All questions of Power Engineering for Mechanical Engineering Exam

Explanation:

Two-Stage Compression Process:
In a two-stage compression process, the gas is compressed in two stages to achieve higher pressures. The work input required for compression primarily depends on the intermediate pressure between the suction and discharge pressures.

Minimum Work Input:
To minimize the work input in a two-stage compression process, the intermediate pressure should be the geometric mean of the suction and discharge pressures.

Geometric Mean:
The geometric mean is calculated by taking the square root of the product of two numbers. In the case of a two-stage compression process, the geometric mean of the suction pressure (P1) and the discharge pressure (P2) is given by the formula:
\[P_{intermediate} = \sqrt{P1 \times P2}\]

Reasoning:
The geometric mean is chosen for minimum work input because it provides a balanced approach between the suction and discharge pressures. This intermediate pressure helps in reducing the overall work input required for compression while maintaining efficient compression ratios.

Therefore, the geometric mean of the suction and discharge pressures is the optimal choice for achieving minimum work input in a two-stage compression process.

Chimney is the producer of natural draught
Natural draught is the flow of air in a chimney or flue due to the difference in density between the hot gases inside the chimney and the cooler air outside. The chimney plays a crucial role in creating this natural draught phenomenon.

How a Chimney Produces Natural Draught:
- Temperature Difference: The hot gases produced by combustion in a furnace or boiler are lighter and less dense than the surrounding air. This temperature difference creates a pressure difference, causing the hot gases to rise up the chimney.
- Height and Length: The height and length of the chimney determine the strength of the natural draught. Taller and longer chimneys provide more space for the hot gases to rise, increasing the draught effect.
- Design: The design of the chimney, including its diameter, shape, and insulation, affects the efficiency of natural draught production. A well-designed chimney can enhance the draught by minimizing air resistance and maximizing the flow of hot gases.
- Wind Effects: Wind can also influence natural draught. When wind blows over the top of the chimney, it can either enhance or reduce the draught depending on the direction and intensity of the wind.

Advantages of Natural Draught:
- Energy-efficient: Natural draught does not require additional energy input, making it a cost-effective way to remove combustion gases.
- Reliable: As long as there is a temperature difference between the inside and outside of the chimney, natural draught will continue to work.
- Environmentally friendly: Natural draught does not rely on mechanical components, reducing the carbon footprint of the system.

Understanding Free Air
Free air refers to the state of air under specific standard conditions, which helps in various engineering calculations, particularly in thermodynamics and fluid mechanics.
Standard Conditions for Free Air
- The term "free air" typically implies air measured at certain standard conditions to ensure consistency in measurements and calculations.
- Option 'D' states that free air is defined as air at 1 bar pressure and 15°C temperature, which is a widely accepted standard in engineering practices.
Why Option D is Correct
- Pressure and Temperature:
- 1 bar pressure is equivalent to 100 kPa or approximately atmospheric pressure at sea level, making it a relevant reference point.
- 15°C is close to average ambient temperature, representing standard conditions for many mechanical systems.
- Relative Humidity:
- While relative humidity can influence air properties, the critical factor in defining free air is primarily focused on pressure and temperature, not humidity.
Comparison with Other Options
- Option A: Refers to atmospheric conditions at any specific location, which may vary significantly and is not standardized.
- Option B: Mentions standard atmospheric conditions at 0°C, which does not represent the commonly accepted definition of free air.
- Option C: Specifies 20°C and relative humidity of 36%, diverging from the standard definitions used in most engineering calculations.
Conclusion
Choosing option 'D' aligns with the accepted definitions in mechanical engineering, allowing for accurate calculations and consistency across various applications. Understanding these standard conditions is vital for engineers working with air properties in design and analysis.

A Cochran boiler is a vertical fire tube boiler. This means that the heat source and the water are contained in a vertical cylindrical shell, with the tubes running vertically through the shell. The Cochran boiler is named after its inventor, John Cochran.

The Cochran boiler is widely used in industries such as power generation and chemical processing due to its compact size and efficient operation. It is particularly suitable for small steam applications and can generate steam up to a maximum pressure of 16 bar.

Below are the key features and advantages of the Cochran boiler:

1. Construction: The Cochran boiler consists of a cylindrical shell with a hemispherical furnace at the bottom. The furnace is surrounded by a water space and fitted with a fire brick lining. The combustion gases pass through the tubes, which are surrounded by water.

2. High heat transfer efficiency: The vertical arrangement of tubes allows for a large heating surface area, resulting in efficient heat transfer from the hot gases to the water. This ensures a high rate of steam generation.

3. Compact design: The vertical orientation of the Cochran boiler makes it compact and space-saving. It can be easily installed in limited space areas.

4. Easy maintenance: The accessibility of the tubes in the vertical arrangement makes maintenance and cleaning of the boiler relatively easy.

5. Quick startup: The Cochran boiler can quickly generate steam due to its small water content and compact design. This makes it suitable for applications that require rapid steam production.

6. Versatile fuel options: The Cochran boiler can be fired with various fuels such as coal, wood, oil, or gas. This flexibility allows for the use of different fuel sources depending on availability and cost.

In conclusion, the Cochran boiler is a vertical fire tube boiler that offers efficient steam generation, compact design, and versatility in fuel options. Its construction and features make it suitable for small-scale steam applications in industries such as power generation and chemical processing.

Answer:

The correct answer is option D, which includes superheaters, economisers, and air preheaters. These devices are used for part recovery of heat from the flue gases leaving the tube banks in a water tube boiler.

Superheaters:
- Superheaters are devices in a boiler that increase the temperature of steam beyond its saturation point.
- They are typically installed in the path of flue gases before the gases exit the boiler.
- Superheaters recover heat from the flue gases by transferring it to the steam, increasing its temperature and energy content.

Economisers:
- Economisers are heat exchangers that recover heat from the flue gases and transfer it to the incoming feedwater.
- They are placed in the flue gas path after the boiler's combustion chamber but before the chimney.
- Economisers preheat the feedwater, reducing the energy required to raise its temperature to the desired level.

Air Preheaters:
- Air preheaters are devices that recover heat from the flue gases and transfer it to the incoming combustion air.
- They are typically installed in the path of flue gases before they enter the chimney.
- Air preheaters preheat the combustion air, increasing the efficiency of the combustion process and reducing fuel consumption.

Explanation:
- The flue gases leaving the tube banks in a water tube boiler contain a significant amount of heat energy.
- By using superheaters, economisers, and air preheaters, a portion of this heat can be recovered and utilized, increasing the overall efficiency of the boiler system.
- Superheaters recover heat from the flue gases by transferring it to the steam, increasing its temperature and energy content.
- Economisers recover heat from the flue gases and transfer it to the incoming feedwater, preheating it before it enters the boiler's combustion chamber.
- Air preheaters recover heat from the flue gases and transfer it to the incoming combustion air, increasing the efficiency of the combustion process.
- By utilizing these devices, the heat energy in the flue gases is maximized, resulting in reduced fuel consumption and improved overall thermal efficiency of the boiler system.

°C and 3500 kJ/kg, respectively. The steam is then expanded in a turbine to a pressure of 0.5 MPa. The condenser pressure is 10 kPa. Determine the following:

a) The quality of the steam at the turbine exit.
b) The thermal efficiency of the cycle.
c) The specific work output of the turbine.

To solve this problem, we will use the properties of water and steam provided in the steam tables. The given values are:
- Boiler outlet pressure (P1) = 3 MPa
- Boiler outlet temperature (T1) = 350 °C
- Boiler outlet enthalpy (h1) = 3500 kJ/kg
- Turbine outlet pressure (P2) = 0.5 MPa
- Condenser pressure (P3) = 10 kPa

First, let's determine the state of the steam at the turbine exit (state 2):
Using the steam tables, we can find the saturation temperature corresponding to the turbine outlet pressure:
Saturation temperature at P2 = Tsat(P2) ≈ 151.85 °C

Comparing this with the given turbine outlet temperature (T2 = 350 °C), we can conclude that the steam is superheated at the turbine exit.

Next, let's determine the quality of the steam at the turbine exit (state 2):
Using the steam tables, we can find the enthalpy at the saturation temperature:
hf2 = h(P2, sf2) ≈ 797.12 kJ/kg
hg2 = h(P2, sg2) ≈ 2765.35 kJ/kg

The quality (x2) can be calculated using the equation:
x2 = (h2 - hf2) / (hg2 - hf2)
x2 = (3500 - 797.12) / (2765.35 - 797.12) ≈ 0.901

a) The quality of the steam at the turbine exit is approximately 0.901.

Next, let's calculate the thermal efficiency of the cycle:
The thermal efficiency (η) of a Rankine cycle is given by the equation:
η = 1 - (Qout / Qin)

First, let's determine the heat input (Qin) to the cycle:
Using the steam tables, we can find the enthalpy at the boiler inlet (state 1):
h1 = 3500 kJ/kg

The heat input is given by the equation:
Qin = m * (h1 - h3)

Next, let's determine the heat output (Qout) from the cycle:
Using the steam tables, we can find the enthalpy at the condenser outlet (state 4):
h4 = hf(P3) ≈ 191.81 kJ/kg

The heat output is given by the equation:
Qout = m * (h2 - h4)

Now, let's calculate the thermal efficiency:
η = 1 - (Qout / Qin)
η = 1 - [(h2 - h4) / (h1 - h3)]

Using the given values and the calculated quality (x2), we can substitute the enthalpy values:
η = 1 - [(3500 - 191.81) / (3500 - h3)]

To find h3, we can use

Pressure Drop in an Impulse Turbine

Introduction:
An impulse turbine is a type of steam turbine used in power plants and other industries to convert the kinetic energy of a high-pressure steam into mechanical work. It operates on the principle of the impulse reaction, where a high-velocity jet of steam is directed onto the blades of the turbine rotor, causing it to rotate.

Pressure Drop:
The pressure drop in an impulse turbine occurs primarily in the nozzles. The nozzles are fixed, stationary components that serve the purpose of channeling the high-pressure steam into high-velocity jets. These jets then impinge on the moving blades, causing them to rotate.

Nozzles and Pressure Drop:
The pressure drop in an impulse turbine primarily occurs in the nozzles due to the conversion of pressure energy to kinetic energy. The nozzles are designed to accelerate the steam to a high velocity by increasing its kinetic energy. This acceleration is achieved by creating a convergent-divergent nozzle geometry, where the steam passes through a converging section followed by a diverging section.

Converging Section:
In the converging section of the nozzle, the steam flow area decreases, leading to an increase in velocity and a corresponding decrease in pressure. This decrease in pressure is due to the conversion of pressure energy into kinetic energy.

Diverging Section:
In the diverging section of the nozzle, the steam flow area increases, causing the velocity to decrease and the pressure to increase. However, the pressure in the diverging section does not reach the same level as the inlet pressure. This is because some of the pressure energy has been converted into kinetic energy in the converging section.

Impact on Moving Blades:
Once the high-velocity jets of steam leave the nozzles, they impinge on the moving blades of the turbine rotor. The impact of the steam on the blades causes a change in momentum, resulting in the rotation of the rotor. However, the pressure drop in the moving blades is relatively small compared to that in the nozzles.

Conclusion:
In an impulse turbine, the pressure primarily drops in the nozzles due to the conversion of pressure energy into kinetic energy. The pressure drop in the moving blades is relatively small. Therefore, the correct answer is option 'A' - Only in the nozzles.

Given:
- Enthalpy at entry (h1) = 3450 kJ/kg
- Enthalpy at exit (h2) = 2800 kJ/kg
- Initial velocity (v1) = 0 (negligible)

To find:
- Velocity at the exit (v2)

We can use the energy equation to solve this problem. The energy equation is given as:

h1 + (v1^2)/2 = h2 + (v2^2)/2

where:
- h1 and h2 are the enthalpies at the entry and exit, respectively
- v1 and v2 are the velocities at the entry and exit, respectively

Since the initial velocity (v1) is negligible, the equation simplifies to:

h1 = h2 + (v2^2)/2

Rearranging the equation to solve for v2:

(v2^2)/2 = h1 - h2

v2^2 = 2(h1 - h2)

v2 = √(2(h1 - h2))

Calculating the values:

v2 = √(2(3450 - 2800))

v2 = √(2(650))

v2 = √(1300)

v2 = 36 m/s

Therefore, the velocity at the exit is 36 m/s, which corresponds to option (c).

Analysis:
The work ratio of a gas turbine plant is defined as the ratio of the net work output to the total energy supplied to the plant. In this case, the work ratio is given as 40%.

Given:
- Power output of the gas turbine plant = 4000 kW
- Work ratio = 40%

Calculations:
- Total power supplied to the plant = Power output / Work ratio
- Total power supplied to the plant = 4000 kW / 0.4 = 10000 kW

Power consumed by the compressor:
- Power consumed by the compressor = Total power supplied - Power output
- Power consumed by the compressor = 10000 kW - 4000 kW = 6000 kW
Therefore, the power consumed by the compressor in the gas turbine plant is 6000 kW. Hence, the correct answer is option 'A'.

Ratio of enthalpy drop in moving blades to the total enthalpy drop in the fixed and moving blades is called the Degree of Reaction.

Explanation:

Enthalpy drop in moving blades:
The enthalpy drop in moving blades refers to the change in enthalpy of the fluid as it passes through the moving blades in a turbine or compressor. This change in enthalpy is typically associated with a decrease in pressure and an increase in velocity of the fluid.

Total enthalpy drop in fixed and moving blades:
The total enthalpy drop in the fixed and moving blades refers to the overall change in enthalpy of the fluid as it passes through both the fixed and moving blades in a turbine or compressor. This includes the enthalpy drop in the fixed blades as well as the enthalpy drop in the moving blades.

Degree of Reaction:
The degree of reaction is defined as the ratio of the enthalpy drop in the moving blades to the total enthalpy drop in the fixed and moving blades. It is denoted by the symbol "R" and is expressed as a percentage.

Mathematically, the degree of reaction (R) is given by the formula:
R = (enthalpy drop in moving blades / total enthalpy drop) * 100%

Significance of Degree of Reaction:
The degree of reaction is an important parameter in the design and analysis of turbomachinery. It provides information about the distribution of work between the fixed and moving blades. A higher degree of reaction indicates that a larger portion of the enthalpy drop occurs in the moving blades, while a lower degree of reaction indicates that a larger portion of the enthalpy drop occurs in the fixed blades.

The degree of reaction affects the performance and efficiency of the turbomachinery. It determines the pressure ratio, work output, and flow characteristics of the machine. By adjusting the degree of reaction, the designer can optimize the performance of the turbomachinery for specific applications.

In conclusion, the ratio of the enthalpy drop in the moving blades to the total enthalpy drop in the fixed and moving blades is called the degree of reaction. It is an important parameter in the design and analysis of turbomachinery, as it provides information about the distribution of work between the fixed and moving blades and affects the performance and efficiency of the machine.