BPSC AE Paper 4 (General Engineering Science) 25 March 2022 Official Paper (Previous Year Paper)

Explanation:

First Law of Thermodynamics: 

The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.

When heat energy is supplied to a gas, two things may occur:

• The internal energy of the gas may change
• The gas may do some external work by expanding

According to the first law of Thermodynamics:

δQ = δW + ΔU

When a process is executed by a system, the change in stored energy of the system is numerically equal to the net heat interaction minus the network interaction during the process:

For the cyclic process: ΔU = 0

$\oint \delta Q = \oint \delta W$

Explanation:

Let E be the total emissive power of the body and α be the absorptivity of the body.

α be the absorptivity of the body.

Emissivity (ϵ) is the ratio of emissive power of a non-black body to the black body.

ϵ = E/Eb

Kirchhoff’s law also holds for monochromatic radiation, for which

\(\frac{{{E_{\lambda 1}}}}{{{\alpha {\lambda 1}}}} = \frac{{{E{\lambda 2}}}}{{{\alpha {\lambda 2}}}} = \frac{{{E{b\lambda }}}}{{{\alpha {b\lambda }}}} = \frac{{{E{b\lambda }}}}{1}\)

∵ Absorptivity of a black body is one.

\(\therefore \frac{{{E_\lambda }}}{{{\alpha \lambda }}} = {E{b\lambda }} \Rightarrow {\alpha \lambda } = \frac{{{E\lambda }}}{{{E_{b\lambda }}}} = {\epsilon_\lambda }\)

Therefore, the monochromatic emissivity of a black body is equal to the monochromatic absorptivity at the same wavelength.

Eλ = αλEbλ

E = α EB

Important Points

According to Kirchhoff’s law, the ratio of total emissive power to absorptivity is constant for all bodies which are in thermal equilibrium with the surroundings. Therefore, it means that the emissivity of a body is equal to its absorptivity.

Explanation:

The air-standard-Otto cycle is the idealized cycle for the spark-ignition internal combustion engines.

The Otto cycle 1-2-3-4 consists of the following four processes:

• Process 1-2: Reversible adiabatic compression of air
• Process 2-3: Heat addition at constant volume
• Process 3-4: Reversible adiabatic expansion of air
• Process 4-1: Heat rejection at constant volume
  

the basic characteristics of the Spark-ignition engine and Compression ignition engine are described in the table below.

Additional Information 

Explanation: 

For the Diesel cycle:

Processes involved in compression engine (diesel; cycle) are:

1-2: Reversible adiabatic compression

2-3: Reversible Constant pressure heat addition

3-4: Reversible adiabatic expansion

4-1: Reversible Constant volume of heat rejection

According to the question:

A. Constant pressure heat addition

B. Constant volume heat rejection

C. Isentropic expansion

D. Isentropic compression

Hence, The correct order of process, DACB

Important Points

Explanation:

Classification of the turbine based on the energy available at the inlet:

i) Reaction Turbine: A turbine for which both pressure energy and kinetic energy is available at the inlet is a reaction turbine.

E.g. Francis Turbine, Kaplan Turbine and Propeller Turbine.

They are useful for low head and high discharge.

ii) Impulse Turbine: A turbine for which only kinetic energy is available at the inlet is an impulse turbine.

E.g. Pelton Turbine and Turgo Impulse Turbine.

Additional Information

Explanation:

The function of centrifugal pumps is mainly considered because energy is imparted to the fluid by the centrifugal action of moving blades from the inner radius to the outer radius. It means the centrifugal pumps transfer energy from rotor to fluid.

In general, all the rotodynamic pumps resemble the reaction type of hydraulic turbines. Therefore, these types of pumps may be known as reversed reaction turbines.

The action of the centrifugal pump is just the reverse of an inward flow reaction turbine. Hence, the flow in centrifugal pumps is in the radial outward direction.

Explanation:

Centrifugal Pump:

Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor.

• The impeller in the centrifugal pumps is immersed in water and imparts a centrifugal force that moves out the water particles readily.
• The Impellers are known to have backward curved vanes that have less than 90 degrees of blade angle. The backward curved blades are the most preferred types as they have better stabilizing power consumption characteristics than the forward and radial types which are less preferred.

Explanation:

Centrifugal Pump:

Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor.

• The impeller in the centrifugal pumps is immersed in water and imparts a centrifugal force that moves out the water particles readily.
• The Impellers are known to have backward curved vanes that have less than 90 degrees of blade angle. The backward curved blades are the most preferred types as they have better stabilizing power consumption characteristics than the forward and radial types which are less preferred.

Superposition Theorem:

• This theorem is used to calculate the voltage and current across any resistance when multiple independent voltage or current sources are present in any electrical circuit.
• During the application of the superposition theorem, when the effect of one current source is considered, all the other current sources are open-circuited.
• And when the effect of one voltage source is considered, all the other voltage sources are short-circuited.
• This theorem is not applicable for the calculation of power across any resistance.

Concept:

The current in an inductive circuit is given by:

$I = {V \over X_L}$

where I = Current

V = Voltage

X_L = Inductive reactance

Explanation:

• XL is inversely proportional to the current.
• Hence, with an increase in the inductive reactance, the current decreases.

Concept:

The Phasor diagram of a purely inductive circuit is:

​

• In a purely inductive circuit, the current lags voltage by 90°
• The power factor in a purely inductive circuit is given by cosϕ, where ϕ is the angle between current and voltage.
• Therefore, cosϕ = cos 90° = 0

Explanation:

The power in a purely inductive circuit is given by:

P = VI cosϕ

where P = Active power

V = Voltage

I = Current

cosϕ = Power factor

∵ cosϕ = 0

∴ P = VI × (0)

P = 0

Therefore the power is zero in a purely inductive circuit.

Additional Information The reactive power in a purely inductive circuit is given by:

Q = VI sinϕ

∵ cosϕ = 0

∴ sinϕ = 1

Q = V× I × (1)

Q = V× I = Maximum

• A pure inductive circuit is an energy-absorbing circuit, hence it only absorbs lagging reactive power.
• It does not dissipate any active power.

The relationship between the impedance and admittance is given by:

$Z= {1\over Y}$

where Z = Impedance

Y = Admittance

The impedance is analogous to admittance in the following ways:

Magnetic effect of current:

• The magnetic effect of electric current was discovered by H.C. Oersted in 1820.
• He observed that the flow of electric current through a conductor produces a magnetic field around it.

The magnetic effect of current was proved by an experiment which was as under:

1. Initially, the magnetic needle was put on the axis of the magnetic meridian. When a current flows through the circuit, the needle got deflected in the direction of the electric current.
2. And when the direction of the electric current was reversed, the needle got deflected in the opposite direction.
3. This proved that the magnetic effect was produced by the electric current and the electric field is a source of the magnetic field and vice-versa.

If magnetic field lines intersect each other, then at the intersection point there will be two directions of the same field which is not possible. 

Hence, magnetic field lines do not cross or intersect each other.

​

Additional InformationMagnetic field and magnetic lines of force: It is the space around a magnetic pole or magnet or current-carrying wire within which its magnetic effect can be experienced is defined as a magnetic field.

• The magnetic field can be represented with the help of a set of lines or curves called magnetic lines of force or magnetic field lines.

Properties of magnetic field line:

1. The magnetic field line is directed from the north pole to the south pole outside and south to the north inside the magnet.
2. Magnetic field lines are closed and continuous.
3. Magnetic field lines are more crowded near poles which shows that the strength of the magnetic field is maximum at its poles.
4. Magnetic field lines never intersect with each other.

Alternative current generator is based on Faraday's Law of electromagnetic induction.

Faraday's Law states that when the magnetic flux linking a circuit changes, an EMF is induced in the circuit proportional to the rate of change of flux linkage.

The induced EMF is an alternating current generator given by:

 $E =- N({d\phi\over dt})$

where E = EMF

N = No. of turns of the coil

${d\phi \over dt}$ = Rate of change of flux

Explanation:

• When an alternating magnetic field is applied to a magnetic material, an EMF is induced in the material as per Faraday's Law of Electromagnetic Induction.
• The produced EMF circulates a current in the magnetic body of the DC machine. This current is known as the eddy current.
• This current produces the losses in the DC machine. These losses are known as the eddy current losses.
• In order to reduce eddy current losses, the resistance in the path of eddy current must be increased.
• Since resistance is inversely proportional to the area. So by using thin lamination sheets in the armature, the effective cross-sectional area decreases.
• Therefore, resistance increases and eddy-current losses decrease.

Explanation

Photochemical smog:

• Photochemical smog is a condition that develops when primary pollutants (such as oxides of nitrogen and volatile organic compounds) interact under the influence of sunlight to produce a mixture of secondary pollutants.
• Thus photochemical smog is mainly composed of oxides of nitrogen, volatile organic compounds (primary pollutants), Carbon monoxide, and peroxyacetyl nitrate (PAN) (secondary pollutants).
• Carbon monoxide accelerates the reaction as measured by nitric oxide oxidation or ozone formation. This finding has relevance to photochemical smog formation.

Note:

It depends on primary pollutants as well as the formation of secondary pollutants.

Primary pollutants include

1. Oxides of nitrogen, particularly nitric oxide (NO) and nitrogen dioxide (NO2),
2. Volatile organic compounds.
3. Carbone monoxide

Secondary pollutants include

1. Peroxyl-acyl nitrates (PAN),
2. Tropospheric ozone,
3. Aldehydes.

Explanation:

Types of pollutants (primary and secondary pollutants)

• Pollutants that are emitted directly from identifiable sources are produced both by natural events (for example, dust storms and volcanic eruptions) and human activities (emissions from vehicles, industries, etc.). These are called primary pollutants.
• There are five primary pollutants that together contribute about 90 percent of the global air pollution.
• These are carbon oxides (CO and CO2), nitrogen oxides, sulfur oxides, volatile organic compounds (mostly hydrocarbons), and suspended particulate matter (SPMs).
• Pollutants that are produced in the atmosphere when certain chemical reactions take place among the primary pollutants are called secondary pollutants. Eg: sulfuric acid, nitric acid, carbonic acid, etc.

Explanation:

Bio-chemical oxygen demand:

(i) Biochemical oxygen demand is used as a measure of the quantity of oxygen required for oxidation of biodegradable organic matter present in water sample by aerobic biological action.

BOD at any time is given by,

BODt = Lo (1 - 10-Kdt)     ---(i)

Where, Lo = Ultimate BOD

For BOD5, t = 5 days

Assume Kd = 0.1 day-1 (Generally taken)

Then from (i), BOD5 = Lo (1 - 10-5 × 0.1) = 0.68 × Lo

BOD5/Lo = 0.68 ≈  2/3

• Hence the BOD of water during 5 days at 20°C is generally taken as the standard and is about 68% of the total demand i.e. ultimate BOD. 10 Days BOD ia about 10% of the total.

Explanation:

Rain Water

• Rainwater is considered the purest form of water.
• Impurities and salts present in water on earth are left behind during vaporization by the sun.
• However, the rainwater we receive on earth is not necessarily pure, as it brings down impurities and particles present in the atmosphere it.

Important Points 

• Rainwater is considered to be the purest form of natural water as it is directly coming from the condensation of water droplets.
• In the presence of the sun, the water evaporates from the seas, oceans, and rivers (from all the natural open resources of water) leaving behind all the impurities and forming the cloud.
• A new scientific study concluded that the world's purest water can be found in freshwaters of Puerto Williams in southern Chile.
• The healthiest type of water is technically hydrogen water because of the potential health benefits of the antioxidants it contains.  ​

Explanation:

The effects of force, acting on the body, we must know these details are as follows:

• the magnitude of the force
• line of action of the force
• nature of the force, i. e., whether the force is push or pull

Additional InformationA body is in equilibrium when the vector sum of external forces and moments is zero.

Types of equilibrium:

Static equilibrium: In static equilibrium the number of forces that are acting on a body causes no change in the state of rest of the body.

$\sum {F_X} = 0,;\sum {F_Y} = 0$

Dynamic equilibrium: According to D Alembert’s principle the resultant of all the external forces that are acted on the body as well as the moment of all the forces are equal to zero, then the body is said to be in dynamic equilibrium.

$\sum {F_X} = 0,;\sum {F_Y} = 0;and ;\sum M = 0$

Explanation:

When two or more forces act on a body, they are called to form a system of forces.

Coplanar forces: The forces, whose lines of action lie on the same plane, are known as coplanar forces.

Colinear forces: The forces, whose lines of action lie on the same line, are known as colinear forces.

Concurrent forces: The forces, which meet at one point, are known as concurrent forces. The concurrent forces may or may not be colinear.

Coplanar concurrent forces: The forces, which meet at one point and their lines of action also lie on the same plane, are known as coplanar concurrent forces.

Coplanar non-concurrent forces: The forces, which do not meet at one point, but their lines of action lie on the same plane, are known as coplanar non-concurrent forces.

Non-coplanar concurrent forces: The forces, which meet at one point, but their lines of action do not lie on the same plane, are known as non-coplanar concurrent forces.

Non-coplanar non-concurrent forces: The forces, which do not meet at one point and their lines of action do not lie on the same plane, are called non-coplanar non-concurrent forces.

Concept:

Equation of motion is given by, v = u + at

where, u = Initial velocity, v = Final velocity, a = Acceleration

Calculation:

Given:

Initial velocity, u = 0.2 m/s. 

Final velocity, v = 0 

Acceleration, a = 0.02 m/s²

v = u + at 

0 = 0.2 - 0.02 x t

0.02 x t = 0.2 

$t=\frac{0.2}{0.02}=10~sec$

Thus, the body will take 10 seconds to stop

Concept:

The moment of force is the product of a force and its distance from an axis, which causes rotation about that axis. unit is N-m

angular momentum can be expressed as the product of the body's moment of inertia, I and its angular velocity, ω. Unit is N·m·s

Explanation:

Strain Energy: 

• Strain Energy of the member is defined as the internal work done in deforming the body by the action of externally applied forces.
• Strain energy is given by:
• $Strain;Energy = ;\frac{1}{2} \times Stress \times Strain \times Volume$

Resilience:

• Resilience is the total strain energy stored in a given volume of material within the elastic limit.
• On removal of load, this energy is released.
• In other words, it is the area under the load-deflection curve within the elastic limit.

Proof resilience:

• The maximum energy which can be stored in a body up to the elastic limit is called proof resilience.

Modulus of resilience:

• Modulus of resilience is defined as proof resilience per unit volume. It is the area under the stress-strain curve up to the elastic limit.

Explanation:

Instruments used in surveying:

Tape: For linear measurement on ground

Chain: It is used for linear measurements

Levels: It is used for levelling

Tripod: It is used for setting up the instrument on ground

Staff: For taking reading for determination of ground levels.

Clinometer: For vertical angle measurement

Abney level: It is used for measuring slopes and vertical angles.

Pantograph: Used for enlarging the plan

Ghat tracer: Used for determining of gradients

Sextant: For measuring angles from a boat

Fathometer: For measuring depth of water bodies like ocean.

Theodolite: For measuring horizontal and vertical angles and taking staff reading.

Substance bar: For horizontal distance measurement

Cross-staff range finder: To establish right angles

Parallax bar: For displacement measurement from photograph

Tacheometer: For horizontal and vertical distance computation

Planimeter: Used for area measurement

Hence, Pitot tube is not a surveying equipment.

Energy meter: 

• The energy meter measures electrical energy in a kilowatt-hour.
• It is also known as kilowatt-hour meter or Induction type watt-hour meter.
• It is a type of ''integrating instruments.''

Components:

Driving System:

• The components of this system are two silicon steel laminated electromagnet
• Upper magnet→ Shunt magnet→ behave as potential coil
• Lower magnet→ series magnet→ behave as current coil

Moving system: 

In this system, a thin aluminum disk placed in the air gap between the two electromagnets and mounted on a vertical shaft that is free to rotate.

Registering system: 

It registers the number of rotations of the disk which is proportional to the energy consumed directly in kilowatt-hour.

Braking system: 

This system has a permanent magnet called a brake magnet. It is located near the disk so that eddy currents are induced and a braking toque to the disk.

Solution:

Disc of the energy meter is made of aluminium.

Explanation:

Straight edge:

• Straight edges may be classified as

1. Tool makers straight edge
2. Wide edge straight edge
3. Angle straight edge

• The figure shows the Tool maker's straight edges have the highest accuracy.
• They are available in lengths from 75 to 175 mm and with one to four working edges.
• With these edges, the straightness and flatness are checked by sight test.
• Straight edges with a single edge are mainly for checking straightness.
• For checking the straightness of an element of a cylindrical or taper surface, the straight edge is applied along the full length of the surface and is held before a bright background.
• The absence of light between the straight edge and work surface indicates the straightness of the elements and vice-versa.
• For checking the flatness, single-edged as well as three and four edged straight edges may be used. WIth single edge straight edge, it is applied in different directions at different places on the surface to be tested.

• Megger is an electrical instrument used to determine the range of resistances between zero to infinity.
• Initially, the pointer is at the infinite position, it gets deflected when an emf is generated from infinity to zero, which depends on Ohm’s law.
• Megger works on the principle of electromagnetic induction.
• A permanent magnet dc generator driven by hand is used as a source of supply to the megger.
• When a primary coil that is carrying current is placed under the vicinity of a magnetic field it experiences a force.
• This kind of force generates a torque that is made to deflect the pointer of the device which gives some reading.

Explanation:

• So it is evident from the graph that the strain is proportional to stress or elongation is proportional to the load giving a straight-line relationship. This law of proportionality is valid upto a point A. Point A is known as the limit of proportionality or the proportionality limit.
• For a short period beyond point A, the material may still be elastic in the sense that the deformations are completely recovered when the load is removed. The limiting point B is termed as Elastic Limit.
• Beyond the elastic limit plastic deformation occurs and strains are not totally recoverable. There will be thus permanent deformation or permanent set when the load is removed. These two points are termed upper and lower yield points respectively. The stress at the yield point is called the yield strength.
• A further increase in the load will cause marked deformation in the whole volume of the metal. The maximum load which the specimen can withstand without failure is called the load at the ultimate strength. The highest point ‘E' of the diagram corresponds to the ultimate strength of a material.
• Beyond point E, the bar begins to form the neck. The load falls from the maximum until a fracture occurs at F.

Explanation

Shear stress at any point in a cross-section is given by the following formula:

${\rm{f}} = \frac{{{\rm{VQ}}}}{{{\rm{Ib}}}}$

Where,

f = shear stress

Q = First moment of area about the neutral axis of the area above the point where we want to calculate the shear stress

Q = A × y

V is Shear force

y is the centroid of the area above the point where we want to calculate the shear stress measured from the neutral axis.

A = Cross-sectional area above the point where we want to calculate the shear stress

I = moment of inertia about the neutral axis

b= width of the section where shear stress is to be calculated.

Shear stress is zero at extreme fibres 

For the symmetric beam section, the intensity of shear stress is maximum at the centroid of the section which is the neutral axis as shown in the figure.

Concept:

Mohr's circle Method

It is very useful in determining the relationships between normal and shear stresses acting on an inclined plane at a point in a stressed body. It is helpful in finding maximum and minimum principal stresses, maximum shear stress, etc.

Major Principal stress is given as:

\({\sigma _{p1}} = \frac{{{\sigma _1} + {\sigma _2}}}{2} + \sqrt {{{\left{ {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right}}^2} + {\tau _{xy}}^2} \)

Minor Principal stress is given as:

\({\sigma _{p2}} = \frac{{{\sigma _1} + {\sigma _2}}}{2} - \sqrt {{{\left{ {\frac{{{\sigma _1} - {\sigma _2}}}{2}} \right}}^2} + {\tau _{xy}}^2}\)

Maximum Shear stress is given as:

${\tau _{max}} = \frac{{\left( {{\sigma _{1}} - {\sigma _{2}}} \right)}}{2}$

The radius of Mohr’s circle is given as:

$R= \frac{{\left( {{\sigma _{1}} - {\sigma _{2}}} \right)}}{2}$

So

The radius of Mohr’s circle is equal to Maximum Shear stress.

Concept:

The following points should be remembered for gradually applied load and suddenly applied load.

• Stress-induced when load is suddenly applied is two times the stress induced when load is gradually applied.
• The maximum deflection or deformation induced in material when load is suddenly applied is two times the deformation or deflection in material when load is gradually applied.
• The strain energy stored in material when load is suddenly applied is four times the strain energy stored in material when load is gradually applied.

Explanation:

Effective length is the distance between two consecutive points of contra-flexure or between points of zero bending moment.

The effective length of column used in calculating the Euler's crippling load are:

• Fixed end: Restrained in both translation and rotation
• Hinged end: Restrained in translation but free in rotation
• Free end: Free in both translation and rotation.

Important Points

Euler's crippling load ( long columns only): ${P_{cr}} = \frac{{{n^2}{\pi ^2}EI}}{{{L_e}^2}}$ where,

n = no. of buckling loop

I = Minimum moment of inertia

Le = effective length of the column

E = elastic modulus

Explanation:

Slenderness ratio is the ratio of the effective length of a column and the least radius of gyration of its cross-section. It is used extensively for finding out the design load as well as in classifying various columns in short/intermediate/long

$\lambda = \frac{{{L_e}}}{{{k_{min}}}}$

$k = \sqrt {\frac{I}{A}}$

Leffective = Effective length of the column

kmin= minimum radius of gyration

I = Moment of Inertia

A = Area of the cross-section

• Cast iron column with a slenderness ratio not greater than 80 and steel columns with a slenderness ratio not greater than 100 are considered as a short column
• Long column are those with a slenderness ratio greater than 100 for ductile materials and greater than 80 for cast iron

Additional Information

Explanation:

Conventional classifications of lime are as follows:

1. Fat lime: 

It slacks rapidly and its volume is increased by 2 to 2.5 times of its original volume hence, it is referred as fat lime. It is also known as pure lime, rich lime, high calcium lime. It has more than 95% purity.

Properties - Slow setting, High plasticity, Soluble in water, Vigorous slaking, Perfectly white colour

Application - White wash & Plastering

Source - Sea shells

2. Hydraulic lime: 

It is also known as water lime as it is capable of setting in water and damp condition. It has 70% to 90% purity.

Properties - Insoluble in water, Low plasticity, Less slaking, Off white colur, High hydraulicity

Application - Brick masonry or Stone masonry

Source - Kankar

3. Poor lime: 

It is also known as Impure or lean lime. It has less than 70% purity.

Properties - Muddy Colour

Application - Used in brick work around foundation

Explanation:

• Magnesium is the most lightweight metal.
• The density of Magnesium is 1740 kg/m³.
• This silvery-white alkaline earth metal makes up 13% of the Earth’s mass.
• Since Magnesium is the lightest construction metal, it is helpful in the making of consumer products, gadgets, power tools as well as the automotive industry.
• The fourth most common element on the Earth is Magnesium. One of the elements essential to all cellular life is Magnesium.
• Magnesium is lighter than aluminum, titanium, and steel. It is totally biocompatible and does not pose any toxicity risks.
• Magnesium and magnesium alloys are non-ferrous metals. They are characterized by moderate strength, low density, good ductility, and corrosion resistance.

Molecular Weight of different metals:

Explanation:

Corrosion:

• Corrosion is the oxidation-induced deterioration of certain materials, both metals, and non-metals.
• When a substance is exposed to air or certain chemicals, it can corrode.
• It can occur on different surfaces of substances like wood, alloys, metal, etc.
• Degradation is a type of corrosion that can occur in materials such as polymers and ceramics.
• Corrosion reduces the durability of these substances.
• Zinc is an element that is highly prone to corrosion. Therefore, it is used as a sacrificial anode or in galvanization.

Explanation:

• Steels and cast irons are represented by the iron-carbon binary system.
• Commercially pure iron contains up to 0.008% C, and cast iron up to 6.67% C, although most cast irons contain less than 4.5% C.
• The Iron-carbon-carbide phase diagram is shown in the figure. Although this diagram can be extended to the right to 100% C (pure graphite); but the range that is significant to engineering applications is up to 6.67%C, because Fe3C is a stable phase.
• Pure iron melts at a temperature of 1539°C, as shown at the left boundary in the figure.
• As the iron cools, it first forms delta ferrite, then austenite, and finally alpha ferrite.

Phase compositions of the iron-carbon alloys at room temperature:

• Hypoeutectoid steels (carbon content from 0 to 0.83%) consist of primary (pro eutectoid) ferrite (according to the curve A3) and pearlite.
• Eutectoid steel (carbon content 0.83%) entirely consists of pearlite.
• Hypereutectoid steels (carbon content from 0.83 to 2.06 %) consist of primary (proeutectoid)cementite (according to the curve ACM) and pearlite.
• Cast irons (carbon content from 2.06% to 4.3%) consist of pro eutectoid cementite C2 ejected from austenite according to the curve ACM , pearlite, and transformed ledeburite (ledeburite in which austenite transformed to pearlite).

Explanation:

• An activity is a physically identifiable part of a project, which consumes both time and resources.
• The particular task performance in CPM is known as activity.
• Activity is represented by an arrow in a network diagram.
• An event represents the accomplishment of some task. In a network diagram, the beginning and end of an activity are represented as events.
• Each event is represented as a node in a network diagram. An event does not consume any time or resources.
• A dummy activity is represented by a dotted arrow and does not consume any time and resources.

Explanation:

Important Factors Affecting the Accuracy and Efficacy of Estimates:

1. Project Size: Larger projects generally involve more complexities, resources, and uncertainties, potentially affecting the accuracy of estimates.
2. Planning Process: A well-defined planning process ensures better understanding of project scope, requirements, and resource allocation, leading to more accurate estimates.
3. Project Complexity: Projects with high complexity (e.g., involving advanced technology, intricate designs, or challenging site conditions) are more challenging to estimate accurately due to unpredictable variables.
4. Degree of Structural Uncertainty: This is a critical factor that significantly impacts the accuracy and efficacy of estimates. Uncertainty in structural design, materials, or conditions can lead to variations in cost and time estimates. High uncertainty requires more contingencies, affecting overall accuracy.

Concept:

• Critical path is the longest path time-wise which can be determined from forward path method only.
• The critical path is the longest path through the network and time along this path gives the project duration. Critical path joins those activities which are critical.
• Critical path can be easily determined with the help of total float calculations. The activities on the critical path are those activities that have total float equal to zero.
• The activities that control the project duration are the ones that have zero total floats and form a continuous chain or path starting at the first node and ending with the last node.

Explanation:

Following are the different  heavy construction equipment used for earthwork and other works are as follows:

1. Excavator
2. Power Shovel
3. Drag Lines
4. Bulldozer
5. Wheel Tractor Scraper
6. Back Hoes
7. Dredgers
8. Ripper
9. Motor Grader

Excavator

• It is the oldest type of machine which removes earth.
• The general purpose of the excavator is excavation work but other than that it is also used for different purposes like heavy lifting, digging of trenches, holes, foundations, river dredging, cutting of trees, etc.

Explanation:

Critical Path Method (CPM):

• The critical path method (CPM) is a technique where you identify tasks that are necessary for project completion and determine scheduling flexibilities. A critical path in project management is the longest sequence of activities that must be finished on time in order for the entire project to be complete. Any delays in critical tasks will delay the rest of the project.
• CPM revolves around discovering the most important tasks in the project timeline, identifying task dependencies, and calculating task durations.
• CPM was developed in the late 1950s as a method to resolve the issue of increased costs due to inefficient scheduling. Since then, CPM has become popular for planning projects and prioritizing tasks.

Program Evolution and Review Technique (PERT):

• Program Evaluation and Review Technique (PERT) is a method used to examine the tasks in a schedule and determine a Critical Path Method variation (CPM). It analyzes the time required to complete each task and its associated dependencies to determine the minimum time to complete a project.
• It estimates the shortest possible time each activity will take, the most likely length of time, and the longest time that might be taken if the activity takes longer than expected.  The US Navy developed the method in 1957 on the Polaris nuclear submarine project.

Additional Information

Difference between PERT and CPM 

Concept:

For laminar flow:

Friction factor (f) $= \frac{{64}}{{{{\rm{R}}_{\rm{e}}}}}$

For turbulent flow:

Case I: Smooth Pipe

Friction factor (f) $= \frac{{0.316}}{{{{\left( {{{\rm{R}}_{\rm{e}}}} \right)}^{1/4}}}}$

Case II: Rough Pipe

$\frac{1}{{\sqrt {\rm{f}} }} = 2{\log _{10}}\left( {\frac{{\rm{r}}}{{\rm{k}}}} \right) + 1.74$

Case III: In between smooth & rough (Transition)

Friction (f) = $\rm{\phi (R_e, \frac{k}{D})}$

∴ For laminar flow friction factor depends only upon the Reynolds number of the flow and is independent of the contact surface.

As can observe, the friction factor is inversely proportional to Reynold’s number. Also, the velocity distribution of laminar flow through the pipe is parabolic.

∴ Statement 3 and 4 are correct.

Mistake Points

• For the Laminar flow, the friction factor depends only on the Reynolds number and is independent of the internal condition of the pipe.
• For turbulent flow, when the Reynolds number Re > 4000, the friction factor f depends not only on Re but also on the internal roughness of the pipe.

Concept:

In the case of pipe flow,

• If Re ≤ 2000 then flow is laminar
• 2000 ≤ Re ≤ 4000 then flow is transitional
• Re ≥ 4000 then flow is turbulent

Laminar Flow: Laminar flow is the flow in which fluid particles flow in layers. Each layer moves smoothly past the adjacent layer with little or no intermixing. There is no intermingling of fluid particles across the cross-section.

Turbulent Flow: Turbulent flow is the flow in which fluid particles flow in a random fashion where intermixing/intermingling is present.

Reynolds number is a dimensionless formula that is used to differentiate laminar flow from the turbulent flow.

Reynolds number is given by

$Re = \frac{{\rho; \times ;V ;\times ;D}}{\mu }$

Where,

ρ = Density of fluid, V = velocity of fluid, D = Diameter of pipe, μ = Dynamic viscosity of the fluid

From the formula,

Re ∝  V

Re ∝ 1/μ

So, at low velocity and higher viscosity will result in a lower value of Re number. The low value of the Reynolds number shows laminar flow.

Explanation:

Bernoulli's equation is obtained by integrating Euler's equation of motion which is given by-

Euler's Equation:

$\frac{{dp}}{ρ } + gdz + vdv = 0;;;;;(1)$

In Euler's equation of motion, the forces due to gravity and pressure are taken into consideration and which is derived considering the motion of a fluid element along a stream-line.

Integrating the above eq(1):

$\smallint \frac{{dp}}{ρ } + \smallint gdz + \smallint vdv = 0$

$\frac{p}{ρ } + gz + \frac{{{v^2}}}{2} = C$

$\frac{p}{{ρ g}} + \frac{{{v^2}}}{{2g}} + z = C;;;;(2)$

This equation is called Bernoulli's Equation.

where $\frac{p}{ρg}$ = pressure head or pressure energy per unit weight, $\frac{v^2}{2g}$ = kinetic head or kinetic energy per unit weight z = potential head or potential energy by unit weight.

Following assumptions are made in the derivation of Bernoulli's equation:

1. Flow is ideal i.e inviscous.
2. Flow is steady i.e. time variation is zero.
3. Flow is incompressible i.e. ρ is constant.
4. Flow is irrotaional i.e. ωx = ωy = ωz = 0.
5. Gravity and Pressure forces are taken only hence all other external forces should be zero.
6. The energy of the system is constant hence there should be no loss of energy.

Explanation:

Mohr's circle 

• Mohr's circle is very useful in determining the relationships between normal and shear stresses acting on any inclined plane at a point in a stressed body.
• It is helpful in finding maximum and minimum principal stresses, maximum shear stress etc.

Maximum and minimum values of normal stresses occur on planes of zero shearing stress. The maximum and minimum normal stresses are called the principal stresses, and the planes on which they act are called the principal plane.

Pure shear planes are planes on which normal stress is zero

${\sigma _{max,;min}} = \frac{{{\sigma _{xx}} + {\sigma _{yy}}}}{2} \pm \sqrt {{{\left( {\frac{{{\sigma _{xx}} - {\sigma _{yy}}}}{2}} \right)}^2} + \tau _{xy}^2}$

${\tau _{max}} = \frac{{{\sigma _{max}} - {\sigma _{min}}}}{2} = \sqrt {{{\left( {\frac{{{\sigma _{xx}} - {\sigma _{yy}}}}{2}} \right)}^2} + \tau _{xy}^2}$

Mohr's circle is used to determine the stresses on an oblique section of a body subjected to:

• direct tensile stress in one plane accompanied by a shear stress
• direct tensile stress in two mutually perpendicular directions
• direct tensile stress in two mutually perpendicular directions accompanied by a simple shear stress

Explanation:

Kirchhoff’s law:

• Let E be the total emissive power of the body and α be the absorptivity of the body.
• Emissivity (ϵ) is the ratio of the emissive power of a non-black body to the black body.
• ϵ = $\frac{E}{E_b}$
• Kirchhoff’s law also holds for monochromatic radiation, for which
• \(\frac{{{E_{\lambda 1}}}}{{{\alpha {\lambda 1}}}} = \frac{{{E{\lambda 2}}}}{{{\alpha {\lambda 2}}}} = \frac{{{E{b\lambda }}}}{{{\alpha {b\lambda }}}} = \frac{{{E{b\lambda }}}}{1}\)
• ∵ Absorptivity of a black body is one.
• \(\therefore \frac{{{E_\lambda }}}{{{\alpha \lambda }}} = {E{b\lambda }} \Rightarrow {\alpha \lambda } = \frac{{{E\lambda }}}{{{E_{b\lambda }}}} = {\epsilon_\lambda }\)
• Therefore, the monochromatic emissivity of a black body is equal to the monochromatic absorptivity at the same wavelength.
• Eλ = αλEbλ
• According to Kirchhoff’s law, the ratio of total emissive power to absorptivity is constant for all bodies which are in thermal equilibrium with the surroundings. Therefore, it means that the emissivity of a body is equal to its absorptivity.
• The emissive power of any body is less than the emissive power of a black body. Hence the emissive power of the grey body is less than the emissive power of the black body.

Additional Information

Stefan-Boltzmann Law 

• The thermal energy radiated by a black body per second per unit area is proportional to the fourth power of the absolute temperature and is given by:
• E ∝ T4
• E = σT4
• σ = The Stefan – Boltzmann constant = 5.67 × 10-8 Wm-2K-4

Wien’s displacement law

• For a black body emissive spectrum, the wavelength λmax giving the maximum emissive power at a temperature is inversely proportional to the absolute temperature.

• λmax = $\frac{c}{T}$

• λmaxT= c

• Wavelength = $\frac{Speed ~of ~Light}{Frequency}$ ⇒ λ = $\frac{c}{V}$

Explanation:

Kirchhoff’s law

The emissive power of a body E is defined as the energy emitted by the body per unit area and per unit time. Assume that a perfectly black enclosure is available, i.e., one that absorbs all the incident radiation falling upon it. Now suppose that a body is placed inside the enclosure and allowed to come into temperature equilibrium with it. At equilibrium the energy absorbed by the body must be equal to the energy emitted; otherwise, there would be an energy flow into or out of the body that would raise or lower its temperature. At equilibrium we may write:

EA = qiAα

For black body (absorptivity α = 1):

EbA = qiA(1)

$\frac{E}{{{E_b}}} = \alpha$

This law states that the ratio of the emissive power of a body to the emissive power of a blackbody at the same temperature is equal to the absorptivity of the body. This ratio is defined as the emissivity ϵ of the body.

$\frac{E}{{{E_b}}} = \epsilon$

∴ α = ϵ

Thus, Kirchhoff’s law states that the emissivity of a body is equal to its absorptivity when the body remains in thermal equilibrium with its surrounding.