Showing posts with label mock question paper. Show all posts
Showing posts with label mock question paper. Show all posts

Saturday, 28 September 2013

FIRST MINOR TEST: IC ENGINES IN SGIT

Shree Ganpati Institute of Technology; Ghaziabad
From 23rd September, 2013 to 26th September first minor test has been organised. This semester, I am teaching IC Engines and Compressors (EME-505) and Thermodynamics (ME-301).
Here is the Question paper of EME-505
  
snapshot of the question paper
ME-301; Thermodynamics
3rd Semester; Mechanical Engg

Saturday, 29 September 2012

FUEL USED IN IC ENGINES AND REFINERY PROCCESSES; EME-505

FUEL USED IN IC ENGINES
An article on fossil fuels

Internal Combustion Engines are the generators of the energy mainly used for transportation. Almost more than 90% of the total IC Engines run on fossil fuels or different derivatives of petroleum.

IC Engines are a kind of open cycle heat engine where heat is supplied to the engine by the combustion of working fluids thus releasing huge amount of energy due to the combustion processes of the working fluids. Combustible working fluids are called fuels.


The natural petroleum oil is the largest single source of internal combustion engine fuels. Petrol and Diesel are the most used among them. The boiling point of petrol is 30°C to 200°C and that of diesel oil is from 200°C to 375°C.


Fuels of most of the IC Engines are the derivatives of Petroleum like gasoline, diesel oil, kerosene, jet fuel etc. All of these fuels are produced during the fractional distillation of Petroleum Oil obtained from crude from oil wells.


The fuels used in the IC Engines are designed to satisfy the performance requirements of the engine system in which they are used. As a result the fuels must have certain


  • (i) physical,
  • (ii) chemical and
  • (iii) combustion properties.

Following are the some characteristics a fuel must have in order to produce the desirable output to the engine performance.
  1. A fuel must have a large energy density to be capable to release huge amount of energy during its combustion in side the combustion chamber.
  2. A fuel must posses a good combustion quality to produce large amount of energy in smooth way.
  3. A fuel must have high thermal stability or pre-ignition may occur.
  4. A fuel must show a low deposit forming tendency else gum formation and other deposit forming processes will hamper the combustion process.
  5. A fuel must be non-toxic, easy to handle and storage.
CRUDE PETROLEUM OIL:

Petroleum or often referred as "Crude Oil" is a naturally occurring inflammable mixtures of liquid and mud and it contains a complex mixture of different hydrocarbons of various molecular weights. It is mainly recovered through a process called "Oil Drilling".


Oil Wells and Gas Wells:


An oil well produces mainly crude oil with some natural gas dissolved in it. In contrast a gas well produces natural gases although it may contain heavier hydrocarbons like pentane, hexane or hepthane in gaseous state due to the extreme pressure and temperature inside the well, but at surface conditions condensation starts and forms "Natural Gas Condensate" or simply known as Condensate.




COMPOSITIONS OF CRUDE WELL:

Basically, crude well is the muddy mixtures of different hydrocarbons of different molecular weights. Alkanes, Cyclo-alkanes or napthenes, aromatics. It contains nitrogen, oxygen, sulfur and phosphorous. It may also contains metallic compounds too.


Four different types of hydrocarbon molecules appear in crude oil. The relative percentages are widely varied from oil to oil. They are:


  • i) Paraffins (alkanes,  CnH2n + 2 )
  • ii) Olefins (alkenes, CnH2n),
  • iii) Napthenes (cyclo-alkanes, CnH2n ),
  • iv) Aromatics (having benzene ring, CnH2n - 6).

It is then refined by fractional distillation in oil refinery to obtain a large number of consumer products, from petrol or gasoline, diesel to kerosene, heavy oil, fuel oil, asphalt, chemical reagents, plastics etc.

Most of the derivatives of the petroleum have been used as fuel or heating purpose. The major products of a petroleum refinery are:



  • (i) Gasoline,
  • (ii) Kerosene,
  • (iii) Diesel Oil,
  • (iv) Fuel oil,
  • (v) Heavy Oil,
  • (vi) Lubricating Oil,
  • (vii) Asphalts
INTRODUCTION: 

As the demands for gasoline, kerosene/ jet fuel and diesel oil are maximum, refineries around the world have started to convert heavy fuels and other higher hydrocarbons into gasoline, kerosene and diesel oil. To perform this, refineries have adopted several thermo-chemical processes those can convert high molecular weight hydrocarbons into lighter ones by breaking them.

GENERAL REFINERY PROCESSES:


Petroleum refining has evolved continuously in response to changing consumer demand for better and different products. The original requirement was to produce kerosene as a cheaper and better source of light than whale oil. The development of the internal combustion engine led to the production of gasoline and diesel fuels. The evolution of the airplane created an initial need for high-octane aviation gasoline and then for jet fuel, a sophisticated form of the original product, kerosene. Present-day refineries produce a variety of products including many required as feedstock for the petrochemical industry.



a) Distillation Processes:

The first refinery, opened in 1861, produced kerosene by simple atmospheric distillation. Its by-products included tar and naphtha. It was soon discovered that distilling petroleum under vacuum could produce high-quality lubricating oils. However, for the next 30 years kerosene was the product consumer wanted. Two significant events changed this situation. The invention of the electric light decreased the demand for kerosene and the invention of the internal combustion engine created a demand for diesel fuel and gasoline (naphtha). 



b) Thermal Cracking Processes:

With the advent of mass production and World War I, the number of gasoline-powered vehicles increased dramatically and the demand for gasoline grew accordingly. However, distillation processes produced only a certain amount of gasoline from crude oil. In 1913, the thermal cracking process was developed, which subjected heavy fuels to both pressure and intense heat, physically breaking the large molecules into smaller ones to produce additional gasoline and distillate fuels. Visbreaking, another form of thermal cracking, was developed in the late 1930's to produce more desirable and valuable products. 



c) Catalytic Processes:

Higher-compression gasoline engines required higher-octane gasoline with better antiknock characteristics. The introduction of catalytic cracking and polymerization processes in the mid- to late 1930's met the demand by providing improved gasoline yields and higher octane numbers.   Alkylation, another catalytic process developed in the early 1940's, produced more high-octane aviation gasoline and petrochemical feedstock for explosives and synthetic rubber. Subsequently, catalytic isomerization was developed to convert hydrocarbons to produce increased quantities of alkylation feedstock. Improved catalysts and process methods such as hydrocracking and reforming were developed throughout the 1960's to increase gasoline yields and improve antiknock characteristics. These catalytic processes also produced hydrocarbon molecules with a double bond (alkenes) and formed the basis of the modern petrochemical industry. 



d) Treatment Processes:

Throughout the history of refining, various treatment methods have been used to remove non-hydrocarbons, impurities, and other constituents that adversely affect the properties of finished products or reduce the efficiency of the conversion processes. Treating can involve chemical reaction and/or physical separation. Typical examples of treating are chemical sweetening, acid treating, clay contacting, caustic washing, hydrotreating, drying, solvent extraction, and solvent dewaxing. Sweetening compounds and acids desulfurize crude oil before processing and treat products during and after processing. 

Following the Second World War, various reforming processes improved gasoline quality and yield and produced higher-quality products. Some of these involved the use of catalysts and/or hydrogen to change molecules and remove sulfur. 



 Basics of Hydrocarbon Chemistry:

Crude oil is a mixture of hydrocarbon molecules, which are organic compounds of carbon and hydrogen atoms that may include from one to 60 carbon atoms. The properties of hydrocarbons depend on the number and arrangement of the carbon and hydrogen atoms in the molecules. The simplest hydrocarbon molecule is one carbon atom linked with four hydrogen atoms: methane. All other variations of petroleum hydrocarbons evolve from this molecule. 
 
Hydrocarbons containing up to four carbon atoms are usually gases, those with 5 to 19 carbon atoms are usually liquids and those with 20 or more are solids. The refining process uses chemicals, catalysts, heat, and pressure to separate and combine the basic types of hydrocarbon molecules naturally found in crude oil into groups of similar molecules. The refining process also rearranges their structures and bonding patterns into different hydrocarbon molecules and compounds. Therefore it is the type of hydrocarbon (paraffinic, naphthenic, or aromatic) rather than its specific chemical compounds that is significant in the refining process. 


Principal Groups of Hydrocarbon
  • Paraffins - The paraffinic series of hydrocarbon compounds found in crude oil have the general formula CnH2n+2 and can be either straight chains (normal) or branched chains (isomers) of carbon atoms. The lighter, straight chain paraffin molecules are found in gases and paraffin waxes. Examples of straight-chain molecules are methane, ethane, propane, and butane (gases containing from one to four carbon atoms), and pentane and hexane (liquids with five to six carbon atoms). The branched-chain (isomer) paraffins are usually found in heavier fractions of crude oil and have higher octane numbers than normal paraffins. These compounds are saturated hydrocarbons, with all carbon bonds satisfied, that is, the hydrocarbon chain carries the full complement of hydrogen atoms.
    • Example of simplest hydrocarbon molecule: Methane (CH4), Examples of straight chain paraffin molecule (Butane) and branched paraffin molecule (Isobutane) with same chemical formula (C4H10)


  • Aromatics - Aromatics are unsaturated ring-type (cyclic) compounds which react readily because they have carbon atoms that are deficient in hydrogen. All aromatics have at least one benzene ring (a single-ring compound characterized by three double bonds alternating with three single bonds between six carbon atoms) as part of their molecular structure. Naphthalenes are fused double-ring aromatic compounds. The most complex aromatics, polynuclears (three or more fused aromatic rings), are found in heavier fractions of crude oil.
    • Example of simple aromatic compound: Benzene (C6H6), Examples of simple double-ring aromatic compound: Naphthalene (C10H8)


  • Naphthenes - Naphthenes are saturated hydrocarbon groupings with the general formula CnH2n, arranged in the form of closed rings (cyclic) and found in all fractions of crude oil except the very lightest. Single-ring naphthenes (monocycloparaffins) with five and six carbon atoms predominate, with two-ring naphthenes (dicycloparaffins) found in the heavier ends of naphtha.
    • Example of typical single-ring naphthene: Cyclohexane (C6H12), Examples of naphthene with same chemical formula (C6H12) but different molecular structure: Methyl cyclopentane (C6H12)
Other Hydrocarbons
  • Alkenes - Alkenes are mono-olefins with the general formula CnH2n and contain only one carbon-carbon double bond in the chain. The simplest alkene is ethylene, with two carbon atoms joined by a double bond and four hydrogen atoms. Olefins are usually formed by thermal and catalytic cracking and rarely occur naturally in unprocessed crude oil.
    • Example of simples Alkene: Ethylene (C2H4), Typical Alkenes with the same chemical formula (C4H8) but different molecular structures: 1-Butene and Isobutene


  • Dienes and Alkynes - Dienes, also known as diolefins, have two carbon-carbon double bonds. The alkynes, another class of unsaturated hydrocarbons, have a carbon-carbon triple bond within the molecule. Both these series of hydrocarbons have the general formula CnH2n-2. Diolefins such as 1,2-butadiene and 1,3-butadiene, and alkynes such as acetylene,occur in C5 and lighter fractions from cracking. The olefins, diolefins, and alkynes are said to be unsaturated because they contain less than the amount of hydrogen necessary to saturate all the valences of the carbon atoms. These compounds are more reactive than paraffins or naphthenes and readily combine with other elements such as hydrogen, chlorine, and bromine.
    • Example of simplest Alkyne: Acetylene (C2H2), Typical Diolefins with the same chemical formula (C4H6) but different molecular structures: 1,2-Butadiene and 1,3-Butadiene
Non-hydrocarbons
  • Sulfur Compounds -  Sulfur may be present in crude oil as hydrogen sulfide (H2S), as sulfur compounds such as mercaptans, sulfides, disulfides, thiophenes, etc. or as elemental sulfur. Each crude oil has different amounts and types of sulfur compounds, but as a rule the proportion, stability, and complexity of the compounds are greater in heavier crude-oil fractions. Hydrogen sulfide is a primary contributor to corrosion in refinery processing units. Other corrosive substances are elemental sulfur and mercaptans. Moreover, the corrosive sulfur compounds have an obnoxious odor.  Pyrophoric iron sulfide results from the corrosive action of sulfur compounds on the iron and steel used in refinery process equipment, piping, and tanks. The combustion of petroleum products containing sulfur compounds produces undesirables such as sulfuric acid and sulfur dioxide. Catalytic hydrotreating processes such as hydrodesulfurization remove sulfur compounds from refinery product streams. Sweetening processes either remove the obnoxious sulfur compounds or convert them to odorless disulfides, as in the case of mercaptans.

  • Oxygen Compounds -  Oxygen compounds such as phenols, ketones, and carboxylic acids occur in crude oils in varying amounts. 

  • Nitrogen Compounds -  Nitrogen is found in lighter fractions of crude oil as basic compounds, and more often in heavier fractions of crude oil as nonbasic compounds that may also include trace metals such as copper, vanadium, and/or nickel. Nitrogen oxides can form in process furnaces. The decomposition of nitrogen compounds in catalytic cracking and hydrocracking processes forms ammonia and cyanides that can cause corrosion. 

  • Trace Metals -  Metals, including nickel, iron, and vanadium are often found in crude oils in small quantities and are removed during the refining process. Burning heavy fuel oils in refinery furnaces and boilers can leave deposits of vanadium oxide and nickel oxide in furnace boxes, ducts, and tubes. It is also desirable to remove trace amounts of arsenic, vanadium, and nickel prior to processing as they can poison certain catalysts. 

  • Salts -  Crude oils often contain inorganic salts such as sodium chloride, magnesium chloride, and calcium chloride in suspension or dissolved in entrained water (brine). These salts must be removed or neutralized before processing to prevent catalyst poisoning, equipment corrosion, and fouling. Salt corrosion is caused by the hydrolysis of some metal chlorides to hydrogen chloride (HCl) and the subsequent formation of hydrochloric acid when crude is heated. Hydrogen chloride may also combine with ammonia to form ammonium chloride (NH4Cl), which causes fouling and corrosion. 

  • Carbon Dioxide -  Carbon dioxide may result from the decomposition of bicarbonates present in or added to crude, or from steam used in the distillation process. 
  • Naphthenic Acids -  Some crude oils contain naphthenic (organic) acids, which may become corrosive at temperatures above 450° F when the acid value of the crude is above a certain level.
 Major Refinery Products
  • Gasoline. The most important refinery product is motor gasoline, a blend of hydrocarbons with boiling ranges from ambient temperatures to about 400 °F. The important qualities for gasoline are octane number (antiknock), volatility (starting and vapor lock), and vapor pressure (environmental control). Additives are often used to enhance performance and provide protection against oxidation and rust formation.
  • Kerosene. Kerosene is a refined middle-distillate petroleum product that finds considerable use as a jet fuel and around the world in cooking and space heating. When used as a jet fuel, some of the critical qualities are freeze point, flash point, and smoke point. Commercial jet fuel has a boiling range of about 375°-525° F, and military jet fuel 130°-550° F. Kerosene, with less-critical specifications, is used for lighting, heating, solvents, and blending into diesel fuel.
  • Liquified Petroleum Gas (LPG). LPG, which consists principally of propane and butane, is produced for use as fuel and is an intermediate material in the manufacture of petrochemicals. The important specifications for proper performance include vapor pressure and control of contaminants.
  • Distillate Fuels. Diesel fuels and domestic heating oils have boiling ranges of about 400°-700° F. The desirable qualities required for distillate fuels include controlled flash and pour points, clean burning, no deposit formation in storage tanks, and a proper diesel fuel cetane rating for good starting and combustion.
  • Residual Fuels. Many marine vessels, power plants, commercial buildings and industrial facilities use residual fuels or combinations of residual and distillate fuels for heating and processing. The two most critical specifications of residual fuels are viscosity and low sulfur content for environmental control.
  • Coke and Asphalt. Coke is almost pure carbon with a variety of uses from electrodes to charcoal briquets. Asphalt, used for roads and roofing materials, must be inert to most chemicals and weather conditions.
  • Solvents. A variety of products, whose boiling points and hydrocarbon composition are closely controlled, are produced for use as solvents. These include benzene, toluene, and xylene.
  • Petrochemicals. Many products derived from crude oil refining, such as ethylene, propylene, butylene, and isobutylene, are primarily intended for use as petrochemical feedstock in the production of plastics, synthetic fibers, synthetic rubbers, and other products.
  • Lubricants. Special refining processes produce lubricating oil base stocks. Additives such as demulsifiers, antioxidants, and viscosity improvers are blended into the base stocks to provide the characteristics required for motor oils, industrial greases, lubricants, and cutting oils. The most critical quality for lubricating-oil base stock is a high viscosity index, which provides for greater consistency under varying temperatures.
Common Refinery Chemicals
  • Leaded Gasoline Additives: Tetraethyl lead (TEL) and tetramethyl lead (TML) are additives formerly used to improve gasoline octane ratings but are no longer in common use except in aviation gasoline.
  • Oxygenates: Ethyl tertiary butyl ether (ETBE), methyl tertiary butyl ether (MTBE), tertiary amyl methyl ether (TAME), and other oxygenates improve gasoline octane ratings and reduce carbon monoxide emissions.
  • Caustics: Caustics are added to desalting water to neutralize acids and reduce corrosion. They are also added to desalted crude in order to reduce the amount of corrosive chlorides in the tower overheads. They are used in some refinery treating processes to remove contaminants from hydrocarbon streams.
  • Sulfuric Acid and Hydrofluoric Acid: Sulfuric acid and hydrofluoric acid are used primarily as catalysts in alkylation processes. Sulfuric acid is also used in some treatment processes.

    USEFUL LINKS:   
    refinery topics

Tuesday, 25 September 2012

MOCK TEST OF I.C. ENGINE; EME-505


1st SESSIONAL EXAMINATION 2012-13
BRANCH – ME
SEMESTER- V
Course: B.Tech.                                                                                                                Year: 3rd
Sub: IC Engines & Compressors                                                           Subject Code: EME- 505
Maximum Marks: 30                                                                                               Time: 1.30 hrs

Section A:                                                                                                       2x6 = 12
Q.1) Answer the following question in brief                                                                                  
(a)    Explain the difference between inlet valve and inlet port.
(b)   What is cracking?
(c)    Define volumetric efficiency of an IC engine with diagram.  
(d)   What are the assumptions of a air standard cycle?
(e)    Explain the concept of indicator thermal efficiency.
(f)    What are the general refinery processes?

Section B:
Q.2) Answer any three of the following questions                                         6 x 3 = 18

(a) Compare between four stroke and two stroke IC engines.

(b)  What is compression ratio? What is its range for (i) the SI engine (ii) CI engine? What factors limit the compression ratio in each type of engine?

(c) An ideal Otto cycle has compression ratio of 8 and initial conditions are 1 bar and 15°C. Heat added during constant volume process is 1045 kJ/kg. Find:
(i)                 Maximum cycle temperature
(ii)               Air standard efficiency
(iii)             Work done per kg of air
(iv)             Heat rejected
Take: Cv = 0.7175 kJ/kg-K and γ = 1.4

(d)  A diesel engine develops 5 kW. It’s indicated thermal efficiency is 30% and mechanical efficiency 57%. Estimate the fuel consumption in (i) kg/hr, (ii) litres/hr,
(iii) Indicated specific fuel consumption, and (iv) brake specific fuel consumption.
L.C.V. of diesel oil = 42000 kJ/kg.

(e) Compare the actual cycle and its deviation from theoretical cycles in IC engines.



Monday, 7 December 2009

ME-101 MOCK QUESTION PAPER; ENGINEERING MECHANICS

Vivekanand Institute of Technology & Science; Ghaziabad
PRE-SEMESTER EXAMINATION (odd SEMESTER 2009-10)
B.Tech…first Semester

Sub Name: Engineering Mechanics Max. Marks: 100
Sub Code: EME-102 Max. Time: 3: 00 Hr

(i) This paper is in three sections, section A carries 20 marks, section B carries 30 marks and section C carries 50 marks.
(ii) Attempt all the questions. Marks are indicated against each question
(iii) Assume missing data suitably if any.

Group A

Q.1 Answer the following questions as per the instructions 2x20=20
Choose the correct answer of the following questions:

(i) The magnitudes of the force of friction between two bodies, one lying above the another depends upon the roughness of the
(a) Upper body;                 (b) Lower body
(c) Both the bodies               (d) The body having more roughness

(ii)The moment of inertia of a circular section of diameter D about its centroidal axis is given by the expression
(a) π(D)4/16               (b) π(D)4/32
(c) π(D)4/64               (d) π(D)4/4

Fill in the blanks in the following questions:

(iii)The distance of the centroid of an equilateral triangle with each side(a) is …………. From any of the three sides.
(iv)Poisson’s ratio is defined as the ratio between ……………………. and
………………………… .
(v)If two forces of equal magnitudes P having an angle 2Ө between them,
then their resultant force will be equal to ________ .

Match the following columns for the following two parts:

(vi) Match the column I to an entry from the column II:
COLUMN – I COLUMN - II
(i) BMD of an UDL(a) stored strain energy per unit volume
(ii) Resilience is(b) brittle materials
(iii) Bulk Modulus (c) parabolic in nature
(iv) Yield Point (d) volumetric stress & strain
(e) Ductile materials
(f) Shear stress

(vii) Match the Following columns:
COLUMN – I COLUMN - II
(i) Square of side (b) (p) π b4 / 64
(ii) Equilateral Triangle of side (b)(q) b4 / 12
(iii) Circle of diameter (b)(r) b4/ 36
(iv) Isosceles right angle triangle of base (b) (s) b4/(32√3)
(e) Ductile materials
(f) Shear stress

Column II gives the value of Moment of Inertia Ixx about a centroidal axis.

Choose correct answer for the following parts:

(viii) Statement 1:
In the yielding zone, strain increases even if stress is decreased.

Statement 2:
At yielding point, the deformation becomes plastic by nature.

(i) Statement 1 is true, Statement 2 is true.
(ii) Statement 1 is true, Statement 2 is true and they are unrelated with
each other
(iii) Statement 1 is true, statement 2 is false.
(iv) Statement 1 is false, Statement 2 is false.

(ix) Statement 1:
For two identical mass, one of which lies on a horizontal plane and another is kept at an inclined plane having same co-efficient of friction, still frictional forces differs from each other.

Statement 2:
Frictional force always depends upon the magnitude of the normal force.

(i) Statement 1 is true, Statement 2 is true.
(ii) Statement 1 is true, Statement 2 is true and they are unrelated with
each other
(iii) Statement 1 is true, statement 2 is false.
(iv) Statement 1 is false, Statement 2 is false.

Choose the correct word/s.
(x) In a truss if the no.of joints (j) is related with no. of links (m) by the equation m > 2j- 3, then it is an example of (redundant/ deficient/ perfect) Truss.

SECTION-B

Q.2: Answer any three parts of the followings: 10X3=30
(a) Find the shear force and moment equation for the beam as shown in the figure. Also sketch SFD (shear force diagram) and BMD (bending moment diagram)

(b) Explain and prove “the parallel axis theorem of moment of inertia.”
Also find the centroid of the following composite area.


(c) Find the centroidal Moment of Inertia of the following shaded area.
(d) Two cylinders P and Q rest in a channel as shown in fig. below. The cylinder P has a diameter of 100 mm and weighs 200 kN, where as the cylinder Q has a diameter of 180 mm and weighs 500 kN. Find the support reactions at all the point of contact.

(e)
Two blocks A and B of weights 1 kN and 2 kN respectively are in equilibrium as Shown in the figure.
If the co-efficient of friction everywhere is 0.3, find the force P required to move the block B.

SECTION C:

(3) Answer any two parts of the following 5X2=10

(a) A simply supported beam of circular cross section of radius 4 cm having a length 2 m long in concentrated load of 5 kN (acting perpendicular to the axis of beam) at a point 0.75 m from one of the supports. Determine
(i) the maximum fiber stress (σb)max); (ii) the stress in a fiber located at a distance of 1 cm from the top of the beam at mid-span.

(b) Describe the procedure of Truss Analysis by Section method.

(c)A flywheel is making 180 rpm and after 20 second it is running at 120 rpm.
How many revolutions will it make and what time will elapse before it stops, if the retardation is constant.


(4) Answer any one part of the following: 1X10=10

(a) Explain the terms polar moment of inertia and radius of gyration.
Derive the area moment of inertias for a quarter circle of radius R.

(b) Analyse the following truss:



(5) Answer any three question;                           3X10=30

(a) Compare the stress – strain diagrams of a ductile material to that of a brittle Material. Also explain the term poisson's ratio and modulus of rigidity.

(b) Explain and prove the “Torsion Equation” (T/J)=(τ/r)=(Gθ/L). What is
called as Section Modulus?

(c) A cylinder of radius R, length L and total mass M is suspended vertically
from the floor, if the modulus of elasticity of the cylinder be E, find the total
deflection and maximum stress induced due to self weight.

(d) A cylinder of 200 mm diameter is subjected to a twisting moment of
250 kN-m, the length of the cylinders is 1 m, if the modulus of rigidity of the
cylinder material be 150 GPa, find the maximum shear stress induced in the
cylinder. Also find the total angular deformation.