsorptive capacity may be lower as a result.

Types of Tower Packing

A wide variety of types of packing have been suggested at one time or another.These may be classified as follows:

1.Wood Slats

These can be used where the solution to be passed over them is neutral or faintly acid or alkaline. The bottom edge of the slats may be notched to aid in liquid distribution. Wood is light and cheapest packing for those cases where it can be used. It can best be used in towers of rectangular cross section. 
There are following shapes of wood slats are used in different sections according to requirement.

• Horizontal wood slats
• Vertical wood slats
• Interior wood slats 
• Dark wood slats
• Joint wood slats
• Weathered wood slats

Samples of pictures are shown below:

Horizontal

Dark

Interior

Joint

Vertical

Weathered

 
2.Broken Rock

This at once suggest itself, since such material is always at hand. It is not always easy to find material that will be inert. This packing has various disadvantages, chief of which are its great weight, its relatively small surface per unit of volume, and its small free cross section. Its is now employed in only two important cases.
First Case: The use of crushed quartz for the packing of Glover towers in sulfuric acid manufacture.
Second Case: In one of the system for making the liquor for use in sulfite pulp manufacture where broken limestone is used. In this latter case it is desired to have the solution produced in the tower react with limestone and the two operations are thus combined in one.

3.Coke

Coke has the advantage of being light in weight and having a large surface per unit weight. Its disadvantages are a small free cross section and a tendency for some slightly soluble constituents of the coke to pass into solution. It is also rather friable. The surface is not so large as might be expected, since many of the pores are so small that they are completely filled or filmed over with liquid and therefore are not effective in furnishing surface at which contact with the gas phase could take place.Coke is usually cheap and generally available, and in many small and simple operations its used is justified.

4.Stoneware Shapes

So many of the operations of gas absorption are carried out with acid liquids as the solvent that chemical stoneware is common material. This has been employed in the most diverse and elaborate forms.
Towers may be packed with ordinary rectangular brick set on edge, but this packing has a large weight and small surface per unit volume, though it may be arranged to give large free volume and large free cross section.
Every conceivable kind of specially shaped brick has been suggested and made at one time or another, but it is not necessary to discuss these forms here.

4(a). Raschig Rings

These are mostly and widely used form of tower packing. They are cylindrical rings, of the same length as the diameter of the cylinder and with the walls as thin as material will permit. Stoneware raschig rings will vary from 2 to 6 inch in diameter and will have a wall from 3/8 to 5/8 inch thick. Where the rings can be made of metal they are correspondingly lighter and give a larger free cross section and a larger free volume. Raschig rings are almost always dumped into the tower at random and not stacked regularly. They offer the best combination of low weight per unit volume, free volume, free cross section and total surface of any type of packing. Stoneware raschig rings are sometimes made with one or two interior webs which increase the surface without greatly decreasing free cross section.

4(b). Berl Saddles

These are saddle shaped porcelain units that are piled at random. The advantage of this type of packing is the comparatively low frictional resistance that it offers to the flow of the gas while maintaining adequate gas liquid surface.

4(c). Spiral Rings

Machines have been devised for making a stoneware packing having the general dimensions of a Raschig ring, but with an internal helix which may partly or completely fill the cross section of the cylinder. Such rings are always stacked and never dumped at random. It is claimed that the helix gives more thorough contact between gas and liquid and that it increases the surface without greatly decreasing either free cross section or free volume. It greatly increases the cost of the packing and especially the labor for installing.

4(d). Grid Blocks

These are rectangular blocks of stoneware, about 4 X 4 X 7 inch, with vertical slots to act as gas passages. They usually stand on short feet (made as part of the block), and the webs between the ribs may be serrated along the bottom edge. They are best used in rectangular towers of relatively large cross section.

5. Miscellaneous Materials

Especially in very small laboratory distillation columns and absorption towers, a wide variety of packing's have been used that have not found application in large scale operations. The list includes glass beads, mats of Fiberglas, rolls of wire gauze, metal turnings, special shapes stamped from sheet metal or wire gauze, wire spirals and many others too.







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The Typical Globe Valves

Valves are used to regulate or control the flow rate of fluids in the pipelines.Globe Valves are specially design in the spherical body shapes with the two halves of the body that are present separately by an internal baffle.Its consist on movable disc and seat rings in the shape of spherical body. The typical Globe Valves are shown in the pictures below:

 

Construction Parts of Globe Valve:

There are following parts of construction of a Globe Valve.

• Hand wheel
• Gland
• Stem
• Bonnet
• Plug or Disc
• Seat
• Packing
• Rings
• Cage
• Body 

1.Hand Wheel

Handle is used to the purpose of moving.When we have a desired to close or open the valve then we use handle wheel .

2.Body

The body is the main part of any equipment or machine that are used in the Chemical or other industries.

3.Bonnet

The bonnet provides a leak-proof closure for the valve body.The threaded section of the stem goes through a hole with matching threads in the bonnet.Globe vales may have a screw-in, union or bolted bonnet.Screw-in is the simplest bonnet of globe valve.It consist on durable and pressure-tight seal.Union bonnet is suitable for applications requiring frequent inspection or cleaning.It also gives the body added strength.A bonnet attached with bolts is used for larger or higher pressure applications.The bonnet also consists a packing, a wearable material that maintains the seal between the bonnet and stem during the valve cycling.

4.Plug or Disc

Plug or disc is another construction part of the globe valve.Its connected to the stem which is slid or screwed up or down to throttle the flow.Plug are the typically of the balance or unbalanced type.Unbalanced type plugs are solids and are used with smaller valves or low pressure drops across the valve.The advantages are simple design, with one possible leak path at the seat and usually lower cost.The disadvantages are that these are with limited body size, with large and unbalanced plug, the forces needed to seat and hold the flow of fluids often becomes impractical.The balanced plugs have holes through the plug.Advantages include easier shut off as the plug does not have to overcome static forces.Therefore, a second leak path is created between the plug and the cage and that cost is generally very high.

5.The Cage

The cage is also a part of the globe valve that surrounds the plug and is located inside the body of the valve.Special thing of it is that the cage is one of the best and greatest determiners of the flow within valve.As the plug is moved more of the openings in the cage are exposed and flow is increased and vise versa.The design and layout of the openings can have a large effect on flow of materials (the flow characteristics of different materials at pressures,temperatures that are in the range). Cages are also used to guide the plug to the seat of the valve for a good shut off, substituting the guiding from the bonnet. 

6.Stem

The stem serves as a connector from the actuator to the inside of the valve and transmits this actuation force.Stems are either smooth for actuator controlled vales or threaded for manual valves.The smooth stems are surrounded with packing material to prevent leaking material from the valve.The packing is a wearable material and will have to be replaced during maintenance.With a smooth stem the ends are threaded to allow connection to the plug and actuator.The stem must not only withstand a large quantity of compression force during valve closure, but its also have high tensile strength during the valve opening.In addition, stem must be very straight, or have a low run-out, in order to ensure good valve closure.The minimum run-out also minimizes wear of the packing contained in the bonnet which provides the seal against leakage.The stem may be provide with a shroud over the packing nut to prevent foreign bodies entering the packing material, which would accelerate the wear.

7.Seat Rings

The seat ring provides a stable, uniform and replaceable shut off surface.Seat rings are usually held in place by pressure from the fastening of the bonnet from to the top of the body of valve.This pushes the cage down on the lip of the seat ring and holds it firmly to the body of valve.Seat rings may also be threaded and screwed into a thread cut in the same area of the body.However, this method makes removal of the seat ring during maintenance difficult if not impossible.Seat rings are also typically beveled at the seating surface to allow for some guiding during the final stages of closing the valves.Economical globe valves or stop valves with a similar mechanism used in plumbing often have a rubber washer at the bottom of the valve disc for the seating surface, so that rubber can be compressed against the seat to form a leak-tight seal when it shut.

Uses for material types:

Globe valves are typically made of metallic alloys, also some synthetic materials are available.These materials are chosen based on pressure, temperature and controlled media properties.Corrosive or erossive process streams mar require a compromise in material selection or exotic alloys or body coatings to minimize these material interactions and extend the life of the valve.