BPSC AE Paper 5 (Mechanical) 14 Oct 2022 Official Paper (Previous Year Paper)

Concept: 

According to Fourier's law of heat conduction, the rate of heat transfer through a material is proportional to the temperature gradient across it, which can be expressed as:

$q = ; - kA\frac{{dT}}{{dx}}$

where q is the rate of heat transfer per unit area, k is the thermal conductivity, A is the cross-sectional area perpendicular to the direction of heat flow, and dT/dx is the temperature gradient.

Where k is the thermal conductivity, A is the area perpendicular to the direction of heat flow, dT is the temperature difference and dx is the thickness of the wall.

Heat flux flowing through the wall remains the same.

∴ Heat flux through  wall 1 = Heat flux through  wall 2

Calculation:

Given:

$\frac{K_1}{K_2}=\frac{3}{2}$

 Let the thickness of each layer be L.

Let  $\Delta{T_1}$ be the temperature drop across the layer with thermal conductivity 3 and $\Delta{T_2}$ be the temperature drop across the layer with thermal conductivity 2.

of heat transfer through the composite wall is the same across each layer, so we have:

q =  $K_1\times A \frac{\Delta{T_1}}{L}=K_2\times A \frac{\Delta{T_2}}{L}$

where $K_1$ and $K_2$ are the thermal conductivities of the two layers.

Dividing the two equations, we get:

$\therefore$(\frac{\Delta T_1}{\Delta T_2}=\frac{K_2}{K_1}=\frac{2}{3}\)

Therefore, the ratio of temperature drop across the two layers is 2 ∶ 3.

Concept:

Thermal diffusivity (α ) of material:

Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.

Thermal diffusivity (α ) of material is given as

 $α = \frac{k}{{ρ c}}$

where k is thermal conductivity in W/m-k, ρ is density in kg/m3 and c specific heat capacity in J/kg-K

It is the property of the material. Larger the value of α, faster heat will diffuse through the material. A high value of α could result either from a high value of thermal conductivity or low value of thermal heat capacity ρc. Thermal diffusivity α has units of square meters per second.

unit of $\alpha =\frac{\frac{W}{m-K}}{\frac{kg}{m^3}\frac{J}{kg-K}}=\frac{m^2}{s}$as Watt is J/s.

Hence from the option, the correct answer is

unit of $\alpha =m^2/hr$

Explanation:

The effectiveness of the fin is the ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin.

${\epsilon_{fin}} = \frac{{{Q_{with;fin}}}}{{{Q_{without;fin}}}} = \frac{{\sqrt {Phk{A_c}} ;\left( {{t_o} - {t_a}} \right)}}{{h{A_c}\left( {{t_o} - {t_a}} \right)}} = \sqrt {\frac{{Pk}}{{h{A_c}}}}$

${\epsilon_{fin}} \propto \sqrt{\frac{P}{A}}$

Where P is Perimeter, A is Cross-sectional area,h is heat transfer Coefficient, and K is thermal Conductivity.

Fins are made as thin as possible to accommodate more number of fins; the smaller the thickness, the more effective will be the fin.

Additional Information 

The efficiency of a fin is defined as the ratio of the actual heat transferred by the fin to the maximum heat transferable by the fin, if the entire fin area were at base temperature, for an infinitely long fin:

$\begin{array}{l} \eta = \frac{1}{{mL}}\ \eta \propto \frac{1}{{\sqrt h }} \end{array}$

Concept :

Coefficient Of Performance (COP) Or Energy Performance Ratio:

It is defined as, “The ratio of the desired effect to the work input.”

${{COP}} = \frac{{{{Desired; Effect}}}}{{{{Work;input}}}}$

Relationship between COPHP and COPRef (For same temperature Limits)

COPHeat Pump = 1 + COPRef

Calculation:

Given:

Work Input = 1 kW, COPRef = 4.

COPHeat Pump = 1 + COPRef

$CO{P_{Heat\ Pump}} = \frac{{Desired;Effect;\left( {Heating;Effect} \right)}}{{Work;Input}}$

Desired effect (Heating effect) = COPHeat Pump × Work Input = 5 × 1 ⇒ 5 kW.

Concept:

In refrigeration cycle, the vapors leaving the evaporator are in saturated vapor state. These vapors are compressed in the compressor and their temperature and pressure increases. These vapors are in the superheated state at the entrance of condenser.

Vapour Compression Refrigeration System:

The four processes in simple VCRS include:

1. Isentropic compression (1-2) in Compressor.
2. Constant Pressure heat removal (2-3) in Condensor.
3. Isenthalpic expansion (3-4) in a Throttling device.
4. Constant pressure heat removal (4-1) in Evaporator.

Explanation:

Basic Vapour Absorption Refrigeration System

• The basic absorption cycle employs two fluids, the absorbate or refrigerant, and the absorbent
• The most common fluids are Water/Ammonia as the refrigerant and lithium bromide/ water as the absorbent
• These fluids are separated and recombined in the absorption cycle
• In the absorption cycle, the low-pressure refrigerant vapour is absorbed into the absorbent releasing a large amount of heat (Absorber pressure is equal to evaporator pressure)
• The liquid refrigerant/absorbent solution is pumped to a high-operating pressure generator using significantly less electricity than that for compressing the refrigerant for an electric chiller
• Heat is added at the high-pressure generator from a gas burner, steam, hot water or hot gases
• The added heat causes the refrigerant to desorb from the absorbent and vaporize
• The vapours flow to a condenser, where heat is rejected and condense to a high-pressure liquid
• The liquid is then throttled through an expansion valve to the lower pressure in the evaporator where it evaporates by absorbing heat and provides useful cooling
• The remaining liquid absorbent, in the generator, passes through a valve, where its pressure is reduced, and then is recombined with the low-pressure refrigerant vapours returning from the evaporator so the cycle can be repeated

Concept:

Azeotrope is a mixture of refrigerant without phase separation.

Azeotropes are essentially a class of non-ideal mixtures having bulb point temperature equal to dew point temperature. Hence, they boil and condense at constant temperature like pure substance.

Azeotropes are generally formed when the difference in the boiling points of the two components is not very large and when the deviations from ideal behavior are large enough.

Additional Information

• Primary refrigerants are those fluids, which are used directly as working fluids, for example in VCR and absorption-based systems. When used in compression or absorption systems, these fluids provide refrigeration by undergoing a phase change process in the evaporator.
• As the name implies, secondary refrigerants are those liquids, which are used for transporting thermal energy from one location to another. Secondary refrigerants are also known referred to as brines or antifreeze.
• Two or more refrigerants can be suitably blended to achieve the required/desired properties. These are Zeotropes and Azeotropes. Azeotropic mixtures are designated by 500 series, whereas zeotropic refrigerants (e.g. non-azeotropic mixtures) are designated by 400 series.
• Azeotropic refrigerants: A stable mixture of two or several refrigerants whose vapor and liquid phases retain identical compositions over a wide range of temperatures. Examples: R-500: 73.8% R12 and 26.2% R152
• Zeotropic refrigerants: A zeotropic mixture is one whose composition in the liquid phase differs from that in the vapor phase. Zeotropic refrigerants, therefore, do not boil at constant temperatures, unlike azeotropic refrigerants. Examples: R404a : R125/143a/134a (44%, 52%, 4%)

Concept:

Greenhouse Effect: The solar energy trapped by the earth atmosphere and radiate it slowly so to cover our earth with a warm blanket. This is the natural process of the greenhouse effect on earth to maintain its temperature and makes the earth perfect for life.

Greenhouse gases are carbon dioxide, other greenhouse gases are methane, water vapour, nitrous oxide, CFCs and ozone. 

Values of radiation absorbed by the greenhouse gases are as follow:

Explanation:

Global Warming

• An increase in the average temperature of the earth surface due to the greenhouse effect is called global warming
• It also refers to the increase in the average temperature of the air and sea at the earth's surface.
• The greenhouse gases combined increased the temperature of planet earth so the correct option is greenhouse gases.

Mistake Points

Global warming and the Greenhouse effect both are different things.

Explanation:

The most commonly used refrigerant - absorbent pairs in commercial systems are:

1. Water - Lithium Bromide (H2O - LiBr) system for above 0°C applications such as air conditioning. Here water is the refrigerant and lithium bromide is the absorbent.
2. Ammonia - Water (NH3 - H2O) system for refrigeration applications with ammonia as refrigerant and water as absorbent.

Explanation:

The most commonly used refrigerant - absorbent pairs in commercial systems are:

1. Water - Lithium Bromide (H2O - LiBr) system for above 0°C applications such as air conditioning. Here water is the refrigerant and lithium bromide is the absorbent.
2. Ammonia - Water (NH3 - H2O) system for refrigeration applications with ammonia as refrigerant and water as absorbent.

Explanation:

Intensive Property: These are the properties of the system which are independent of mass under consideration.

e.g. Pressure, Temperature, density, Specific enthalpy etc.

Extensive Properties: The properties which depend on the mass of the system under consideration.

e.g Internal Energy, Enthalpy, Volume, Entropy etc.

Note: All specific properties are intensive properties. For e.g. specific volume, specific entropy etc.

thus, Density is not an extensive property.

Concept:

Zeroth law of thermodynamics:

• Zeroth law of thermodynamics states that "if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other" as shown below.

• This figure shows that when body A is in thermal equilibrium with body B, and also separately with body C, then B and C will be in thermal equilibrium with each other.

• This is the basis of temperature measurement and is used to explain the concept of temperature.

First law of thermodynamics:

• The first law of thermodynamics enables to calculate the change in internal energy of the system
• As, δQ = ΔU + δW
• or, ΔU = δQ – δW
• The first law of thermodynamics only gives information about the energy balance when a system undergoes a change of state.
• But it does not help to predict whether the change of state is feasible or not.
• The second law of thermodynamics provides the criterion for the probability of various processes.
• The first law of thermodynamics enables one to determine the property, the internal energy.

Second law of thermodynamics:

• Second law of thermodynamics leads to expressions that involve inequalities. The important inequality that has a major consequence is Clausius inequality.
• It is expressed as,  $\oint \frac{{\delta Q}}{T} \le 0$
• For a reversible process,  $\oint \frac{{\delta Q}}{T} = 0$
• Since the cyclic integral of a property is zero, therefore the quantity $\oint \frac{{\delta Q}}{T}$ must represent a property, this property is named as entropy as designated as S.
• $S = {\left( {\frac{{\delta Q}}{T}} \right)_{rev}}$
• Therefore entropy is related to second law of thermodynamics.

Important Points 

1. Zeroth law – concept of temperature
2. First law – concept of internal energy
3. Second law – concept of entropy

Explanation:

• The fluid whose properties in all three phases are made use of in thermodynamics is water.
• Water is commonly used in various applications of thermodynamics because it exists in all three phases (solid, liquid, and gas) under normal temperature and pressure conditions, and its thermodynamic properties such as specific heat, enthalpy, entropy, and viscosity vary significantly across its phases. Additionally, water has a high heat capacity, which makes it an ideal working fluid in many heat transfer applications, including power generation, refrigeration, and air conditioning.
• Furthermore, the phase transitions of water, such as melting, freezing, evaporation, and condensation, are of great importance in thermodynamics. These transitions involve the exchange of heat and work, and understanding their underlying principles is essential in various engineering applications.
• Water also exhibits several unique properties, such as anomalous expansion upon freezing, high surface tension, and high dielectric constant, which have significant implications in various thermodynamic systems. For example, the anomalous expansion of water upon freezing is critical in the formation of ice caps and the maintenance of aquatic ecosystems.
• Overall, the wide availability, unique properties, and varied thermodynamic behavior of water make it an essential component in various thermodynamic applications, ranging from power generation to climate modeling.

Explanation:

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 net work interaction during the process:

For the cyclic process: ΔU = 0

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

$\oint \left( {dQ - dW} \right) = 0$

The first law of thermodynamics states that for a cyclic process, the cyclic integral of heat is equal to the cyclic integral of work.

Mistake Points Please read the question properly, the question has asked about the cyclic integral in words, not in terms of the sign. Therefore, it should be zero as (the difference of heat and work) is internal energy which is a property and all properties are zero for their cyclic integral.

Explanation:

Enthalpy of a substance is defined as:

h = u + pV

δh = δu + pdV + VdP        

According to the First Law of Thermodynamics for a process 

δQ = du + δW

δQ = du + p.dV     [process involving just pdV work]

$\therefore$ δh = δQ + VdP

At constant pressure,

The change in pressure will be zero.

$\therefore$ (δQ)p = dh

i.e. heat transferred at constant pressure equal to enthalpy of the system.

Additional Information

For an ideal gas pV = RT

h = u + pV

∴ h = u + RT

The internal energy (u) of an ideal gas is a function of temperature i.e. u = f(T) since there are no intermolecular forces of attraction and repulsion.

∴ the enthalpy of an ideal gas also depends on the temperature i.e. h = f(T).

Explanation:

• Since the volume of the pressure cooker is constant hence it is an Isochoric process.
• Food is cooked faster in a pressure cooker because due to high pressure the boiling point of water is raised.
• A pressure cooker works on the principle that with rising pressure the boiling point of water increases.
• Due to the high-pressure boiling point of water rising from 100o C to around 120o C.
• So, the steam also becomes hotter and is also trapped inside the cooker resulting in faster cooking of food.
• When cooked in open vessels the hot air escapes.
• But in the pressure cooker moisture surrounding the food itself reaches higher temperatures than it would without the pressure which speeds the cooking.
• So, the cooking speed is increased nearly four times.

Explanation:

Clausius statement:

“It is impossible to construct a device that operates on a cycle to produce no effect other than the transfer of heat from a lower-temperature body to a higher temperature body”

The conclusion of this statement is commonly known to us that heat does not, on its own, flow from a cold medium to a hot medium. On the surface, it looks that as per Clausius statement it is impossible to construct a device that transfers heat from a colder medium to warmer medium.

The Clausius statement implies that a refrigerator will not operate unless its compressor is driven by a power source, such as an electric motor.

Additional Information

Kelvin-Planck statement:

It is impossible to construct an engine, which while operating in a cycle produces no other effect except to extract heat from a single reservoir and do the equivalent amount of work.

Therefore if the engine has to work in a cycle then some amount of heat is rejected in the cycle, the Closed-cycle gas turbine, internal combustion engine and steam power plant rejects some heat to produce the work continuously in a cycle, therefore these devices imply with the Kelvin-Planck statement.

Explanation:

There are 4 laws to thermodynamics:

Zeroth law of thermodynamics 

• If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

First law of thermodynamics 

• Energy can neither be created nor destroyed. It can only change forms. In any process, the total energy of the universe remains the same.
• For a thermodynamic cycle, the net heat supplied to the system equals the net work done by the system.
• δQ = ΔU + δW

Second law of thermodynamics

• The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
• ΔS = ΔQ/T
• ΔSTotal = ΔSSystem + ΔSsurrounding
• The second law of thermodynamics introduces the concept of entropy.

Third law of thermodynamics

• As the temperature approaches absolute zero, the entropy of a system approaches a constant minimum.
• ΔST = 0K = 0

Joule – Thomson coefficient:- When the gas in steady flow passes through a construction, e.g. in an orifice or valve, it normally experiences a change in temperature. From the first law of thermodynamics, such a process is isenthalpic and one can usually define a Joule – Thomson coefficient as:

$\mu = {\left( {\frac{{\partial T}}{{\partial P}}} \right)_H}$

The numerical value of the slope of an isenthalpic on a T-p diagram at any point is called Joule-Thomson coefficient and is denoted by μ_j

As a measure of the change in temperature which results from a drop in pressure across the construction.

If μ is +ve, then the temperature will fall during throttling.

So from the figure it is clear that temperature may increase or decrease it will depend on the value of μ.

Explanation:

• Pulverized coal is coal that has been crushed into a fine powder, which is then blown into the boiler furnace for combustion. The use of pulverized coal in the boiler furnace provides better combustion because the coal particles are able to mix more evenly with the oxygen in the air, leading to more complete combustion.
• The combustion of pulverized coal produces a lot of heat, which can be harnessed to generate steam, and subsequently electricity. Pulverized coal combustion is also more efficient than other coal combustion techniques, resulting in a higher calorific value.
• However, the use of pulverized coal in the boiler furnace may also result in higher emissions of pollutants such as sulfur dioxide and nitrogen oxides, which can contribute to air pollution and acid rain. Therefore, technologies such as flue gas desulfurization and selective catalytic reduction are often used to reduce these emissions.

Pulverized Coal-Fired Boilers:

• Pulverized coal firing ensures complete combustion of coal, thus ensuring higher efficiency of steam generators.

• It is predominantly adopted in large coal-fired utility boilers. The finer the grinding of coal, the more efficient its combustion. The total time required from the entry of a coal particle to a furnace to the combustion of the particle is very short. This time, however, is dependent on various factors.

• The heart of a pulverized coal-fired boiler is the pulverizer, also known as the mill. Depending on speed pulverizers are classified as low-speed, medium-speed, and high-speed mills.

• Pulverized coal burners may be located on the front or opposed walls or in the corners of the furnace.

There are two types of fuel-firing systems:

• bin system and direct-firing system.
• Coal feeders are either the volumetric or gravimetric type.

Explanation:

Boiler Blowdown

• Concentrated solid precipitates at the drum bottom are removed through blowdown, which may be either intermittent or continuous the amount of blowdown being governed by the allowable solids concentration and the purity of feedwater.
• It is usually expressed as a percentage.
• For instance, 5% blowdown means that 5 percent of the total amount of feedwater supplied is removed as a liquid by blowdown of the drum.
• The continuous blowdown has the advantage of closer control of concentration and the recovery of part of the energy of the blowdown.
• Since water purity is controlled by blowdown in drum-type boilers, condensate polishing is not required in such boilers.
• The general arrangement of boiler blowdown is shown in the figure.

​

Explanation:

• A Steam Trap is an automatic drain valve which distinguishes between steam and condensate.
• A steam trap holds back steam & discharges condensate under varying pressures or loads.
• The steam traps should have a good capacity to vent out air and other non - condensable gases quickly while holding back the live steam.

Explanation:

Equivalent evaporation: It is defined as the amount of dry and saturated steam generated from feed water at 100°C at normal atmospheric pressure.

\({\rm{Equivalent;evaporation}} = \frac{{{\rm{Mass;of;steam;generated;per;hour}} \times {\rm{Heat;supplied;to;steam;in;boiler}}}}{{{\rm{Heat;supplied;for;steam;generation;at;}}100^\circ {\rm{C;from;water;at;}}100^\circ {\rm{C;}}\left( {{\rm{i}}.{\rm{e}}.{\rm{;Latent;heat}}} \right)}}\)

\({\rm{Equivalent;evaporation;of;the;boiler}} = \frac{{{{\dot m}s}\left( {{\rm{h}} - {{\rm{h}}{\rm{f}}}} \right)}}{{{\rm{enthalpy;of;evaporation;of;water;at;}}100^\circ {\rm{C}}}}\)

ṁ­s = Mass of steam output

h = enthalpy of steam at the exit of the boiler

hf = enthalpy of feed-water at the inlet of the boiler

The enthalpy of evaporation of water at 100°C = 2257 kJ/kg

 $The ~equivalent ~evaporation =\frac{{Total;heat;required;to;evaporate;feed;water}}{{2257}}$

Explanation:

Convergent-divergent nozzle:

• Convergent-Divergent nozzles are used to increase the flow of gas to supersonic speeds (as in the case of rockets).

• Their cross-sectional area first decreases and then increases. The area where the diameter is minimum is called the throat.

• As the gas enters the converging section, its velocity increases, considering the mass flow rate to be constant.

• As the gas passes through the throat, it attains sonic velocity (Mach number = 1).

• As the gas passes through the divergent nozzle, the velocity increases to supersonic (Mach number >1).

• The flow rate is maximum for a given nozzle if the flow is sonic at the throat. This condition is achieved by managing the back-pressure.

• For the compressible fluid flow, the Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.

• Choked flow is a limiting condition where the mass flow will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed.

• For chocked flow in the convergent-divergent nozzle, the Mach number at the throat is equal to 1 and the pressure at the throat is equal to the critical pressure.

• Critical pressure ratio for a choked nozzle:

• $\frac{{{p^*}}}{{{p_o}}} = {\left( {\frac{2}{{\gamma + 1}}} \right)^{\frac{\gamma }{{\gamma - 1}}}}$

 where p* is the critical pressure and p0 is the inlet pressure.

Explanation:

The critical pressure ratio for isentropic nozzle flow with a ratio of specific heats can be calculated using the following equation:

$Critical;pressure;ratio ={\left( {\frac{P_2}{P_1}} \right)}_{critical}= {\left( {\frac{2}{{n + 1}}} \right)^{\frac{n}{{n - 1}}}}$

where P₁ is the inlet pressure and  P​2 is the outlet pressure, and n is the ratio of specific heats.

Substituting n = 1.5, we get:

${\left( {\frac{P_2}{P_1}} \right)}_{critical}= {\left( {\frac{2}{{1.5 + 1}}} \right)^{\frac{1.5}{{1.5 - 1}}}}$

${\left( {\frac{P_2}{P_1}} \right)}_{critical}= {\left( 0.8 \right)^{3}}$

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Concept:

Pressure distribution in a converging-diverging nozzle

• Let us assume that flow is taking place in a converging-diverging nozzle.
• Initially, the outlet valve is closed and there is no flow.
• Thus, the pressure at inlet and outlet is the same, and we get a straight line pressure throughout the nozzle.
• As the valve is opened gradually the pressure drops in the converging section and increases in the diverging section.
• Once the flow becomes supersonic at the throat (minimum area section), pressure variation becomes the same in the converging section.
• Further decrease in pressure at the outlet, in the diverging part of the flow, tries to maintain the supersonic level.
• But due to insufficient energy, it becomes subsonic and generates a shock wave during the transition.
• With more drop in pressure, the location of the shock wave moves towards the exit.
• The nozzle is designed to have shock-free flow.

We know that,

$\frac{{dA}}{A} = \frac{{dP}}{{\rho {v^2}}}\left( {1 - {M^2}} \right)$

The value of M = 1 gives dA = 0 which means that area is constant, i.e. at the point where the change in area is zero (at the throat), M becomes 1 (sonic) and the flow-through nozzle reaches its maximum value and the nozzle gets chocked.

When the flow becomes maximum, the pressure at the throat is called critical pressure P*.

Explanation:

• Shock waves involving an abrupt rise of pressure and increase of entropy generally occur in the divergent section of the nozzle.
• When the flow in the nozzle is supersonic, a shock wave may form in the divergent section due to the sudden increase in area, which leads to a decrease in velocity and an increase in pressure. This shock wave is called an expansion wave or a Prandtl-Meyer expansion wave.
• In contrast, shock waves can also occur in the convergent section of the nozzle, where they are caused by the sudden decrease in area, which leads to an increase in velocity and a decrease in pressure. These shock waves are called compression waves or oblique shocks.

Shock wave:

• A shock wave can be considered as a discontinuity in the properties of the flow field.
• The fluid crossing a shock wave, normal to the flow path, will experience a sudden increase in pressure, temperature, and density, accompanied by a sudden decrease in speed, from a supersonic to a subsonic range.
• In case of convergent divergent nozzle shock weave form in the divergent section of nozzle.
• If the shock wave is perpendicular to the flow direction it is called normal shock wave.

However, if the divergent section is too short, the flow may not be able to expand to a subsonic velocity, resulting in a shock wave in the divergent section. The shock wave causes an abrupt rise in pressure and temperature, and an increase in entropy. This can cause damage to the nozzle and reduce its efficiency. Therefore, it is important to design the nozzle geometry carefully to prevent the occurrence of shock waves in the divergent section.

Concept:

velocity compounding

• In the velocity compounding of turbines, there are more friction losses due to very high velocity in nozzles and less efficiency because ratio of blade velocity to steam velocity is not optimum. >In this type of turbine, compounding is used to reduce the velocity only. It is also called a Curtis turbine.
• For an ideal centrifugal compressor, the pressure rise depends only on the peripheral velocity or tip speed of the blade and not on diameter.
• As the fluid enters the axial flow compressor, the rotor reduces the relative kinetic head of the fluid and adds it to the absolute kinetic head of the fluid i.e. the impact of the rotor on the fluid particles >increases their absolute velocity and thereby reduces the relative velocity between the fluid and the rotor.

Pressure compounding: 

In this type of turbine, compounding is used for reducing the pressure of fluid in more than 1 stage.

Its efficiency is higher than the velocity compounding. It is also called a Rateau turbine.

Explanation:

Reaction turbine

In the reaction turbine, a number of fixed and moving blades are assembled alternately inside the casing.

The fixed blade acts as nozzles for each stage, and are attached to the turbine casing, whereas the moving blades are fixed with the rotor.

Parson reaction turbine

• In Parson's reaction turbine, the steam is first expanded by a ring of fixed blades and then directed to a ring of moving blades, whereas, the direction of steam is altered for the first stage.
• The steam leaving the first stage enters the second ring of fixed moving blades, where the further expansion of the steam takes place.
• This continuous until its pressure drop to the exhaust pressure.
• The drop in pressure causes an increase in the velocity of steam in moving blades.
• As a result of this, the relative velocity of steam at the outlet (Vr2) is greater than the relative velocity at the inlet (Vr1).
• In Parson reaction turbine, fixed and moving blades are symmetrical i.e. the exit angle of the moving blade is equal to the exit angle of the fixed blade (β2 = α1) and the inlet angle of the moving blade is equal to inlet angle of the fixed blade (β1 = α2).
• Since blades are symmetrical, velocity diagram is also symmetrical. In such a case, the degree of reaction is 50%
• In parson's reaction turbine the power is obtained by an impulsive force of the incoming steam and small reactive force of the outing steam.
• The blades receive the incoming steam, below is the velocity diagram of blade

where above symbols depict:

u = Tangential velocity of blades

va1,va2 = the absolute velocity of steam at inlet and outlet of a moving blade.

vw1, vw2 = the velocity of whirl at inlet and outlet of a moving blade.

vf1, vf2 = the velocity of flow at the inlet and outlet of a moving blade.

vr1, vr2 = the relative velocity of steam at inlet and outlet of a moving blade.

α1, α2 = outlet, and inlet angle of a fixed blade.

β1, β2 = inlet, and outlet angle of a moving blade.

Maximum efficiency of Parson's reaction turbine is given by:

 $(\eta_b)_{max}=\frac{{2{{\cos }^2}\alpha_1 }}{{1 + {{\cos }^2}\alpha_1 }}$

Concept:

Degree of reaction:

• Degree of reaction or reaction ratio (R) is defined as the ratio of the static pressure drop in the rotor (moving blade) to the static pressure drop in the stage (both fixed blade and moving blade).
• In other words it is defined as the ratio of static enthalpy drop in the rotor(moving blade) to the static enthalpy drop in the stage.

$\rm Degree;of;reaction = \frac{{Enthalpy;drop;in;Rotor}}{{Enthalpy;drop;in;Stage}}$

Calculation:

Given:

Let Enthalpy drop in fixed blade = h

enthalpy drop in moving blade or rotor = $\frac{2}{3}$h

Enthalpy drop in stage = Let enthalpy drop in moving blade + Enthalpy drop in fixed blade = h + $\frac{2}{3}$h= $\frac{5}{3}$h

$\rm Degree;of;reaction = \frac{{Enthalpy;drop;in;Rotor}}{{Enthalpy;drop;in;Stage}}$

∴ $\rm Degree;of;reaction = \frac{\frac{2}{3}h}{\frac{5}{3}h}= 0.4$

The correct answer is greater than 1.

Key Points

• Fast breeder reactor (FBR) which uses fast (i.e. unmoderated) neutrons to breed fissile plutonium and possibly higher transuranic from fertile uranium-238.
• The fast spectrum is flexible enough that it can also breed fissile uranium-233 from thorium.
• One measure of a reactor's performance is the "conversion ratio", defined as the ratio of new fissile atoms produced to fissile atoms consumed.
• A breeder reactor is a nuclear reactor that generates more fissile material than it consumes i.e., the ratio of fissile material produced to fissile material consumed is greater than 1.
• When the conversion ratio is greater than 1, it is often called the "breeding ratio".

Therefore, the correct answer is greater than 1.

Explanation:

• A boiling water nuclear reactor (BWR) is a type of nuclear reactor that uses water as both a coolant and a neutron moderator. It is called a boiling water reactor because the coolant water is allowed to boil in the reactor core, creating steam that is used to drive a turbine and generate electricity.

• In boiling water reactor no heat exchanger is required a mixture of water and steam comes out through the core and steam is separated and allowed to expand in the turbine.

• In a BWR, fuel assemblies made up of enriched uranium pellets are submerged in water, which acts as both a coolant and a neutron moderator. The reactor core contains a large number of fuel assemblies, which are arranged in a grid pattern and surrounded by control rods that can be inserted or removed to regulate the nuclear reaction.

• As the nuclear reaction occurs, heat is produced and the water in the reactor core boils, creating steam that is used to drive a turbine and generate electricity. The steam is then condensed back into water and returned to the reactor core to repeat the cycle.

• BWRs are a common type of nuclear reactor and are used in many countries around the world for the generation of electricity. They have several advantages, including a relatively simple design and the ability to use low-enriched uranium fuel. However, they also have some safety concerns, including the potential for steam explosions and the release of radioactive materials in the event of a severe accident. As a result, BWRs are subject to strict safety regulations and operating procedures to minimize the risk of accidents.

Explanation:

The efficiency of the thermodynamic cycle is given by

$\eta = 1 - \frac{{Heat;Rejected}}{{Heat;Supplied}}$

Since all the cycles (i.e otto, diesel and dual) reject their heat at the same specific volume, process line from state 4 to 1, the quantity of heat rejected from each cycle is represented by the appropriate area under the line 4 to 1 on the T-S diagram.

As is evident from the equation

The cycle which has the least heat rejected will have the highest efficiency.

Thus, the Otto cycle is the most efficient and the Diesel cycle is the least efficient of the three cycles.

${\eta _{otto}} > {\eta _{dual}} > {\eta _{diesel}}$

Explanation:

Morse Test:

• The Morse test is a test conducted to determine the power developed in each cylinder in a multi-cylinder IC engine.
• In this test first of all the power developed by all the cylinders together is determined experimentally.
• Then the power of the individual cylinders is determined by cutting off the power supply to the spark plug of the cylinder under test.
• Then the power developed by the engine with the remaining cylinders is determined experimentally and this value is subtracted from the first value and this gives you the power developed in the cylinder, whose spark plug was cut off.
• Similarly, this test is carried out on all the cylinders of the SI and CI engine individually.

Concept:

• Cetane rating, also known as cetane number is a measurement of the quality or performance of diesel fuel.
• The higher the number, the better the fuel burns within the engine of a vehicle.
• The cetane number is similar to the Octane Rating in that it is a rating assigned to fuel to rate the quality of its combustion.
• The main difference between cetane and octane ratings is that the octane rating represents how well a fuel can resist pre-ignition due to compression—ensuring the fuel ignites only from a spark from the spark plug. However, the cetane number measures the delay in the ignition time of the fuel.
• A higher cetane number resulting in quicker ignition of the fuel leads to less non-ignited fuels building up inside the combustion chamber, as well as more complete fuel combustion.
• Better fuel combustion and quick ignition lead to quicker starting for vehicles, as well as an engine that operates more quietly as only misted fuel is ignited and build-up inside the engine is minimized.
• Moreover, fuel efficiency improves with more complete combustion and harmful emissions are reduced.

Additional Information

The octane number is a measure of the knock resistance of gasoline. It defines a numerical value from 0 to 100, and describes the behavior of the fuel in the engine during combustion.

Knock resistance is a fuel’s ability not to self – ignite and burn in an uncontrolled way while the fuel is being compressed.

A high octane number can help increase the efficiency thus the performance of the engine.

Due to minimum work input required in isothermal compression, it is the ideal process for compression.

Constant pressure line 4-1 represents the suction stroke.

 Area 1234 represents the adiabatic work.

Isothermal compression:

If the compression is carried out isothermally, then it follows the curve 1-2 which has less slope than both isentropic and polytropic processes. This work done that is area 1234 in isothermal process is considerably less than that due to adiabatic compression.

Thus, compressor will have higher efficiency if compression follows isothermal process.

It is not possible in practice as to achieve isothermal process, as the compressor must run very slowly.

In practice compressors run at high speeds which results in polytropic process.

The cold-water spray and multi-stage compression are used for approximating to isothermal compression while still running the compressor at high speeds.

Concept:

If there are N number of stages, then the condition for minimum work required is:

Overall pressure ratio = (pressure ratio in each stage)N

Calculation:

$\frac{{27}}{1} = {\left( {\frac{{{P_2}}}{{{P_1}}}} \right)^3}$

Pressure ratio in each stage

$\frac{{{P_2}}}{{{P_1}}} = {\left( {125} \right)^{\frac{1}{3}}} = 5$

The delivery pressure of the first stage is

⇒  P2 = 5P1 = 5 × 1 = 5 bar

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.

Concept:

Gas turbine operates under the Brayton cycle, in which gas is the working fluid.

Calculation:

Given,

Work done by the turbine (WT)

WT = 600 kJ/kg

Compressor work (Wc)

Wc = 400 kJ/kg

Heat addition (Qs)

Qs = 1000 kJ/kg

Efficiency is calculated as

$n = \frac{{\mathop W\nolimits_T - \mathop W\nolimits_C }}{{\mathop Q\nolimits_S }} = \frac{{600 - 400}}{{1000}} = 0.2$

Concept:

Closed cycle gas turbine:

It works on the Brayton's cycle/Joule's cycle.

Joule Cycle:

Process 1-2: Isentropic compression of gas takes place in the compressor.

Process 2-3: It denotes the heating of gas in the heating chamber at constant pressure.

Process 3-4: In this process, the expansion of gas takes place isentropically.

Process 4-1: This process shows the cooling of gas at constant pressure in the cooling chamber.

Regeneration:

• Regeneration, a process during which heat is transferred to a thermal energy storage device (called a regenerator) during one part of the cycle and is transferred back to the working fluid during another part of the cycle.

• In a gas turbine regeneration is done between the exit gas from the turbine and the air coming out of the compressor.

• In the regeneration process, there is reduction in heat supplied to the gas but there is no effect on the turbine and compressor work.

• Therefore, the regeneration will not increase the work ratio in the turbine but the efficiency of the turbine increases in the regeneration process.

Concept:

For incompressible steady flow, the Laplace equation must be satisfied

$\begin{array}{l} \frac{{{d^2}\phi }}{{d{x^2}}} + \frac{{{d^2}\phi }}{{d{y^2}}} = 0\ \frac{{d\phi }}{{dx}} = - u = - A{e^x} \Rightarrow \frac{{{d^2}\phi }}{{d{x^2}}} = - A{e^x}\ - A{e^x} + \frac{{{d^2}\phi }}{{d{y^2}}} = 0\ \therefore \frac{{{d^2}\phi }}{{d{y^2}}} = A{e^x}\ V = - \frac{{d\phi }}{{dy}} = A{e^x}y + f\left( x \right) \end{array}$

-V = Aex.y + f(x)

∴ V = -Aex.y + f(x)

Explanation:

A very thin layer of fluid in the immediate neighborhood of the solid boundary, where the variation of velocity from zero at the solid boundary to the free stream velocity in the direction normal to the boundary takes place is known as the boundary layer. In this layer, the flow is viscous and rotational.

Outside the boundary layer, flows can be regarded as ideal, i.e. irrotational and frictionless.

Concept:

• When a solid body is immersed in a flowing fluid, a thin layer of fluid called the boundary layer is formed adjacent to the solid body.
• In this thin layer of fluid, velocity varies from zero to free stream velocity in the direction normal to a solid body. Along the length of solid body, the thickness of the boundary layer increases.
• The fluid layer adjacent to a solid surface has to do work against surface friction at the expense of its kinetic energy.
• This loss of kinetic energy is recovered from the immediate fluid layer in contact with the layer adjacent to the solid surface through the momentum exchange process.
• Thus, the velocity of the layer goes on decreasing.
• Along the length of the solid body, at a certain point, a stage may come when the boundary layer may not be able to keep sticking the solid body if it can’t provide the kinetic energy to overcome the resistance offered by the solid body. In other words, the boundary layer will be separated from the surface.

This phenomenon is called boundary layer separation. The point on the body at which the boundary layer is on the verge of separation is called the point of separation.

A favourable pressure gradient is one in which the pressure decreases in the flow direction (i.e., dp/dx < 0)

On the other hand, an adverse pressure gradient is one in which pressure increases in the flow direction (i.e., dp/dx > 0)

Following are some of the methods generally adopted to retard separation:

1. Streamlining the body shape.
   
2. Tripping the boundary layer from laminar to turbulent by provision roughness.
   

3. Sucking the retarded flow.

4. Injecting high velocity fluid in the boundary  layer.
   
5. Providing slots near the leading edge.
   
6. Guidance of flow in a confined passage.
   
7. Providing a rotating cylinder near the leading edge.
   
8. Energizing the flow by introducing optimum amount of swirl in the incoming flow.

Concept:

Mach number

Mach number is defined as the ratio of inertia force to elastic force.

\(M = \sqrt {\frac{{Inertia;force}}{{Elastic;force}}} = \sqrt {\frac{{\rho A{V^2}}}{{KA}}} = \sqrt {\frac{{{V^2}}}{{\frac{K}{\rho }}}} = \frac{V}{{\sqrt {\frac{K}{\rho }} }} = \frac{V}{C};;;;\left{ {\sqrt {\frac{K}{\rho }} = C = Velocity;of;sound} \right}\)

$M = \frac{{Velocity;of;body;moving;in;fluid}}{{velocity;of;sound;in;fluid}}$

If Mach number is less than 0.3, fluids are said to be incompressible.

For the compressible fluid flow, Mach number is an important dimensionless parameter. On the basis of the Mach number, the flow is defined.

Other important dimensionless numbers are described in the table below

Concept:

Reaction turbine:

A reaction turbine is a type of turbine that develops torque by reacting to the pressure or weight of a fluid. The principle of reaction turbines is described by Newton's third law of motion.

Component of a reaction turbine,

1. Spiral Casing
2. Guide Vane
3. Runner Blades or Impeller
4. Draft tube

Wicket gate is are the series of adjustable vanes used to guide water in reaction turbines. It is a type of Guide vane. 

Wicket gate:

• The movable wicket gates of a reaction turbine are used to control the flow of water to the turbine blades, thereby regulating the speed and power output of the turbine. A reaction turbine works by utilizing the pressure of water to turn its blades, so controlling the amount of water flowing through the turbine is crucial to maintaining its operation within safe limits.
• The movable wicket gates are positioned between the turbine's fixed guide vanes and rotating blades. By adjusting the position of the wicket gates, the operator can increase or decrease the amount of water that enters the turbine, which, in turn, changes the force exerted on the blades. As a result, the speed and power output of the turbine can be adjusted to meet the needs of the power grid or other applications.
• The wicket gates can be operated either manually or automatically, depending on the specific design of the turbine. In modern hydropower plants, computerized control systems are often used to adjust the position of the wicket gates based on real-time data on power demand and water flow rates.

Concept:

Pelton wheel turbine:

• A Pelton wheel turbine is a tangential flow impulse turbine.
• In an impulse turbine total energy at the time of inlet of the turbine is only kinetic energy.
• A Pelton wheel turbine is used for the high head of water.
• The pressure of water both at entering and leaving the vanes is atmospheric.

Explanation:

In a Pelton turbine, energy conversion occurs in a specific sequence starting from the fluid's potential energy at the reservoir. The conversion steps are as follows:

Potential Energy:

Water stored at a high elevation has potential energy due to its height above the turbine.

Kinetic Energy:

Water is directed through nozzles where it is converted into high-velocity jets, thus transforming potential energy into kinetic energy.

Mechanical Energy:

The high-velocity jets impact the turbine buckets and cause them to rotate, thus converting kinetic energy into mechanical energy that drives the turbine shaft.

∴ The correct sequence is Potential energy - Kinetic Energy - Mechanical energy.

Explanation:

If the water flows parallel to the axis of rotation of the shaft, the turbine is known as an axial flow turbine.

• For the axial flow reaction turbine, the shaft of the turbine is vertical. The lower end of the shaft is made larger, which is known as a hub or boss.
• When the vanes on the hub are adjustable then the turbine is known as the Kaplan turbine, and
• when the vanes are fixed to the hub, then the turbine is known as the Propeller turbine.

Kaplan turbine is a low head axial flow turbine with adjustable vane.

So, option (2) is the Correct answer.

Classification of turbines on the various basis is given in the table below:

Explanation:

Specific speed: 

The specific speed of a turbine is defined as, the speed of a geometrically similar Turbine that would develop unit power when working under a unit head (1m head).

It is prescribed by the relation ${N_s} = \frac{{N\sqrt P }}{{{H^{{5}/{4}}}}}$ = ${N_s} = \frac{{N\sqrt P }}{{{H^{{1.25}}}}}$

Where,

P = power

H = Net head of turbine

Specific speed plays an important role in the selection of the type of turbine. By knowing the specific speed of a turbine, the performance of the turbine can also be predicted.

• Low specific speed turbine: The specific speed is less than 50. (varying from 10 to 35 for a single jet and up to 50 for a double jet) Example: Pelton wheel turbine
• Medium-specific turbine: The specific speed varies from 50 to 250. Example: Francis turbine
• High specific turbine: the specific speed is more than 250. Example: Kaplan or propeller turbine

Concept:

The specific speed of a centrifugal pump is defined as the speed of a geometrically similar pump which would deliver one cubic metre of liquid per second against a head of one metre.

${N_s} = \frac{{N\sqrt Q }}{{H_m^{3/4}}}=\dfrac{\omega \sqrt Q}{(gH)^{3/4}}$

Specific speed for the turbine, 

$N_s=\frac{N\sqrt{P}}{H^{5/4}}$

Explanation:

The classification of fluid flow machines based on whether they supply energy to the fluid or extract energy from it is as follows:

Compressors: Compressors supply energy to the fluid by increasing the pressure of the fluid. They are used in gas turbines, jet engines, refrigeration and air conditioning systems, and other applications where a high-pressure gas is required.

Hydraulic turbines: Hydraulic turbines extract energy from the fluid by converting the kinetic energy of the fluid into mechanical energy. They are used in hydroelectric power plants, where the kinetic energy of falling water is converted into mechanical energy to generate electricity.

Torque converters: Torque converters are a combination of both compressors and hydraulic turbines. They supply energy to the fluid to increase its pressure and then extract energy from the fluid by converting its kinetic energy into mechanical energy. They are used in automatic transmissions in vehicles.

Windmills: Windmills extract energy from the fluid (in this case, air) by converting the kinetic energy of the air into mechanical energy. They are used to generate electricity in wind farms and for pumping water in rural areas.

Overall, fluid flow machines play an important role in many industries and applications, and their classification based on whether they supply energy to the fluid or extract energy from it helps to understand their fundamental principles and applications.