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Themal conductivity of materials, definition

Thermal conductivity of a material can be defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. The thermal conductivity of a material is a measure of the ability of the material to conduct heat. A high value for thermal conductivity indicates that the material is a good heat conductor, and a low value indicates that the material is a poor heat conductor or insulator.

Temperature is a measure of the kinetic energies of the particles such as the
molecules or atoms of a substance. In a liquid or gas, the kinetic energy of the
molecules is due to their random translational motion as well as their vibrational and rotational motions. When two molecules possessing different kinetic energies collide, part of the kinetic energy of the more energetic (higher-temperature) molecule is transferred to the less energetic (lower-temperature) molecule, much the same as when two elastic balls of the same mass at different velocities collide, part of the kinetic energy of the faster ball is transferred to the slower one. The higher the temperature, the faster the molecules move and the higher the number of such collisions, and the better the heat transfer.




Mechanical seals, importance, advantages, disadvantages, classification, basic functions of mechanical seals, seal failures, prevention of failure, factors affecting selection of mechanical seals

MECHANICAL SEALS


INTRODUCTION :


        In process industry, reliability of rotating equipment’s such as pumps, compressors, agitators, mixers etc., is of utmost importance, which depends largely on the ability to avoid leakage through shafts. The industry spent well over a billion dollars annually world over in maintenance of rotating equipment’s and a substantial amount of this expenditure was leakage through shafts related. Mechanical seals play an important role in avoiding leakage.
In general today the process industry is demanding in terms of requirements for safety and component reliability that the industry is increasingly conscious of the need for safer improved performance of mechanical seals.

        It is important that the mechanical seals are properly maintained by users / operators. Therefore it is important that a thorough functional understanding, installation requirement and failures of mechanical seals. Here an attempt has been made to compile the various failures that are encountered with mechanical seals by consolidating failure analysis report on mechanical seal failures in the complex. The study of this report and understanding the reason of seal failures will help to great extent, in avoiding premature failure of mechanical seal and costly shutdown of equipment’s and in case of critical equipment’s, the plant.

     Struggling to meet ever-tightening, stringent emission regulations, hydrocarbon processing plants are evaluating all possible alternatives that can cut or  eliminate fugitive releases. Nearly 70% of centrifugal pump maintenance is due to mechanical seal failures, a leading contributor to fugitive emissions. The new standard-API 682 was developed to set  guidelines that dictate mechanical seal performance and specifications. API-682 defines centrifugal seal-sealing system performance and design criteria that will improve reliability and increase pump-seal life.

BASIC FUNCTIONS OF MECHANICAL SEALS :


Mechanical seal is one of the technique to seal the gap formed between a rotary shaft and a stationary stuffing box. This situation is mostly commonly encountered in centrifugal pumps. Mechanical seals are used to prevent leakage of gases and liquids in rotating shaft applications that exceeds the capabilities of radial lip shaft seals and packing.
 
A rotating face forms a seal with a mating face or mating ring. Successful operation depends on maintaining a thin lubricating film of fluid between the faces. Mechanical seals can withstand high operating pressure, temperature and shaft speeds and give longer life with less leakage than packing and radial lip seals. The initial cost of mechanical seal is high as compared to soft packings. However the power consumed, maintenance and down time spent in renewing or tightening the packings overweigh the initial cost of mechanical seals, which works unattended for a long time. From the ecological point of view also seals are preferred over packings. Mechanical seals functions, statistically and dynamically, can withstand large pressure changes, are compatible with many fluids and will function in applications where shaft rotation changes directions.
 
Mechanical seals of conventional design and material can be selected to function at
pressures up to 200 atmosphere, at speeds up to 50,000 rpm and with a temperature
ranging from -200 deg C to 650 deg C.
 

MECHANICAL SEAL COMPONENTS :

 
The Basic components in a mechanical seals include the following
  1. A stationary sealing face.
  2. A Rotating sealing face
  3. A Static secondary seal for stationary face.
  4. A Static secondary seal for rotating face.
  5. A spring or a bellow to press the sealing faces together.
  6. A system to flush seal area.
  7. A method to prevent slippage of sealing faces (Keyways, pins or secondary seal friction).
In a simple mechanical seal the rotary sealing face acts as the primary sealing ring and stationary sealing face as mating ring. The primary seal ring is flexibly mounted in the seal head assembly which rotates with shaft and the mating ring is mounted on the pump gland plate. The seal head assembly consists of the method of driving and the method of pressing the two seal ring faces axially. The secondary seals (elastomers ) is installed in the confined space between rotating seal ring and shaft or sleeve, and in the confined space between stationary ring and gland plate.
 

ADVANTAGES / DISADVANTAGES OF MECHANICAL SEALS :


Some of the advantage and disadvantage of mechanical seals over conventional packings and lip seals are listed below.

Advantages :
  1. Handles all types of fluids (Acids, salts and abrasive particles)
  2. Handle slightly misaligned / non concentric
  3. Handle Bi-directional shaft rotation, large pressure, temperature and speed excursions.
  4. Shaft condition is not critical (Finish roughness, roundness, hardness and material)
  5. Operation does not cause shaft wear.
  6. Long operating life.
  7. Positive sealing for food processing, hazardous chemicals and radioactive fluids.
Disadvantages :

  1.  Requires more space than radial lip seals.
  2.  Cannot handle axial end play.
  3. Sealing faces must be finished smooth (0.08 to 0.4 micrometer) and can get easily damaged.
  4. High initial cost.

 CLASSIFICATION OF MECHANICAL SEAL DESIGNS :

SINGLE SEAL :

90% of the installations are of single seal type. Single seal is the most economical sealing device among mechanical seals as it has minimum number of parts. Further generally pumping fluid is used for seal lubrication. Generally in single seals the pumped fluid should be cool, non volatile, have good lubricity, not contain abrasive or dissolved solids. If the pumped fluid is not satisfactory as a sealing fluid, an auxiliary fluid can be injected across the seal face.

The limitations with single seals is that, in case seal leaks there is no back up available. Also system upset causes the flashing of liquid and flashing causes damage of faces.
 
a) Inside Seal :
 
Figure 1 illustrates a single inside mechanical seal. The material of construction for the inside seal are selected to withstand corrosive liquids in the stuffing box. Inside seals requires a suitable stuffing box housing for installation and cannot be adjusted without dismantling the equipment unless they are cartridge mounted. In inside mounted seals the fluid under pressure acts with spring load to keep the seal faces in contact. Inside seals are easily modified to accommodate environmental controls and can be balanced to withstand high stuffing box pressures.

There are many advantages of locating seals inside. The liquid pressure acts on the OD of the seal. The pressure acts to force the seal faces together. Solids are thrown away from the seal faces by centrifugal force. Seal force leakage is opposite direction to centrifugal force. The seal is submerged in the liquid making it easier to flush and carry away heat.

b) Outside Seal :
 
If an extremely corrosive liquid has satisfactory lubricating properties, an outside seal offers an economical alternative to the expensive metallurgy’s required for an inside seal to resist corrosion. Seals are mounted outside in little pumps that have no room inside for a seal. Figure.2 shows a typical outside seal arrangement in which only the insert seal ring and secondary seals are exposed to the product. All these components can be non-metallic. The metallic rotary unit parts are exposed to the atmosphere.

The outside seals are easier to access for adjustment and trouble shooting. The disadvantages being, it is difficult to flush this seal. The service must be free of solids which might collect under the seal. The hydraulic pressure in an unbalance outside seal tends to open, rather than to close the seal faces. All outside seals are limited to applications having moderate pressures.

MULTIPLE SEAL :

Some fluids are not compatible with a single mechanical seal. Often these liquids carry abrasive material in suspension that would rapidly wear the seal faces or the liquid may be corrosive and hazardous. There are two solutions to this problem. One is the application of environmental controls and the other is the use of Multiple seals or double seals.

A multiple seal may be mounted as double - Back to back, double - face to face or tandem arrangement.

a) Double - Back to Back seal :

Figure 3 illustrates a typical double- back to back seal arrangement. A  clean and non-corrosive liquid called barrier fluid is injected in the cavity between the inboard and outboard seals at a pressure higher than the product being pumped. In this design the buffer fluid prevents the product from contacting the inner portion of the seal and provides lubrication to both seal faces. The inboard seal prevents the buffer fluid from entering the pump where the outer seal prevents the buffer fluid from escaping to the atmosphere. The double seal is unaffected by the product being pumped. 
          
The life of double back to back seal can be up to five times that of a single seal in certain severe environments. Both inboard and outboard seals can be either balanced or unbalance depending upon the pressure encountered. Back to back seal does not tolerate the pressure reversals. Pressure upsets can result in a seal failure. It can not be bench tested, hence seal performance cannot be verified until it is actually assembled in the pump.

b) Double - Face to Face Seal :

The double face to face seal is usually cartridge mounted with one seal inside the stuffing box and one seal on the outside. Both seals rotate against a common or separate stationary insert. Figure 4 represents a double face to face cartridge seal. Face to face seal can be used as either a tandem seal or a double seal. If the liquid between the seals is at higher pressure than the product in the stuffing box, the inner seal is lubricated by a sealing liquid. If the liquid is circulated between the seals at a lower pressure than the stuffing box pressure, the purpose of the inner seal is same as that of any single seal and the outer seal simply serves as a back up or a tandem seal.

This seal is compact and can be bench tested using air as a buffer fluid before assembly. Pressure reversal will not cause it to blow up. The main limitation is in the exposure of inner seal to the product. Viscous, abrasive, thermosetting or corrosive products can damage the inner seal and cause leakage.

c) Tandem Seal :

The purpose of this seal is not to create an artificial environment as is the case with double seal, but to provide a back up seal in the event of inner seal failure. A typical tandem seal is illustrated in the Figure. 5 . The inner seal functions similar to a conventional single seal. The cavity between inner and outer seal is flooded from a closed reservoir, which provide lubrication to outer seal. The inner seal is lubricated by the product. If the inner seal fails, the resulting pressure rise in the area between seals is sensed at the reservoir, where it can be
either registered on gauge or activate an alarm. In any event, failure of the inner seal can be detected while the outer seal assumes the responsibility of sealing the shaft until pump is taken for seal repair. Hence reliability of tandem is high compared to other seals.
 

BALANCED :


Balancing seal involves a simple design change which reduces the hydraulic forces acting to close the seal faces. As seal faces rub together excessive heat is generated. This heat can be removed by increasing the lubrication between the faces. Lubrication can be increased by reducing the effect of seal cavity hydraulic pressure on the seal faces. This is done usually by building a step in the sleeve which allows the wear nose of stationary insert to be moved toward the centre of the seal. More of the seal face is thus exposed to the seal
chamber pressure which in-turn reduces the forces acting to close the seal faces.

 Because balanced seal enable seal face contact pressure to be kept low, a thicker film of stable liquid can exist between faces, reducing friction and the consequent heat generation. Normally a balanced seal is designed to operate with the lowest face pressure that will effectively prevent leakage between the faces. 
 UNBALANCED :

Unbalanced seals are often the design of choice for inside seals. In unbalanced arrangement, all of the seal face contact area lies outside of the shaft diameter. The amount of seal face leakage is inversely proportional to the amount of seal face loading. Higher the loading, the lower is the leakage. Unbalanced seals are having higher face loading than balanced seals, leak less and are more stable when subjected to vibration, misalignment or cavitation. They are often less expensive and more adaptable to standard stuffing boxes without need for modification of either the shaft sleeve or the stuffing box.

One of the disadvantage of an unbalanced seal is its relatively low pressure limit. If the closing force exerted on the seal face exceeds that limit, the lubricating film between the faces is squeezed out and soon the faces get destroyed. This problem is overcome by balancing seals.

SINGLE AND MULTIPLE SPRING DESIGN :

 The single spring is less critical in its compression setting. This makes it a good choice for pumps which have a lot of thermal expansion, with the impeller between the bearings. The single spring is less prone to clogging in dirty service. Multiple springs are small springs and are not susceptible to distortion at high speeds and exert even closing pressure on the seal ring at all times. The same size spring can be used in a range of seal sized just by varying quantity.

PUSHER AND NON-PUSHER TYPE :

Pusher seals have a dynamic secondary seal under the movable seal ring. The dynamic seal ring can take several forms like., ‘O’ ring, Teflon ‘V’ ring, wedge ring, ‘U’ cup etc.,. For high temperature (upto 500 deg.F) or aggressive chemicals a Teflon wedge ring may be used. Since Teflon is plastic and does not rebound like elastomer, it has to be pushed by spring force into the wedge shaped opening to maintain a seal on the shaft. Non-Pusher type or Bellow seals have no dynamic secondary seal under the movable seal ring. This makes them more flexible and better able to tolerate mating ring misalignment.
 
The bellows can be made of rubber, Teflon and metal. Rubber bellows are used for less critical applications like car water pumps, circulating hot water pumps etc., Teflon bellows are used for low pressure, moderate temperature acid services. Metal bellow seal is its ability to run at a very high temperature (750 degF) if the elastomer ‘o’ rings are replaced with grafoil for the secondary seals. The use of bellow seal is limited to 400 PSI on OD.

CARTRIDGE SEALS :

Nearly all mechanical seals can be provided in a cartridge design. The seal is mounted usually with a gland ring on a sleeve which fits directly over the equipment shaft or shaft sleeve. Major benefit of cartridge seal is that they do not require the usual seal setting measurement for their installation. Cartridge seals are used to reduce installation errors and turn around time for repair. This optimum seal solves five common causes of component seal failure.

FACTORS AFFECTING THE SELECTION OF MECHANICAL SEALS


1. Media Handled :

• Corrosiveness of media decides the material of construction.
• Density of viscosity shows the lubricating properties of the media. This
decides the seal arrangement.
• Abrasives in the media decides the type of flushing plan required.

2. Stuffing box pressure :

• When stuffing box pressure < 10 kg. / cm2, unbalanced seals are used.
• When stuffing box pressure . 10 Kg. / cm2 , balanced seals are used.

3. Shaft Speed :

• With increase in speed the chance of seal running dry increases. So proper
flushing plan has to be decided which can give positive flush between the
faces.

4. PV Factor :

• PV factor is defined as the product of the pressure drop across the seal and
the average rubbing velocity. As a general guide, Seal capabilities can be
classified as, Low , if the PV value is 0.7 MPa m/s ( about 20,000 psi ft/min)
Medium, if the PV value is between 0.7 and 10 MPa m/s ( about 285,000 psi
ft/min) High , if the PV value ranges from 10 to 70 MPa m/s (about 2,000,000 psi
ft/min). Balanced seals reduce the pressure acting on the seal faces, therefore they have higher PV values than unbalanced seals.

 5. Temperature :

• This decides the material of construction so that the seal does not fail at operating temperature.
• This will decides the seal flushing plan.

potential flow, ideal fluid, definition

Ideal fluid is incompressible and it is having zero viscosity. Flow of Ideal fluid is known as potential flow. Potential flow is highly developed. Main characteristics of potential flow are:

  1.  No eddies, no circulations within the fluid flow. So potential flow is irrotational flow.
  2.  No friction is developed in the fluid. Therefore there is no dissipation of mechanical energy into heat.

Therefore: Potential flow is incompressible, irrotational, highly developed and having zero viscosity.

What are the units of Dynamic Viscosity?

Dynamic viscosity has the units of cP (Centi Poise), Poise(P) or in M.K.S units it has the units Kg/m.s.





what is a fluid, define fluid

Fluid is a substance which does not resist distortion. In the sense it does not offer any resistance to the force which is going to deform the fluid.

Examples: liquids and gases are fluids.

What is Elutriation ?

Elutriation: It is a separation method, which depends on the settling velocity of the particles in the fluid.

In this process of separation, the material is placed in a rising fluid having a fixed upward velocity, particles whose normal falling velocity is less than the velocity of the fluid will be carried upward and out of the vessel. If fractions obtained from a series of fluid velocities are collected and weighed, a complete size analysis may be obtained.

What is jigging and where it is used ?

 Jigging:

Jigging is a separation method in which the particle are separated by using the density difference between them. 

Jigging is a method of gravitational preparation of natural resources, based on separation of mineral mixture on density in vertically oscillating water stream.

Usually it is used to separate metal slag form metals.

When reflux ratio to the column is minimum and zero, what are the requirements in column

When reflux ratio is minimum, column requires maximum number of trays and minimum reboiler load for a required separation. To avoid this problem of infinite trays we use optimum reflux ratio.

When reflux ratio is zero, column requires infinite number of trays and minimum reboiler load for a required separation. To avoid this problem of infinite trays we use optimum reflux ratio.

Define Intensive and extensive properties, give examples for them

Intensive and Extensive properties:


Extensive property: Is defined as one which depends on quantity of matter specified in the system.

Examples: Total mass, volume, Energy, enthalpy,

Intensive property:

It is defined as one which depends on the quantity of matter present in the sysytem.


Examples: Temperature, pressure,Molar enthalpy, molar volume

IFS Chemical Engineering question paper, 2005, Indian Forest Service, test papers

SECTION A

1. Answer any four of the following: 

(a) Find the first-order rate constant for the disappearance of A in the gaseous reaction 2A → R, holding the pressure constant, the volume of the reaction mixture starting with 80 per cent A decreases by 20 per cent in 3 mm. (10)

(b) A solution contains 50 per cent benzene, 30 per cent toluene and 20% xylene by weight at 100° C. The vapours are in contact with the solutions. Calculate total pressure and mole per cent composition of liquid and vapour: (10)

(c) Show that the internal energy of an ideal gas is a function of temperature only. (10)


(d) For adiabatic batch reactor, derive an expression to determine the time required to achieve a desired conversion. (10)


(e) Define Bubble point and Dew point. Explain in detail how to calculate bubble point or dew point of given binary mixture. (10)


2. The elementary reaction. A + B R + S is effected in a set up consisting of a mixed reactor into which two reactant solutions are introduced followed by a PFR. A large enough of excess of B is used so that the reaction is first order w.r.t. A. It is proposed to reverse the order of two units. How does this change affect the conversion? (40)

 
3. A high purity limestone is burnt in a lime kiln which is fired externally with a coal containing 75.5 per cent C, 5.5 per cent H, 1.6 per cent N, 1.1 per cent S, 7.6 per cent and rest ash. The stack gas analysis is 20.2% CO2, 7.1% O2 and rest N2, Calculate-
(a) kg limestone burnt/kg of coal;
(b) excess air used for combustion. (40)


4. One mole of an ideal gas initially at P1 and T1 is compressed reversibly and adiabatically till the pressure is P2 and then it is cooled at constant volume to the initial pressure, finally the gas is restored to the initial state through an isobaric process. Calculate the work done by the process. (40)

SECTION – B

5. Answer any four of the following:(a) Define depreciation. What are the different methods for determining depriciation? Explain the method, sum of the years digit method. (10)


(b) Explain briefly the factors to be considered for the location of a chemical plant. (10)
(c) Describe the manufacture of caustic soda by either diaphragm or mercury cell process. Discuss the pollution aspects of this industry. (10)


(d) Explain briefly the pollutants emitted from a tanning industry. (10)


(e) Explain the cracking and polymerisation of petroleum fractions. (10)


6. (a) Explain the break-even analysis and its equation. (10)


(b) A Project can produce 12000 units per year at 100 per cent capacity. The variable cost per unit is Rs. 3 at 100 per cent capacity. Fixed costs are Rs. 10,000 per year. Find the break-even point if the selling price is Rs. 5/ unit. Now the manufacturer finds that he can sell only 80% at Rs 5/ unit. How much should he charge for additional units if he brings production upto 100 per cent capacity and increases profits after taxes by an additional amount of Rs. 1,000? Use tax rate for the above problem 52 per cent. . (30)


7. (a) Describe the process with neat flow sheet of the manufacture of ethyl alcohol. (30)(b) Discuss the applications of following products: (10)


(i) Enamel paint (ii) Rancidity.


8. (a) Discuss the methods possible for preventing various industrial hazards. (20)(b) Explain primary treatment method of waste-water treatment. (20)

Why distillation? Why not adsorbption or leaching ?



In distillation the new phase generated is different from the original by phase, or heat content only. This heat can be removed or added by easy operations. But in case of adsorption or leaching the a foreign substance is introduced to separate the phases. The new phase generated using these processes is a new solution which in turn may be separated using other separation methods unless the new solution is directly useful. This makes the distillation process to more economical.

Distillation process depends on the relative volatilities of the components. If the difference is too low separation is difficult and it makes the process as more expensive.

What is Dew point

Dew Point:

It is the temperature at which the partial pressure of the water vapour in the mixture is equal to the vapour pressure of water. It can also be defines as, the temperature  where condensate formation will start upon constant cooling of  vapour mixture .

Dew point is a saturation temperature

Dew point is always lower than or equal to the dry bulb temperature.

Dew point is always lower than or equal to the wet-bulb temperature.

At 100% saturation :

Dry bulb temperature = wet bulb temperature = Dew point.

Emission spectroscopy, Absorption spectroscopy, Energy level trasitions

Emission spectroscopy

In emission spectroscopy, sample is subjected to thermal, electrical, or other excitation, and the excited atoms or molecules emit energy as they drop to lower energy levels. The emitted radiation is collected at the detector and its intensity is measure as a function of wavelength.

Absorption spectroscopy

In Absorption spectroscopy, a sample of material to be studied is subjected to radiation in desired part of the spectrum, and the molecules absorb energy, under going transitions to higher energy levels. This results in a series of spectral lines . This radiation is collected at the detector and its intensity is measured.

See Also:

What is spectrometer ? what are components of spectrometer ?

Spectrometers are used to observe the spectrum of the energy transition in a sample of interest. Experimental spectrometer contains the following components,

  1. Sample: The sample to be detected for spectrum is kept in the sample holder. This sample holder should be transparent to the radiation that we are going to use for the test. For example if we are using UV below 2000 angstroms air becomes opaque in that case we must use a vacuum chamber for the observation.
  2. Radiation source: Radiation source is chosen according to sample we are testing. For absorption spectra in the visible and ultraviolet regions older sources were the standard types of continuous light sources: tungsten filament lamps, electric discharges and arcs, spectrum tunable lasers are also available. In emission spectroscopy, the sample is the radiation source. In this the sample is heated, by electric discharge, by radiation or by chemical reaction.
  3. Optical system: The optical system is usually used to select or disperse the radiation of different wavelengths and collect it at detectors. Usually, prisms and lenses can be used as optical system. Other systems like, diffraction gratings, dispersing elements can also used.
  4. Detector: This is to detect the radiation coming from the sample for intensity measurement. This is designed in such a way that it will record and display the relation between wavelength and intensity. Normally a photographic emulsion is used as a detector. In visible and ultraviolet regions, photosensitive semiconductors are used. In infrared region thermocouples and bolometers are used. In microwave region, crystal diodes are used.

What is a spectrum, spectral lines, Fluorescence spectroscopy

Spectrum:

spectrum is representation of the amount of absorption as a function of wavelength  or frequency. Fluorescence spectroscopy is a process of exciting emission spectra, usually by excitation with radiation. In this process one may measure the distribution of wavelengths of  emitted radiation, as in any other kind of emission spectroscopy.


What is pseudopotential, core electrons, solid structure, method

Pseudopotential:

The property of the solids depend upon the electrons in valence-conduction bands and these electrons which move in the solid are found outside the atomic core. Thus we should concerned about the description of the wave function outside the atomic core. Hence, the pseudo-potential is  one which gives rise to essentially the same wave function outside the atomic core as the original atomic potential.

Pseudo-potential concept is to replace the atomic potentials by a weak potential which gives rise to the same scattering amplitude for the conduction electrons.


What are differences between pipe and tube,Birmingham wire gauge,schedule number

Pipes and tubes are specified in terms of their diameter and wall thickness.
 
Pipes:
  • Heavy walled
  • Relatively large in diameter
  • comes in moderate lengths (20 to 40 ft)
  • Threading is not possible
  • Pipe walls are rough
  • Lengths of pipes are joined by screwed, flanged and welded fittings
  • Made by welding , casting, or piercing a billet in a piercing mill
  • The wall thickness of the pipe is indicated using schedule number
  • Size of the pipe is indicated as nominal diameter
Tubes:
  • Thin walled
  • Less diameter
  • available in the form of coils also, several hundred meters
  • Can be threaded
  • Tube walls are smooth
  • These are joined by compression fittings, flare fittings, or soldered fittings
  • These can be cold drawn
  • Tube thickness is indicated using BWG (Birmingham wire gauge) 
  • Size of the tube is indicated as outside diameter

What is Differential Distillation, Simple Distillation, Rayleigh distillation,Rayleigh equation, material Balance equation


Differential Distillation:

Simple distillation, also known as Rayleigh distillation or differential distillation, is the most elementary example of batch distillation. In this distillation system, the vapor is removed from the
still during a particular time interval and is condensed in the condenser. The more volatile component is richer in the vapor than in the liquid remaining in the still. Over time, the liquid remaining in the still begins to experience a decline in the concentration of the more volatile component, while the distillate collected in the condenser becomes progressively more enriched in the more volatile component.

Schematic representation of differential distillation is as shown in in fig.1

Fig:1 Differential distillation




No reflux is returned to the still, and no stages or packing materials are provided inside the column; therefore, the various operating approaches are not applicable to this distillation system. The early analysis of this process for a binary system, proposed by Rayleigh is given below. Let F be the initial binary feed to the still (mol) and xF be the mole fraction of the more volatile component (A) in the feed. Let B be the amount of compound remaining in the still, xB be the mole fraction of component A in the still, and xD be the mole fraction of component A in the vapor phase. The differential material balance for component A can then be written as:

xD dB = d ( B xB ) = B dxB + xB dB

Upon integration:


or
In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid; hence, the vapor composition (xD) is related to the liquid composition (xB) by an equilibrium relation of the form xD = F(xB). The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperature and pressure. For a system following the ideal behavior given by Raoult’s law, the equilibrium relationship between the vapor composition y (or xD) and liquid composition X (or xB) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility (α), which is given by:

Substitution of the above equation in Equation (2)



Although the analysis of simple distillation historically represents the theoretical start of batch distillation research, a complete separation using this process is impossible unless the relative volatility of the mixture is infinite. Therefore, the application of simple distillation is restricted to laboratory-scale distillation, where high purities are not required, or when the mixture is easily separable.

ISRO question paper, ISRO sample paper, Indian Space Research Organisation, question papers,technical, aptitude, interview pattern, 2009,chemical engineering

1) Special software to create a job queue is called
a) driver
b) spooler
c) interpreter
d) linkage editor
2)When a process is rolled back as a result of deadlock the difficulty arises is
a) Starvation
b) System throughput
c) low device utilisation
d) cycle stealing
3)On receiving an interrupt from an I/O device the CPU
a) Halts for a predefined time.
b) Branches off the interrupt service routine after completion off the current instruction.
c) Branches off to the interrupt service routine immediately.
d) hands over the control of address bus and data bus to the interrupting service.
4) Which of the following is true of the auto increment addressing mode?
1. It is useful in creating sef relocating code.
2)If it is induced in an instruction set architecture , than an additional ALU is required for effective
address calculation.
3) The amount of increment depends on the size of the data item accessed.
a) 1 only.
b)2 only
c) 3 only
d) 2 and 3 only
5) The primary purpose of an operating system is
a) To make the most efficient use of the computer hardware.
b) to allow people to use the computer.
c) To make the system programmers employed.
d) to make computers easy to use.
6)consider the cpu intensive processes which require 10,20,30 time units and arrive at time 0,2,6
respectively.how many context switches are needed if the operating system implements a shortest
remaining time first scheduling algorithm?Do not count the context switches at the time 0 and end.
a) 1
b) 2
c) 3
d) 4
7) consider a system having n resources of the same type.These resources are shared by 3 processes
A,B,C .These have peak demands of 3,4,6 respectively.For what value of n deadlock won't occour.
a) 15
b) 9
c) 10
d) 13
8) In which addressing mode the effective address of the operand is computed by adding a constant
value to the content of the register?
a) absolute mode.
b) indirect mode
c) immediate mode
d) index mode
9)the process of organising the memory into two banks to allow 16 bit and 8 bit data operation is called
a) bank switching
b) indexed mapping
c) two way memory interleaving
d) memory segmentation
10)a one dimensional array A has indices 1-75.Each element is a string and takes up three memory
words. The array is stored in location 1120 decimal. The starting address of A[49] is
a) 1267
b) 1164
c) 1264
d) 1169
11) The micro systems stored in the control memory of a processor have a width of 26 bits. Each
microinstruction is divided into three fields : a microoperation field of 13 bits, a next address field(X),
and a MUX select field(Y). There are 8 status bits in the inputs of the MUX.How many bits are there in
the X and Y fields and what is the size of the control memory in number of words?
a) 10,3,1024
b) 8,5,256
c) 5,8,2048
d) 10,3,512
12)The use of multiple register windows with overlap causes a reduction in the number of memory
accesses for
1.function locals and parameters
2. register saves and restores.
3. instruction fetches.
a) 1 only
b) 2 only
c) 3 only
d) 1,2,and 3
13)Which of the following about relative addressing mode is false?
a) it enables reduced instruction size.
b) it allows indexing of array element with same instruction.
c) it enables easy relocation of data.
d) it enables faster address calculation than absolute addressing.
14)Substitution of values for names (whose values are constants) is done in '
a) local optimisation
b) loop optimisation
c) constant folding
d) strength reduction
15)A root a of eq f(x)=0 can be computed to any degree of accuracy if a good initial approximation x0
is chosen for which
a) f(x0)>0
b) f(x0)f''(x0)>0
c) f(x0)f''(x0)<0
d) f''(x0)>0
16) consider the polynomial p(x)=a0+a1x+a2x*x+a3x*x*x. The mininum number of multiplications needed to evaluate p on an input x is
a) 3
b) 4
c) 6
d) 9
17)Activities which ensure that the software that has been built , is tracable to customer is covered as
part of
a) verification
b) validation
c) maintenance
d) modelling
18) A testing method which is normally used as the acceptance test for a software system is
a) regression testing
b) integration testing
c) unit testing
d) system testing
19)A locked database file cab be
a) accessed by only one user
b) modified by the users with the correct password.
c) used to hide the sensitive information.
d) updated by more than one user

ISRO sample paper, Indian Space Research Organisation, question papers,technical, aptitude, interview pattern, chemical engineering


1 The concept of ---------------------------------- derived from the “ZEROTH LAW OF THERMODYNAMICS”.
TEMPERATURE

2 The concept of ------------------------------------- derived from the “SECOND LAW OF THERMODYNAMICS”.
ENTROPY

3 The expression for isentropic index [?] in terms of number of degrees of freedom

( n ) ------------------------
1+ [ 2 / n]

4 The critical Reynolds no upto which the viscous flow exists in pipe -------------------
2000

5 Two forces of equal magnitude P acts at right angles to each other and having same directions. Find out the expression for their resultant [R ]--------------------
[2]½ P

6 The angular frequency of handclock------------------
?/30 rad/s

7 The equation for free torsional vibration----------------------------
[1/2?] [q/I]½


8 A thin cylinder is subjected to longitudinal stress s0 and internal pressure P , findout the maximum shearstress developed in it [ q max] ------------------------
0.5 s0

9 Rate of moment of momentum is equal to the -------------------------
Torque applied by the body

10 The expression for loss of energy [he ] due to sudden enlargement of the pipe--------
he =[v1-v2]²/2g

11 A spring of stiffness K is divided into “n” number of springs. Each spring having stiffness ---------------------------
nK

12 The non-dimensional number corresponds to
[inertia force\compressibility force]½------------------------------ Euler number

13 Equation for forced vortex flow-----------------------------
v/r = constant

14 The causes of cavitation
Metallic surfaces are damaged
Noise & vibrations

15 How to increase the thermal efficiency in Carnot cycle by-------------------------------
Decreasing low temperature

16 The slenderness ratio in columns can be obtained from the ---------------
Least radius of gyration

17 50:1 gear reduction ratio possible in-----------------
worm gear

18 Wire drawing property named as -------------------------
ductility

19 One man is standing in the elevator and the elevator is moving in the upward direction. What type of reading regarding the weight of man will we get from gauge---------------
The weight of man shown by the gauge will more the actual weight of the man.

20 LMTD for counterflow heat exchanger is compared to parallel to heat exchanger-----
More

21 The free damping equation 2yºº + 3yº +8y =0. Calculate damping factor (D.F )--------
3/8



22 The discharges for the two parallel pipes of same lengths are Q1 & Q2 respectively and their diameters are 200 mm & 800 mm respectively. Calculate the ratio of discharge of smaller pipe to larger pipe.
1/32

23 A compressor is used to compress the air from 5 bar to 10 bar .Calculate its critical pressure [ P?]----------------------
2.64 bar

24 Equivalent twisting moment------------------------------
Te = [T² + M²]½

25 The shear stress distribution in pipe flow -----------------------------
Centre is zero and linearly varying from the center to the wall

26 The irrational component in x-y is--------------
dv/dx = du/dy

27 The ratio kinetic viscosity/thermal diffusivity is -------------
Nusselt Number

28 The cylinder is subjected to insulations K & 2K at the outside surface to avoid heat transfer. In order to arrest heat transfer effectively , which insulation should be provided first at the outer surface?
2K & K respectively

29 The wall having conductivities
K1 K2

Findout the equivalent conductivity of the material--------------------?

29 The maximum amplitude in this vibration equation y = 6 sin?t --------
6

30 The thermal boundary layer in an ideal fluid flow is --------------
0

31 What does tend to stagnation point -----------------------
The velocity is 0 at the stagnation point due to the increase in pressure energy from the conversion of K.E into P.E.
32 Match the following:
i. subsonic nozzle : figure
ii. Supersonic nozzle : figure
iii. Subsonic diffuser : figure
iv. Centrifugal compressor : figure

40 Cold working of metal increases ----------------------
Tensile strength

41 The power absorbed in belt drive depends on-----------------------
Tension in tight side, Tension in slack side, coefficient of friction & Radius of pulley.

42 The temperature loss related -------------- hysteresis loss

43 The convergent pipe having entry and exit diameters are 100 and 50 mm respectively, find out their velocity ratio from entry to exit…………..
1/4

44 They had given one composite circular pipe having 4 varying cross sections . They are 2D, 1.5D, 4D & D respectively. The water is entering at velocity V at section 1 and leaving at section 4. Find out the pressure decreasing order……………
P4>P2>P1>P3

45 The bulb having weight 150N supported by two ropes and attached to the walls having angles 45º & 60º. Findout the reaction forces in the ropes ?
This is related to Lamis theorem
46 A hollow sphere of radius r . A particle is moving with coefficient of friction 1/[3]½ inside the sphere from wall . which height will it become rest?

47 The disc is resting on the rough wall by a rope tied at the center . The rope makes angle with the wall around 30º. The tension in the string is ----------than the weight of the disc. more

48 A railway wagon containing partially full of water. Which angle----------------

49 Findout the graph between discharge [Q] in the x-axis and head [H] in the y-axis----------

50 In welding pitch dimension is limited to----------------------

51 The composition of inconel alloy-------------------

52 There is a heat transfer between two walls having thickness and conductivities k1 & K2 respectively. The linear temperature profile of first wall is more steeper than the second wall . Findout the ratio K1/K2 ---------------------
a) >0 b) <0 c)=0 d) the given data is insufficient

53 The max shear stress developed in solid circular shaet is 100 MPa . Calculate the max normal stress developed in it? ??????



54 This question related to welding -------------

55 Bearing liner-------------------------
a) Babbit metal b) Gun metal

56 Electrical resistance material --------------Nichrome

57 This question related to radiation

58 A sun emits 1150K at 0.5µ. A furnace emits 300k from small door --------------

59 In the simple pendulum , the maximum amplitude depends on ------------------- increase in length

60 The fuel flow increases if-------------------------
a) exhaust valve burnt b) filter choke c) silencer choke

61 The jet propulsion depends on-------------
a) jet velocity b) weight ratio

62 What is the condition for perfect frame-------------------------------------

63 Depth of cut can be increased by-----------------------



64 The workpiece can be held in-----------------

65 This is related toNucleate boiling

66 What is the expression for Reynolds number in terms of diameter of the pipe…………..Re =?VD/µ

67 Air conditioning means---------------
a) cooling & heating b)dehumidifying c) removing impurities from air d)all

68 Fibrous fracture occurs in ------------------------
a)brittle fracture b) ductile fracture c)shear fracture d)none

69 In laser beam machining , the workpiece should be--------------
a)absorbed by all the rays b) reflected by all the rays

70 Foam and coke are good insulators. Why?-----------------------
a)less density b)

71 Gold property------------------
a)good conductor b)good insulator


72 In lathe , the workpiece can be held in --------------------------------------
a) live center b)steady rest c)3-way chuck d)4-way chuck


INTERVIEW PATTERN:I. Project ExplanationII. Fluid Mechanics:i. Define laminar flow & Turbulent flow
ii. What is the value of Reynolds no in pipe flow
iii. What is the significance of Reynolds no
iv. Head losses in pipe
v. Define boundary layer in pipe flow & thickness of boundary layer
vi. What is the variation of d in laminar & turbulent flow
III. Strength of materialsi. Draw the figure for spring damper system
ii. Differential equation for spring damper system
iii. Find out the deflection of spring damper system
iv. Define stiffness and unit of stiffness
IV. Material Sciencei. Ferrous materials
ii. Non-ferrous materials
iii. Define fatigue
iv. Define fatigue resistance?
v. Curve for fatigue
vi. Fatigue limit

IFS Chemical Engineering question paper, 2005, Indian Forest Service, test papers


SECTION A

1. Answer any four of the following:(a) Find the first-order rate constant for the disappearance of A in the gaseous reaction 2A R, holding the pressure constant, the volume of the reaction mixture starting with 80 per cent A decreases by 20 per cent in 3 mm. (10)

(b) A solution contains 50 per cent benzene, 30 per cent toluene and 20% xylene by weight at 100° C. The vapours are in contact with the solutions. Calculate total pressure and mole per cent composition of liquid and vapour: (10)

(c) Show that the internal energy of an ideal gas is a function of temperature only. (10)
(d) For adiabatic batch reactor, derive an expression to determine the time required to achieve a desired conversion. (10)
(e) Define Bubble point and Dew point. Explain in detail how to calculate bubble point or dew point of given binary mixture. (10)
2. The elementary reaction. A + B R + S is effected in a set up consisting of a mixed reactor into which two reactant solutions are introduced followed by a PFR. A large enough of excess of B is used so that the reaction is first order w.r.t. A. It is proposed to reverse the order of two units. How does this change affect the conversion? (40)
3. A high purity limestone is burnt in a lime kiln which is fired externally with a coal containing 75.5 per cent C, 5.5 per cent H, 1.6 per cent N, 1.1 per cent S, 7.6 per cent and rest ash. The stack gas analysis is 20.2% CO2, 7.1% O2 and rest N2, Calculate-
(a) kg limestone burnt/kg of coal;
(b) excess air used for combustion. (40)
4. One mole of an ideal gas initially at P1 and T1 is compressed reversibly and adiabatically till the pressure is P2 and then it is cooled at constant volume to the initial pressure, finally the gas is restored to the initial state through an isobaric process. Calculate the work done by the process. (40)

SECTION – B

5. Answer any four of the following:(a) Define depreciation. What are the different methods for determining depriciation? Explain the method, sum of the years digit method. (10)
(b) Explain briefly the factors to be considered for the location of a chemical plant. (10)
(c) Describe the manufacture of caustic soda by either diaphragm or mercury cell process. Discuss the pollution aspects of this industry. (10)
(d) Explain briefly the pollutants emitted from a tanning industry. (10)
(e) Explain the cracking and polymerisation of petroleum fractions. (10)
6. (a) Explain the break-even analysis and its equation. (10)
(b) A Project can produce 12000 units per year at 100 per cent capacity. The variable cost per unit is Rs. 3 at 100 per cent capacity. Fixed costs are Rs. 10,000 per year. Find the break-even point if the selling price is Rs. 5/ unit. Now the manufacturer finds that he can sell only 80% at Rs 5/ unit. How much should he charge for additional units if he brings production upto 100 per cent capacity and increases profits after taxes by an additional amount of Rs. 1,000? Use tax rate for the above problem 52 per cent. . (30)
7. (a) Describe the process with neat flow sheet of the manufacture of ethyl alcohol. (30)(b) Discuss the applications of following products: (10)
(i) Enamel paint (ii) Rancidity.
8. (a) Discuss the methods possible for preventing various industrial hazards. (20)(b) Explain primary treatment method of waste-water treatment. (20)

IFS Chemical Engineering question paper, 2007, Indian Forest Service, test papers


SECTION A

1. Answer any four of the following (Maximum 150 words):
(a) Discuss reversible thermodynamic processes.
(10)
(b) Write short note on fugacity.
(10)
(c) Write short note on reactors in series.
(10)
(d) A solution of naphthalene, C10H8, in benzene, C6 H6, contains 25 mole per cent of
naphthalene. Express the composition of the solution in weight percent.
(10)
(e) A solution of Sodium Chloride in water contains 230 grams of NaCl per liter at 20°C. The
density of solution at this temperature is 1.148 grams per cubic centimeter, calculate :
(i) Volumetric percent of water
(ii) Composition in mole percent
(iii) Modality.
Note : density of water at 20° C = 0.998 g/cc.
2. (a) The liquid phase reaction,
(where K1=8 liter/mol.min
K2=3 liter/mol.min)
is carried out in 150 litre stirred tank reactor under steady state conditions. Reactants A and B
are fed to the reactor at equal volumetric flow rates. The concentrations of A and B streams
are 2.8 mole A/ litre and 1.6 mole B/litre. What should be the flow rate of each stream to get
75% conversion of the limiting reactant?
(25)
(b) Prove that the heat transferred equals the enthalpy change of the system for a mechanically
reversible, constant-volume, constant-pressure, non- flow processes.
(15)
3 (a) A steel casting [Cp = 0.5 kJ kg-1 K-1] weighing 40 kg and at a temperature of 450°C is
quenched in 150 kg of oil [Cp = 2.5 kJ kg-1 K-l at 25°C. If there are no heat losses, what is the
change in entropy of :
(i) the casting,
(ii) the oil and
(iii) both considered together? (25)
(b) Derive the expression for the design equation of tubular reactor. (15)
4. (a) One litre/mm of liquid containing A and B [CA0 = 0.10 mol/litre, CBO =0.01 mol/litre] flow
into a mixed reactor of volume of one litre. The materials react in a complex manner for
which the stoichiometry is unknown. The outlet streak from the reactor contains A, B and
C(CAf = 0.02 mol/litre, Cbt= 0.03 mol/litre, Ccf = 0.04 mol/litre). Find the rate of reaction of
A, B and C for the conditions within the reactor. (20)
(b) Chlorobenzene is nitrated using a mixture of nitric acid and sulphuric acid. During the pilot
plant studies, a charge consisted of 100 kg chlorobenzene (CB), 106.5 kg 65.5% (by weight)
nitric acid and 108 kg 93.6% (by weight) sulphuric acid. After two hours of operation, the
final mixture was analysed. It was found that the final product contained 2% unreacted
chlorobenzene. Also the product distribution was found to be 66% p-nitrochlorobenzene and
34% o-nitrochloro benzene, calculate:
(i) The analysis of charge
(ii) The percentage conversion of chlorobenzene.
(20)

SECTION B

5. Answer any four of the following in brief (Maximum 150 words):
(a) PERT
(10)
(b) Break-even analysis
(10)
(c) Biogas
(10)
(d) Essential oils
(10)
(e) Norms for air emission.
(10)
6. Describe manufacture of ammonia giving neat flow diagram and discuss its major pollution
problems.
(40)
7. (a) Suggest and justi1’ a location for a soda ash plant.
(20)
(b) Discuss greenhouse effect.
(20)
8. (a) Discuss cracking in brief.
(20)
(b) The original value of a piece of equipment is Rs. 22,000. Its salvage value is Rs. 2,000 at the
end of service life of 10 years. Determine the book value of the equipment at the end of 5
years using:
(i) Straight-line method
(ii) Textbook declining-balance method
(iii) Double declining-balance method.

IFS Chemical Engineering question paper, 2004, Indian Forest Service, test papers


SECTION A

1. Answer any four of the following (10 x 4 = 40)
(a)
(i) What is time dependent flow ? With the help of this phenomenon, explain the meaning of Thixotropic liquid and Rheopeptic substances.
(ii) Write the power law equation for dilatant and pseudo plastic fluids, and explain the terms ‘flow consistency index’ and ‘flow behaviour index’.
(b) Derive an equation for steady conduction in the radial direction of a hollow cylinder. From the equation, explain the term log-mean radius. Under what condition, can the log-mean radius be replaced by arithmetic mean radius?
(c) In a double pipe heat exchanger, a hot fluid is cooled from 150 to 100°C by using cold water, which is heated from 30 to 50°C. Derive a suitable expression to prove that there is a distinct advantage of using the exchanger in counter-current flow over that of using it in parallel flow.
(d) Explain how thermal condition of feed influences the liquid or vapour flow rate around the feed plate of a rectification column. What common factor can be used for characterizing five different feed conditions? From the value of this common factor, explain the meaning of horizontal and vertical feed lines.
(e) Explain the phenomenon of primary nucleation in the process of crystallization, and illustrate the difference between homogeneous and heterogeneous nucleation.
2. (a) For an incompressible fluid, write the Bernoulli equation for fractionizes flow. What correction would you apply for incorporating fluid friction? Explain the difference between skin friction and form friction. (10)
(b) What is terminal velocity? Write the equation for terminal velocity for the flow of a single particle through a fluid under the action of (i) gravity and (ii) centrifugal force. How is the equation for terminal velocity under free settling condition modified for hindered settling conditions? (10)
(c) What is a ball mill? Derive an equation for the critical speed of a ball mill. (10)(d) What is a venture meter? Describe the principle of working of a venture meter and write an expression for the venture coefficient. (10)
3. (a) An air water system has a dry bulb temperature of 65.5°C and a wet bulb temperature of 54.5°C.
(i) If the air is cooled to 37.8°C, what per cent of the moisture will condense?
(ii) If the air is again heated to 65.5°C, how much heat will be required per kg of dry air? Specific heat of air = 0.23 kcal/ (kg 0C). (10)
(b) A spherical particle of ethanol of 10 mm diameter is evaporating in an air stream at 26°C. The thickness of the stagnant air surrounding the particle is 1.5 mm. Vapour pressure of ethanol at 26°C is 60 mm Hg and the mole fraction of ethanol in the main stream of the air is 0.005. The diffusion coefficient of ethanol in air is 1.04 × 10-5 m2/sec and the value of R is 82.06 × 10-3 m3 atm/kg mole. Determine,
(i) The mole fraction of ethanol at different positions across the stagnant layer.
(ii) Rate of evaporation of the particle per second. (10)
(c) What are different types of packing that are used in an absorption tower? Explain a simple procedure for calculating the height of a packed tower for absorption of a single component from a gas mixture. (10)
(d) What is critical moisture content? Describe the method for drying of a wet solid before it reaches the critical moisture content. (10)
4. (a) Develop a relation between heat transfer and fluid friction by using the Reynolds’s Analogy. (10)
(b) (i) What is a radiation shield? How does it help in reducing radiant heat loss?
(ii) A double walled spherical container is used for storing liquid oxygen. The diameter of the inner and outer walls of the container is 30 cm and 36 cm, respectively. The surfaces of both the spheres are plated, so that their emissivity is 0.05. Determine the rate at which oxygen will evaporate at -183°C, when the outer wall of the sphere ismaintained at 20°C. Latent heat of evaporation of oxygen is 57.2 kcal/kg. (5 + 5)
(c) What are drop wise and film wise condensation? Mention the conditions that favour drop wise condensation. Describe how the heat transfer coefficient in a vertical condenser is influenced by the height of the condenser. (10)

(
d) What is effectiveness of a heat exchanger? Derive a relation between the effectiveness and number of transfer units for a countercurrent heat exchanger. (10)


SECTION B

5. Answer any four of the following (10 × 4 = 40)(a) What are the relative advantages and disadvantages of the proportional, integral and derivative control actions? What are their characteristic effects on the closed loop response for a process?

(b) Explain briefly the essential elements of a computer controlled process system.
(c) What is reverse osmosis? How can it be used for the separation of a solute from an aqueous solution?
(d) What is molecular distillation? With a neat sketch describe the working of a molecular distillation unit.
(e) Discuss how wind load is taken care of in the design of a tall vertical vessel.
6. (a) Illustrate the principle of separation of gases by using non-porous membrane. (10) (b) Discuss about electrolytic regeneration of mixed bed ion exchange resins. (10)
(c) Explain the process of diffusion dialysis and mention its applications. (10)
(d) What are absorption and extraction type separation processes? Illustrate them with examples. (10)
7. (a) Discuss how to find the frequency response of a proportional + integral controller, (10)(b) Explain how a strain gauge is used for pressure measurement. (10)(c) Illustrate the process of feed forward control. (10)(d) Write a relationship that will give the molar or specific enthalpy of a multi-component liquid at temperature T, with known composition for N components. What are the principal control considerations that affect the scope of mathematical modeling of a chemical process? (10)

8. (a) Illustrate the method for the design of a conical head of a cylindrical pressure vessel. (10)
(b) Discuss about major loads and subsidiary loads that must be considered for the design of a pressure vessel. (10)
(c) What are skirt supports? Discuss the method for calculating the thickness of a skirt support. (10)
(d) Discuss the method for calculating the thickness of the shell of a thin wall pressure vessel. (10)