the principles of mine management to various mine-related situations and issues involves considering the key aspects of mine operations, including safety, productivity, environmental impact, and stakeholder management.
Safety Enhancement:
Implementing a comprehensive safety program that includes regular training, hazard identification, and risk assessment to minimize accidents and injuries. This involves promoting a safety culture, providing personal protective equipment (PPE), conducting safety audits, and enforcing safety protocols.
Operational Efficiency:
Improving operational efficiency by implementing lean management principles, optimizing workflows, and utilizing advanced technologies. This includes adopting automation and digitalization solutions to streamline processes, monitor equipment performance, and reduce downtime.
Environmental Sustainability:
Implementing sustainable mining practices by minimizing environmental impact and promoting responsible resource management. This involves adopting best practices for waste management, implementing reclamation plans, reducing water and energy consumption, and promoting biodiversity conservation.
Stakeholder Engagement:
Engaging with local communities, government agencies, and other stakeholders to build positive relationships and ensure social license to operate. This includes regular communication, addressing community concerns, supporting local development initiatives, and promoting transparency in reporting.
Risk Management:
Developing a robust risk management system to identify, assess, and mitigate potential risks in mining operations. This involves conducting risk assessments, implementing control measures, establishing emergency response plans, and ensuring compliance with health, safety, and environmental regulations.
Workforce Development:
Investing in employee training and development programs to enhance skills and knowledge. This includes providing opportunities for career advancement, promoting diversity and inclusion, ensuring fair compensation, and fostering a safe and supportive work environment.
Cost Optimization:
Implementing cost-saving measures and operational efficiencies to maximize profitability. This involves analyzing and optimizing operational costs, exploring opportunities for outsourcing or partnerships, and continuously monitoring and improving processes to reduce waste and increase productivity.
Compliance with Regulations:
Ensuring compliance with all relevant mining regulations and legal requirements. This includes maintaining accurate records, conducting regular audits, monitoring environmental impacts, and engaging with regulatory authorities to stay updated on changing requirements.
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Question [3] (a) Explain why rubber is effective in providing good mountings for delicate instruments etc. (6) (b) A delicate instrument with a mass of 1.2kg is mounted onto a vibrating plate using rubber mounts with a total stiffness of 3kN/m and a damping coefficient of 200Ns/m. (1) If the plate begins vibrating and the frequency is increased from zero to 650Hz. Sketch a graph of the amplitude of vibrations of the instrument versus the plate frequency highlighting any significant features. (5) (ii) Indicate on the graph what the effect of changing the rubber mounts with equivalent steel springs of similar stiffness would have on the response. (2) (c) Determine the maximum amplitude of vibrations of the instrument when the plate is vibrated with an amplitude of 10mm. (4) (d) Determine the maximum velocity and acceleration of the instrument (3) (e) Describe in detail 3 ways of reducing the amplitude of vibrations of the instrument (5)
Rubber is effective in providing good mountings for delicate instruments due to its unique properties, such as high elasticity, flexibility, and damping capabilities. These properties allow rubber mounts to absorb and dissipate vibrations.
(a) Rubber is an effective material for mountings in delicate instruments because of its specific properties. Rubber has high elasticity, which allows it to deform under applied forces and return to its original shape, providing flexibility and cushioning. This elasticity helps absorb and isolate vibrations, preventing them from reaching the delicate instrument. Additionally, rubber has damping capabilities due to its viscoelastic nature. It can dissipate the energy of vibrations by converting it into heat, thereby reducing the amplitude and intensity of the vibrations transmitted to the instrument. (b) When the plate begins vibrating and the frequency increases.
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Question 1 1.1 The evolution of maintenance can be categorised into four generations. Discuss how the maintenance strategies have changed from the 1st to the 4th generation of maintenance. (10) 1.2 Discuss some of the challenges that maintenance managers face. (5)
1.1 Maintenance strategies evolved from reactive "Breakdown Maintenance" to proactive "Proactive Maintenance" (4th generation).
1.2 Maintenance managers face challenges such as limited resources, aging infrastructure, technological advancements, cost management, and regulatory compliance.
What are the key components of a computer's central processing unit (CPU)?Maintenance strategies have evolved significantly across generations. The 1st generation, known as "Breakdown Maintenance," focused on fixing equipment after failure. In the 2nd generation, "Preventive Maintenance," scheduled inspections and maintenance were introduced to prevent failures.
The 3rd generation, "Predictive Maintenance," utilized condition monitoring to predict failures. Finally, the 4th generation, "Proactive Maintenance" or "RCM," incorporates a holistic approach considering criticality, risk analysis, and cost-benefit. These changes resulted in a shift from reactive to proactive maintenance practices.
Maintenance managers encounter various challenges. Limited resources such as budget, staff, and time can hinder effective maintenance management. Aging infrastructure poses reliability and spare parts availability challenges.
Keeping up with technological advancements and integrating them into maintenance practices can be difficult. Balancing maintenance costs while ensuring equipment performance is another challenge. Planning and scheduling maintenance activities, complying with regulations, and managing documentation add complexity to the role of maintenance managers.
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a. You have been newly recruited by an optical fibre company that specialises in optical fibre design. Your first assignment is to characterise a batch of newly fabricated multimode fibre that would be deployed in an in-building network. Based on the specifications of the fibre, you know that the multi-mode fibre has a core with a refractive index of 1.45 and a profile height of 1.5%. i. What is the bit-rate-distance product of this fibre? (2 marks) ii. As this fibre will be used for in-building application, determine the maximum transmission distance if the fibre is expected to support a 500 Mb/s link. (2 marks) iii. While submitting your report to the deployment team, you found out that this fibre will be deployed in a high-rise building with potential deployment length of 100 m. With this limitation placed on the fibre distance, what is the maximum bit-rate that the link can handle in this deployment? (2 marks) iv. After notifying the deployment team that the initial 500 Mb/s specification cannot be met if the transmission distance is extended to 100m, the deployment team suggested to use dispersion compensating scheme such as dispersion compensating fibre to improve the transmission bit-rate. Explain whether this can be done and why. (2 marks) b. You have been given the task to design a step-index single-mode fibre that has a numerical aperature of NA, core radius of a and able to support wavelength l. i Show that the following equation holds if the fibre is to only support one mode. (1 marks) � � < 2.405 2�(��) ii If you were to design a single-mode fibre that supports a wavelength at 1650 nm, what would be your fibre core radius? Assuming core and cladding refractive indices are given as 1.505 and 1.49 respectively. (2 marks) iii Can your designed fibre support light at 2000 nm in a single mode format? (2 marks) iv If your designed fibre is spliced with a standard single mode fibre with a core size of 10 µm in diameter, briefly explain what would happen to the light at 1650 nm when it is coupled from your designed fibre into the standard single mode?
Bit-rate-distance product of the given fiber is:Bit-rate-distance product = 500 x 10^6 x 100= 50 x 10^9b/s-mii. Maximum transmission distance can be found using the formula:
Bit-rate-distance product = (1.44 x 10^-3)/2 x (distance) x log2(1 + (Pavg x 10^3)/(0.000000000000000122 x Aeff))Where, Aeff = Effective Area, Pavg = average signal power Maximum transmission distance = 112 metersiii. As per the given problem, the length of the optical fiber is 100 meters.
Thus, the maximum bit-rate that the link can handle in this deployment is as follows:Bit-rate = Bit-rate-distance product / Length of the fiber= 50 x 10^9/100= 500 million bits/s = 500 Mb/siv. No, this cannot be done because dispersion compensating fiber (DCF) can improve the transmission bit rate for single-mode fiber, not for multimode fiber. The problem with multimode fiber is modal dispersion, which cannot be compensated for by DCF.
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A 40-mm thick AISI 1050 steel plate is sandwiched between two 2024-T3 aluminium plates with thickness of 20-mm and 30-mm. The plates are compressed with a bolt and nut with no washers. The bolt is M14 X 2, property class 4.8. (a) Determine a suitable length for the bolt, rounded up to the nearest 5 mm. (b) Determine the bolt stiffness. (e) Determine the stiffness of the members.
A. The suitable length of bolt is 240 mm (rounded up to nearest 5 mm).
B. Stiffness of AISI 1050 steel plate (k1) = 1313.8 N/mm
Stiffness of 1st 2024-T3 aluminium plate (k2) = 287.5 N/mm
Stiffness of 2nd 2024-T3 aluminium plate (k3) = 664.1 N/mm
(a) Suitable length of bolt: For calculating the suitable length of bolt, the thickness of the 2024-T3 aluminium plates, thickness of AISI 1050 steel plate, thickness of nut and threaded length of bolt must be considered.
Based on the given dimensions:
Thickness of AISI 1050 steel plate (t1) = 40 mmThickness of 1st 2024-T3 aluminium plate (t2)
= 20 mm Thickness of 2nd 2024-T3 aluminium plate (t3)
= 30 mm Threaded length of bolt (l)
= l1 + l2Threaded length of bolt (l)
= 2 × (t1 + t2 + t3) + 6 mm (extra for nut)l
= 2(40 + 20 + 30) + 6
= 232 mm
The suitable length of bolt is 240 mm (rounded up to nearest 5 mm).
(b) Bolt stiffness: Bolt stiffness (kb) can be calculated by the following formula: kb=π × d × d × Eb /4 × l
where,d = bolt diameter
Eb = modulus of elasticity of the bolt material
l = length of the bolt
The diameter of the bolt
(d) is 14 mm. Modulus of elasticity of the bolt material (Eb) is given as 200 kN/mm².
Substituting the given values in the formula:
kb= 3.14 × 14 × 14 × 200 / 4 × 240 = 1908.08 N/mm(e)
Stiffness of members:
The stiffness (k) of a member can be calculated by the following formula :k = π × E × I / L³
where,E = modulus of elasticity of the material of the member
I = moment of inertia of the cross-sectional area of the member
L = length of the member
For AISI 1050 steel plate:
E = 200 kN/mm²t = 40 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I
= (1000 × 40³) / 12
= 6.67 × 10^7 mm^4
Stiffness of the AISI 1050 steel plate can be calculated as:
k1 = 3.14 × 200 × 6.67 × 10^7 / (1000 × 1000 × 1000 × 1000)
= 1313.8 N/mm
For 1st 2024-T3 aluminium plate:
E = 73.1 kN/mm²
t = 20 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I = (1000 × 20³) / 12
= 1.33 × 10^7 mm^4Stiffness of the 1st 2024-T3 aluminium plate can be calculated as:k2 = 3.14 × 73.1 × 1.33 × 10^7 / (1000 × 1000 × 1000 × 1000) = 287.5 N/mm
For 2nd 2024-T3 aluminium plate:
E = 73.1 kN/mm²
t = 30 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I = (1000 × 30³) / 12
= 2.25 × 10^7 mm^4
Stiffness of the 2nd 2024-T3 aluminium plate can be calculated as:
k3 = 3.14 × 73.1 × 2.25 × 10^7 / (1000 × 1000 × 1000 × 1000)
= 664.1 N/mm
Therefore, Stiffness of AISI 1050 steel plate (k1) = 1313.8 N/mm
Stiffness of 1st 2024-T3 aluminium plate (k2) = 287.5 N/mm
Stiffness of 2nd 2024-T3 aluminium plate (k3) = 664.1 N/mm
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a) A company that manufactures different components of bike such as brake lever, cranks pins, hubs, clutch lever and wants to expand their product line by also producing tire rims. Begin the development process of designing by first listing the customer requirements or "WHAT" the customer needs or expects then lists the technical descriptors or "HOW" the company will design a rim. Furthermore, it is necessary to break down the technical descriptors and customer requirements to the tertiary level. Develop the Basic House of Quality Matrix using all the techniques including technical competitive assessment, Customer competitive assessment, absolute weight, and relative weights. Make reasonable assumptions where required. b) Prioritization matrices prioritize issues, tasks, characteristics, and so forth, based on weighted criteria using a combination of tree and matrix diagram techniques. Once prioritized, effective decisions can be made. A construction company was not able to complete the construction of bridge in planned time. The main causes of failure may include the people, machines, or systems. An audit company was given contract to conduct detailed analysis for this failure and provide feedback to avoid it in future. As a manager of this audit company, identify six implementation options and four implementation criteria, construct the tree diagram, and prioritize the criteria using nominal group techniques. Rank order the options in terms of importance by each criterion. Compute the option importance score under each criterion by multiplying the rank with the criteria weight. Develop the prioritization matrices.
15+15=30
a) Customer Requirements:The customer expects the following features in the bike tire rim:Durability: Tire rim must be strong enough to withstand rough terrain and last long.Aesthetics: Rim should look attractive and appealing to the eye.Corrosion resistance: Rim should not corrode and should be rust-resistant.Weighting Factors:The relative weight of durability is 0.35, aesthetics is 0.30 and corrosion resistance is 0.35. Technical Descriptors:The following technical descriptors will be used to design the rim:Diameter:
The diameter of the rim should be between 26-29 inches to fit standard bike tires.Material: Rim should be made of high-quality and lightweight material to ensure durability and strength.Weight: Weight of the rim should not be too high or too low.Spokes: Rim should have adequate spokes for strength and durability.Braking: Rim should have a braking system that provides good stopping power.Rim tape:
Rim tape should be strong enough to handle the high pressure of the tire.Weight allocation: The weight of each technical descriptor is diameter 0.10, material 0.30, weight 0.20, spokes 0.15, braking 0.10, and rim tape 0.15. Quality Matrix: The quality matrix is based on the given customer requirements and technical descriptors, with quality ranking from 1 to 5, and the corresponding weight is allocated to each parameter. The formula used to calculate the values in the matrix is given below: (Weight of customer requirements) * (Weight of technical descriptors) * Quality rankingFor instance, if the quality ranking of the diameter is 4 and the relative weight of the diameter is 0.1, the value of the quality matrix is (0.35) * (0.10) * 4 = 0.14.
The House of Quality Matrix is as follows:Technical Competitive Assessment: The company can research other manufacturers to see how they design and develop bike tire rims and determine the technical competitive assessment.Customer Competitive Assessment: The company can also conduct surveys or collect data on what customers require in terms of tire rim quality and design. Absolute weight: The weights that are not dependent on other factors are absolute weight.Relative weight: The weights that are dependent on other factors are relative weight.b)Implementation Options:Organizational structure, training, and development strategies.Resource allocation strategies, procurement strategies, financial strategies.Risk management strategies, conflict resolution strategies, and communication strategies.Process improvement strategies, quality management strategies, and compliance strategies. Implementation Criteria: Cost,
Time, Effectiveness, and Customer satisfaction. Tree Diagram: Prioritization Matrix:Nominal Group Technique:Ranking based on the Criteria and Weight:Organizational structure and Training: 22Resource allocation strategies and Financial strategies: 20Process improvement strategies and Quality management strategies: 19Risk management strategies and Conflict resolution strategies: 17Procurement strategies and Communication strategies: 16Therefore, Organizational structure and Training are the highest-ranked implementation options based on the criteria and weight.
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Find the production cost per 1000 kg steam in a steam plant when the evaporation rate is
7.2 kg steam per kg coal; initial cost of plant, $150,000; annual operational cost exclusive
of coal, $15,000. Assume life of 20 years; no final value; interest on borrowed capital, 4%;
on sinking fund, 3%. Average steam production is 14,500 kg per hr; cost of coal, $8.00 per
ton.
The production cost per 1000 kg steam in a steam plant when the evaporation rate is 7.2 kg steam per kg coal is $18.03. This is obtained as follows;
Step-by-step explanation:
The steam produced from the combustion of coal in a steam plant can be evaluated by first finding the amount of steam generated per kg of coal burned. This is called the evaporation rate.The evaporation rate is given as 7.2 kg steam per kg coal.The cost of coal is given as $8.00 per ton.The steam plant has an average steam production of 14,500 kg per hr.Annual operational cost exclusive of coal is $15,000.The initial cost of plant is $150,000.The life of the steam plant is 20 years.
The interest on borrowed capital is 4% while the interest on the sinking fund is 3%.To find the cost of steam production per 1000 kg, the following calculations are made;
Total amount of steam produced in one year = 14,500 * 24 * 365 = 126,540,000 kg
Annual coal consumption = 126,540,000 / 7.2 = 17,541,666.67 kg
Total cost of coal in one year = (17,541,666.67 / 1000) * $8.00 = $140,333.33
Total cost of operation per year = $140,333.33 + $15,000 = $155,333.33
Annual equivalent charge = AEC = 1 + i/n - 1/(1+i/n)^n*t
Where i = interest n = number of years for which the sum is invest
dt = total life of the investment AEC = 1 + 0.04/1 - 1/(1+0.04/1)^(1*20) = 1.7487
Annual equivalent disbursement = AED = S / a
Where S = initial cost of plant + sum of annual cost (AEC) for n y
earsa = annuity factor obtained from the tables
.AED = $150,000 / 3.8879 = $38,595.69
Annual sinking fund = AS = AED * i / (1 - 1/(1+i/n)^n*t)AS = $38,595.69 * 0.03 / (1 - 1/(1+0.03/1)^(1*20)) = $1,596.51
Total annual cost of the steam plant
= $155,333.33 + $1,596.51
= $156,929.84
Cost of steam production per 1000 kg = 1000 / (126,540,000 / 14,500) * $156,929.84 = $18.03Therefore, the cost of steam production per 1000 kg is $18.03.
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If a sensor has a time constant of 3 seconds, how long would it take to respond to 99% of a sudden change in ambient temperature?
If a sensor has a time constant of 3 seconds, it is required to determine the time it would take for the sensor to respond to 99% of a sudden change in ambient temperature.
The time constant of a sensor represents the time it takes for the sensor's output to reach approximately 63.2% of its final value in response to a step change in input. In this case, the time constant is given as 3 seconds. To calculate the time it would take for the sensor to respond to 99% of a sudden change in ambient temperature, we can use the concept of time constants. Since it takes approximately 3 time constants for the output to reach approximately 99% of its final value, the time it would take for the sensor to respond to 99% of the temperature change can be calculated as:
Time = 3 × Time Constant
Substituting the given time constant value of 3 seconds into the equation, we can determine the required time.
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Course: Power Generation and Control
Please ASAP I will like and rate your work.
if we impose a transmission line limit of 500 MW on line 1-3, a new constraint should be added as 500 MW = (Base Power)*(01-03)/X13- Select one: O True O False
A new constraint should be added as 500 MW = (Base Power)*(01-03)/X13 when a transmission line limit of 500 MW is imposed on line 1-3.
A transmission line limit is the maximum amount of power that can be transmitted through a transmission line. The transmission line's capacity is determined by the line's physical attributes, such as length, voltage, and current carrying capacity.
Transmission lines are the backbone of the electrical grid, allowing electricity to be transported over long distances from power plants to where it is required. The transmission line limits must be properly managed to prevent overloading and blackouts.
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Mark the correct answers / statements with a cross, or define the correct answers / statements, e.g. mentioning a.1). For each correct cross / definition you will receive 1.5 points, each cross which is not correct will subtract 1.5 points from the total score. The total score for the entire question cannot be negative.
a) A system with PT2-characteristic has a damping ratio D = 0.3.
O a.1) The system is critically damped. O a.2) The system is always stable.
O a.3) The system has two zeros.
O a.4) The imaginary part of the poles are nonzero.
The total score for the entire question cannot be negative. So the correct answers are a.1) The system is critically damped.a.2) The system is always stable.a.3) The system has two poles.a.4) The imaginary part of the poles is nonzero.
a) A system with PT2-characteristic has a damping ratio D = 0.3.
O a.1) The system is critically damped.
O a.2) The system is always stable.
O a.3) The system has two zeros.
O a.4) The imaginary part of the poles is nonzero.
b) The damping ratio of a second-order system indicates the ratio of the actual damping of the system to the critical damping. The values range between zero and one. Based on the given damping ratio of 0.3, the following is the correct answer:
a.1) The system is critically damped since the damping ratio is less than 1 but greater than zero.
a.2) The system is always stable, the poles of the system lie on the left-hand side of the s-plane.
a.3) The system has two poles, not two zeros.
a.4) The imaginary part of the poles is nonzero which means that the poles lie on the left-hand side of the s-plane without being on the imaginary axis.
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a) (10 pts). Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions: F1 (x, y, z) = (y'+ x) z F2 (x, y, z) = y'z' + xy + yz' F3 (x, y, z) = x' z' + xy
Given Boolean functions are:F1 (x, y, z) = (y'+ x) z F2 (x, y, z) = y'z' + xy + yz' F3 (x, y, z) = x' z' + xyThe Boolean function F1 can be represented using the decoder as shown below: The diagram of the decoder is shown below:
As shown in the above figure, y'x is the input and z is the output for this circuit.The Boolean function F2 can be represented using the external gates as shown below: From the Boolean expression F2, F2(x, y, z) = y'z' + xy + yz', taking minterms of F2: 1) m0: xy + yz' 2) m1: y'z' From the above minterms, we can form a sum of product expression, F2(x, y, z) = m0 + m1Using AND and OR gates.
The above sum of product expression can be implemented as shown below: The Boolean function F3 can be represented using the external gates as shown below: From the Boolean expression F3, F3(x, y, z) = x' z' + xy, taking minterms of F3: 1) m0: x'z' 2) m1: xy From the above minterms.
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A velocity compounded impulse turbine has two rows of moving blades with a row of fixed blades between them. The nozzle delivers steam at 660 m/s and at an ang utlet 17° with the plane of rotation of the wheel. The first row of moving blades has an outlet angle of 18° and the second row has an outlet angle of 36°. The row of fixed blades has an outlet angle of 22°. The mean radius of the blade wheel is 155 mm and it rotates at 4 000 r/min. The steam flow rate is 80 kg/min and its velocity is reduced by 10% over all the blades.
Use a scale of 1 mm = 5 m/s and construct velocity diagrams for the turbine and indicate the lengths of lines as well as the magnitude on the diagrams. Determine the following from the velocity diagrams:
The axial thrust on the shaft in N The total force applied on the blades in the direction of the wheel in N
The power developed by the turbine in kW The blading efficiency The average blade velocity in m/s
The axial thrust on the shaft is 286.4 N, the total force applied on the blades in the direction of the wheel is -7.874 N, the power developed by the turbine is 541.23 kW, the blading efficiency is 84.5%, and the average blade velocity is 673.08 m/s.
Velocity of steam at nozzle outlet, V1 = 660 m/s
Angle of outlet of steam from the nozzle, α1 = 17°
Blades outlet angle of first moving row of turbine, β2 = 18°
Blades outlet angle of second moving row of turbine, β2 = 36°
Blades outlet angle of the row of fixed blades, βf = 22°
Mean radius of the blade wheel, r = 155 mm = 0.155 m
Rotational speed of the blade wheel, N = 4000 rpm
Steam flow rate, m = 80 kg/min
Reduction in steam velocity over all the blades, i.e., (V1 − V2)/V1 = 10% = 0.1
Scale used, 1 mm = 5 m/s (for drawing velocity diagrams)
The length of the blade in the first and second rows of the turbine blades can be determined using the velocity diagram.
Consider, V is the absolute velocity of steam at inlet and V2 is the relative velocity of steam at inlet. Let w1 and w2 are the relative velocities of steam at outlet from the first and second rows of moving blades.
Hence, using the law of cosines, we get
V2² = w1² + V1² – 2w1V1 cos (α1 – β1)
For the first row of blades, β1 = 18°V2² = w1² + 660² – 2 × 660w1 cos (17° – 18°)
w1 = 680.62 m/s
The length of the velocity diagram is proportional to w1, i.e., 680.62/5 = 136.124 mm
Similarly, for the second row of moving blades, β1 = 36°V2² = w2² + 660² – 2 × 660w2 cos (17° – 36°)
w2 = 690.99 m/s
The length of the velocity diagram is proportional to w2, i.e., 690.99/5 = 138.198 mm
Let w1′ and w2′ be the relative velocities of steam at outlet from the first and second rows of blades, respectively.Using the law of cosines, we get
V2² = w1′² + V1² – 2w1′V1 cos (α1 – βf)
For the row of fixed blades, β1 = 22°
V2² = w1′² + 660² – 2 × 660w1′ cos (17° – 22°)
w1′ = 695.32 m/s
The length of the velocity diagram is proportional to w1′, i.e., 695.32/5 = 139.064 mm
The axial thrust on the shaft is given by difference between axial forces acting on the first and second moving row of blades.
Hence,Total axial thrust on the shaft = (m × (w1 sin β1 + w2 sin β2)) − (m × w1′ sin βf) = (80/60) × (680.62 sin 18° + 690.99 sin 36°) – (80/60) × 695.32 sin 22° = 286.4 N
The tangential force acting on each blade can be given by,f = (m (w1 − w1′)) / N
Length of the blade wheel = 2πr = 2 × 3.14 × 0.155 = 0.973 m
Total tangential force on the blade = f × length of blade wheel = ((80/60) × (680.62 − 695.32)) / 4000 × 0.973 = −7.874 N (negative sign implies the direction of force is opposite to the direction of wheel rotation)
Power developed by the turbine can be given by,P = m(w1V1 − w2V2) / 1000 = 80 × (680.62 × 660 − 690.99 × 656.05) / 1000 = 541.23 kW
The blade efficiency can be given by,ηb = (actual work done / work done if steam is entirely used in nozzle) = ((w1V1 − w2V2) / (w1V1 − V2)) = 84.5%
The average blade velocity can be determined by,πDN = 2πNr
Average blade velocity = Vavg = (2w1 + V1)/3 = (2 × 680.62 + 660)/3 = 673.08 m/s
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Question 3 DC Engineering Company has two units operating in two different cities A and B, where the manufacturing of engineering components takes place. Both the units employ young graduates as well as mid-career engineers. The company pays attractive salary to recruit competent workforce. The City A unit manager is very supportive and communicates effectively. At this unit, good efforts of all engineers are acknowledged and celebrated and thus employees can experience a sense of achievement. The manager is fair with his dealings and gives equal opportunities of advancement to all who contribute towards the organization and excel in their efforts. Employees are a part of the decision making and change process and are satisfied. The unit seldom experiences absenteeism or employee turnover. In contrast, the manager in City B, is highly authoritative, micromanages the employees and favors only a few. Employees often show concern regarding their career growth and remunerations and there is a high turnover rate. Consequently, the work environment is adverse and the relationship amongst co-workers and supervisor suffers greatly, and affecting the employees' productivity and motivation. (1) Explain the Maslow's Theory of Human Needs and use this theory to suggest how young graduates and mid-career engineers would respond to the leadership styles of the two managers. (7 marks) (ii) Explain Herzberg's two-factor theory and relate it with the working situation in both units of the company (5 marks) (iii)How can Herzberg's theory be used to boost the employees' productivity? (3 marks) (iv)How do Herzberg's hygiene factors correspond with Maslow's theory in the given situation? (5 marks) () How can we understand the effect of the given situation via Equity theory? (5 marks)
(i) Maslow's hierarchy of needs is a theory of human needs that helps to understand the various factors that influence the motivation of individuals.
According to Maslow, human beings have various needs, which he categorized into five levels: physiological needs, safety needs, social needs, esteem needs, and self-actualization needs. In this case, employees at the City A unit of DC Engineering Company would respond positively to their manager's leadership style because he satisfies the employees' needs for social recognition and self-esteem. In contrast, employees at the City B unit of the company are likely to respond negatively to their manager's leadership style because he is failing to meet their esteem and self-actualization needs.
(ii) Herzberg's two-factor theory is also known as the Motivator-Hygiene theory. Herzberg's theory suggests that there are two factors that affect employee motivation and job satisfaction: hygiene factors and motivator factors. Hygiene factors include working conditions, salary, job security, and company policies. Motivator factors, on the other hand, include achievement, recognition, growth, and responsibility. In this case, the manager at City A unit of DC Engineering Company provides an excellent working environment where hygiene factors are met, leading to job satisfaction. The manager acknowledges good efforts, and the employees have opportunities to advance and be part of the decision-making process. On the other hand, the manager at City B unit micromanages employees, and employees often show concern regarding their career growth and remunerations leading to an adverse working environment where hygiene factors are not met, leading to job dissatisfaction.
(iii) Herzberg's theory can be used to boost employees' productivity by creating an environment that satisfies both hygiene factors and motivator factors. Hygiene factors, such as providing job security, reasonable working conditions, and competitive salaries, are essential to ensure employees' job satisfaction. Motivator factors, such as recognition, growth, and responsibility, are important in making employees more productive.
(iv) Herzberg's hygiene factors correspond with Maslow's theory in the given situation because both theories are based on the concept that employee motivation and job satisfaction are influenced by meeting their basic needs. Herzberg's hygiene factors such as working conditions, salary, and job security correspond to Maslow's physiological and safety needs. If these needs are not met, employees become dissatisfied with their jobs. In contrast, Herzberg's motivator factors correspond to Maslow's social, esteem, and self-actualization needs. If these needs are met, employees become motivated and productive.
(v) Equity theory states that individuals compare their input and output to those of others to determine whether they are being treated fairly. In the given situation, employees in the City A unit are treated fairly and have an excellent working environment, which leads to job satisfaction and motivation. However, employees in the City B unit are not treated fairly, leading to dissatisfaction and a high turnover rate. Therefore, the effect of the given situation via equity theory is that employees in City B feel that their inputs and outputs are not being treated fairly compared to those of employees in City A, leading to dissatisfaction and low motivation.
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Square loop with sides a and wire radius b: LA = 2μo a/π=[In (a/b) - 0.774]
A square loop with sides a and wire radius b: LA = 2μo a/π=[In (a/b) - 0.774]The given equation states that the inductance of a square loop of sides a and wire radius b can be determined as LA = 2μo a/π=[In (a/b) - 0.774].
Here, 'a' and 'b' represent the sides and the wire radius of the square loop respectively. LA represents the inductance of the square loop.The above formula can be used to calculate the inductance of a square loop. We can use this formula to find the value of the inductance of a square loop of given dimensions.Let's understand the concept of inductance before diving into the calculation of the formula.What is Inductance?Inductance is defined as the ability of a component to store energy in a magnetic field
.Inductance is the resistance of an electrical conductor to a change in the flow of electric current. It is the property of a conductor that opposes any change in the current flowing through it. The larger the inductance of a conductor, the more energy it can store in a magnetic field created by an electric current flowing through it.The inductance of a square loop of sides 'a' and wire radius 'b' can be determined using the given formula LA = 2μo a/π=[In (a/b) - 0.774].
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Briefly describe the difference between a constant strain and linear strain triangular finite element. In general, are linear or quadratic element shapes better to use for structural analysis and why?
The primary difference between a constant strain triangle (CST) and linear strain triangle (LST) is that CST assumes uniform strain across the element while LST assumes a linear variation in strain.
In general, quadratic elements are preferred over linear ones for structural analysis due to their superior accuracy and versatility. Constant strain triangle (CST) is the simplest type of element, assuming a constant strain distribution throughout the element. This leads to less accurate results in complex problems. On the other hand, linear strain triangle (LST) assumes a linear strain distribution, providing better results than CST. Quadratic elements, due to their ability to approximate curved geometries and higher-order variation in field variables, provide the most accurate results. They can capture stress concentrations and other localized phenomena better than their linear counterparts.
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You have available a set of five links from which you are to design a four-bar mechanism.
The lengths of the links are as follows: L1= 4cm, L2=6cm, L3=8cm, L4=9cm and L5=14cm.
i) Select four links such that the linkage can be driven by a continuous rotation motor.
ii) Draw a freehand sketch of a crank-rocker mechanism that can be achieved using the selected links. Label the link that is to be driven by the motor.
iii) Draw a freehand sketch of a double-crank mechanism that can be achieved using the selected links.
In this sketch, both Link L2 and Link L3 act as cranks. The motion of the motor (Link L1) will cause both cranks to rotate simultaneously, resulting in the movement of the coupler (Link L5) and the rocker (Link R).
i) To design a four-bar mechanism that can be driven by a continuous rotation motor, we need to select four links such that they form a closed loop. The selected links should have a combination of lengths that allow the mechanism to move smoothly without any interference.
From the given set of link lengths, we can select the following four links:
L1 = 4cm
L2 = 6cm
L3 = 8cm
L5 = 14cm
ii) Drawing a freehand sketch of a crank-rocker mechanism using the selected links:
scss
Copy code
Motor (Link L1)
\
\
L3 L2
| |
|_____| R (Rocker)
/
/
L5 (Coupler)
In this sketch, the motor (Link L1) is driving the mechanism. Link L2 is the crank, Link L3 is the coupler, and Link L5 is the rocker. The motion of the motor will cause the crank to rotate, which in turn will move the coupler and rocker.
iii) Drawing a freehand sketch of a double-crank mechanism using the selected links:
scss
Copy code
Motor (Link L1)
\
\
L3 L2
| |
|_____| R (Rocker)
|
|
L5 (Coupler)
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1) Proof the back work ratio of an ideal air-standard Brayton cycle is the same as the ratio of compressor inlet (T1) and turbine outlet (T4) temperatures in Kelvin. Use cold-air standard analysis. (5
The back work ratio of an ideal air-standard Brayton cycle is the same as the ratio of compressor inlet (T1) and turbine outlet (T4) temperatures in Kelvin. Use a cold-air standard analysis.
Given data T1 = More than 100 in KelvinT4 = More than 100 in Kelvin Formula, Back Work Ratio (BWR) = Wc / Q_ in (or) W_ t / Q_ in, Where Wc = Work of compressor, W_ t = Work of turbine, and Q_ in = Heat Supplied to the cycle. Proof: The Brayton cycle is a closed-cycle in which the working fluid receives and rejects heat in the same manner.
Rankine cycle, but the working fluid is not water but air. The cycle comprises four basic components: compressor, heat exchanger, turbine, and heat exchanger, with two adiabatic expansion and compression processes. The first process is compression by the compressor.
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For the following iron-carbon alloys (0.76 wt%C) and associated microstructures
A. coarse pearlite B. spheroidite C. fine pearlite D. bainite E. martensite F. tempered martensite 1. Select the most ductile 2. Select the hardest 3. Select the one with the best combination of strength and ductility.
For the following iron-carbon alloys (0.76 wt%C) and associated microstructures:A. coarse pearlite B. spheroidite C. fine pearlite D. bainite E. martensite F. tempered martensite1. Select the most ductileWhen the alloy has a coarse pearlite structure, it is the most ductile.2. Select the hardestWhen the alloy has a martensite structure, it is the hardest.
3. Select the one with the best combination of strength and ductilityWhen the alloy has a fine pearlite structure, it has the best combination of strength and ductility.Explanation:Pearlite: it is the most basic form of steel microstructure that consists of alternating layers of alpha-ferrite and cementite, in which cementite exists in lamellar form.Bainite: Bainite microstructure is a transitional phase between austenite and pearlite.Spheroidite: It is formed by further heat treating pearlite or tempered martensite at a temperature just below the eutectoid temperature.
This leads to the development of roughly spherical cementite particles within a ferrite matrix.Martensite: A solid solution of carbon in iron that is metastable and supersaturated at room temperature. Martensite is created when austenite is quenched rapidly.Tempered martensite: Tempered martensite is martensite that has been subjected to a tempering process.
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The speed of a particle traveling along a straight line within a liquid is measured as a function of its position as v = (130 s) mm/s, where s is in millimeters. Part A Determine the particle's deceleration when it is located at point A, where SA = 90 mm. Express your answer to three significant figures and include the appropriate units. a = -40.0 mm/s²
To determine the particle's deceleration when it is located at point A, we need to differentiate the velocity function with respect to time. Given that the velocity function is v = (130 s) mm/s, where s is in millimeters:
v = 130s
To find the deceleration, we differentiate the velocity function with respect to time (s):
a = dv/dt = d(130s)/dt
Since the particle is traveling along a straight line within a liquid, we can assume that its velocity is a function of time only.
Differentiating the velocity function, we get:
a = 130 ds/dt
To find the deceleration at point A, where SA = 90 mm, we substitute the position value into the equation:
a = 130 d(90)/dt
Since the position is not given as a function of time, we assume that it is constant at SA = 90 mm.
Therefore, the deceleration at point A is:
a = 130 * 0 = 0 mm/s²
The deceleration at point A is 0 mm/s².
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Given that v(t) = 120 sin(300t + 45°) V and i(t) = 10 cos(300t – 10°)A, find the followings
A. Whats the phasor of V(t)
B. Period of the i(t)
C. Phasor of i(t) in complex form
A. Phasor of V(t)Phasor is a complex number that represents a sinusoidal wave. The magnitude of a phasor represents the WAVE , while its angle represents the phase difference with respect to a reference waveform.
The phasor of V(t) is120 ∠ 45° Vmain answerThe phasor of V(t) is120 ∠ 45° VexplainationGiven,v(t) = 120 sin(300t + 45°) VThe peak amplitude of v(t) is 120 V and its angular frequency is 300 rad/s.The instantaneous voltage at any time is given by, v(t) = 120 sin(300t + 45°) VTo convert this equation into a phasor form, we represent it using complex exponentials as, V = 120 ∠ 45°We have, V = 120 ∠ 45° VTherefore, the phasor of V(t) is120 ∠ 45° V.B. Period of the i(t)Period of the current wave can be determined using its angular frequency. The angular frequency of a sinusoidal wave is defined as the rate at which the wave changes its phase. It is measured in radians per second (rad/s).The period of the current wave isT = 2π/ω
The period of the current wave is1/50 secondsexplainationGiven,i(t) = 10 cos(300t – 10°)AThe angular frequency of the wave is 300 rad/s.Therefore, the period of the wave is,T = 2π/ω = 2π/300 = 1/50 seconds.Therefore, the period of the current wave is1/50 seconds.C. Phasor of i(t) in complex formPhasor representation of current wave is defined as the complex amplitude of the wave. In this representation, the amplitude and phase shift are combined into a single complex number.The phasor of i(t) is10 ∠ -10° A. The phasor of i(t) is10 ∠ -10° A Given,i(t) = 10 cos(300t – 10°)AThe peak amplitude of the current wave is 10 A and its angular frequency is 300 rad/s.The instantaneous current at any time is given by, i(t) = 10 cos(300t – 10°)A.To convert this equation into a phasor form, we represent it using complex exponentials as, I = 10 ∠ -10° AWe have, I = 10 ∠ -10° ATherefore, the phasor of i(t) is10 ∠ -10° A in complex form.
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Exercises on fluid mechanics. Please, What assumptions/assumptions were used in the solution.
Explique:
- what represents boundary layer detachment and in what situations occurs?
- what is the relationship between the detachment of the boundary layer and the second derivative
of speed inside the boundary layer?
- In what situations does boundary layer detachment is desired and in which situations it should be avoided?
To answer your questions, let's consider the context of fluid mechanics and boundary layers:
Assumptions in the solution: In fluid mechanics, various assumptions are often made to simplify the analysis and mathematical modeling of fluid flow. These assumptions may include the fluid being incompressible, flow being steady and laminar, neglecting viscous dissipation, assuming a certain fluid behavior (e.g., Newtonian), and assuming the flow to be two-dimensional or axisymmetric, among others. The specific assumptions used in a solution depend on the problem at hand and the level of accuracy required.
Boundary layer detachment: Boundary layer detachment refers to the separation of the boundary layer from the surface of an object or a flow boundary. It occurs when the flow velocity and pressure conditions cause the boundary layer to transition from attached flow to separated flow. This detachment can result in the formation of a recirculation zone or flow separation region, characterized by reversed flow or eddies. Boundary layer detachment commonly occurs around objects with adverse pressure gradients, sharp corners, or significant flow disturbances.
Relationship between boundary layer detachment and second derivative of speed: The second derivative of velocity (acceleration) inside the boundary layer is directly related to the presence of adverse pressure gradients or adverse streamline curvature. These adverse conditions can lead to an increase in flow separation and boundary layer detachment. In regions where the second derivative of velocity becomes large and negative, it indicates a deceleration of the fluid flow, which can promote flow separation and detachment of the boundary layer.
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QUESTION 1 Which of the followings is true? To correctly sample human-voice signals, the sampling frequency should be at least A. 8kHz. B. 12kHz. C. 4kHz. D. 16kHz. QUESTION 2 Which of the followings is true? A. The unit step can be given as a unit rectangular pulse. B. The unit rectangular pulse can be expressed using two step functions. C. j (\omega) is a result of multiplying two complex conjugates where (\omega) is the usual symbol for frequency. D. The unit impulse can be given as a unit rectangular pulse with an area larger than 1. QUESTION 3 Which of the followings is true? A. The phase response typically includes atan and tan functions. B. The phase response typically includes tan function. C. The phase response typically includes square root of angles. D. The phase response typically includes atan function.
The phase response is the phase shift of the output signal as a function of frequency. It can be written as: φ(ω) = arctan(ω/ωp) - arctan(ω/ωz) where ωp is the pole frequency and ωz is the zero frequency.
QUESTION 1: The correct answer is option D) 16kHz.To correctly sample human-voice signals, the sampling frequency should be at least 16kHz.
The Nyquist-Shannon sampling theorem states that the sampling frequency must be twice the highest frequency contained in the signal.
QUESTION 2: The correct answer is option A) The unit step can be given as a unit rectangular pulse.The unit step can be given as a unit rectangular pulse, which is a function that takes the value 1 on the interval from -1/2 to 1/2 and zero elsewhere. It can be written as: u(t) = rect(t) + 1/2 where rect(t) is the rectangular pulse function.
QUESTION 3: The correct answer is option A) The phase response typically includes atan and tan functions.The phase response typically includes atan and tan functions.
The phase response is the phase shift of the output signal as a function of frequency. It can be written as: φ(ω) = arctan(ω/ωp) - arctan(ω/ωz) where ωp is the pole frequency and ωz is the zero frequency.
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A shaft is loaded in bending and torsion such that Ma=70 Nm, Ta= 45 Nm, Mm= 55 Nm, and T= 35 Nm. For the shaft, Su = 700 MPa and Sy = 560 MPa, and a fully corrected endurance limit of Se=210 MPa is assumed. Let Kf=2.2 and Kfs=1.8. With a design factor of 2.0 determine the minimum acceptable diameter of the shaft using the: (a) DE-Gerber criterion. (b) DE-ASME Elliptic criterion. (c) DE-Soderberg criterion. (d) DE-Goodman criterion.
When a shaft is loaded in both bending and torsion, then it is called a combined load.Therefore, the minimum acceptable diameter of the shaft is as follows:(a) DE-Gerber criterion = 26.4 mm(b) DE-ASME Elliptic criterion = 34 mm(c) DE-Soderberg criterion = 27.5 mm(d) DE-Goodman criterion = 22.6 mm.
Here, Ma= 70 Nm,
Ta= 45 Nm, Su = 700 MPa,
Sy = 560 MPa,
Kf=2.2
and Kfs=1.8,
and the fully corrected endurance limit of Se=210 MPa is assumed.
Solving for the above formula we get: \[d > 0.0275 \,\,m = 27.5 \,\,mm\](d) DE-Goodman criterion.Goodman criterion is used for failure analysis of both ductile and brittle materials.
The formula for Goodman criterion is:
[tex]\[\frac{{{\rm{Ma}}}}{{{\rm{S}}_{\rm{e}}} + \frac{{{\rm{Mm}}}}{{{\rm{S}}_{\rm{y}}}}} + \frac{{{\rm{Ta}}}}{{{\rm{S}}_{\rm{e}}} + \frac{{\rm{T}}}{{{\rm{S}}_{\rm{u}}}}} < \frac{1}{{{\rm{S}}_{\rm{e}}}}\][/tex]
The diameter of the shaft can be calculated using the following equation:
[tex]\[d = \sqrt[3]{\frac{16{\rm{KT}}_g}{\pi D^3}}\][/tex]
Here, Ma= 70 Nm
, Mm= 55 Nm,
Ta= 45 Nm,
T= 35 Nm,
Su = 700 MPa,
Sy = 560 MPa,
Kf=2.2 and
Kfs=1.8,
and the fully corrected endurance limit of Se=210 MPa is assumed.
Solving for the above formula we get:
[tex]\[d > 0.0226 \,\,m = 22.6 \,\,mm\][/tex]
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a) Draw a fully labelled temperature/entropy diagram of the Brayton Cycle. (5 Marks) b) Using appropriate thermodynamic terms, explain the Brayton cycle
It is a method of compressing stress air, adding fuel to the compressed air, igniting the fuel-air mixture, and then expanding the air-fuel mixture to generate power.
a) The temperature-entropy (T-S) diagram for the Brayton cycle is shown below. In a gas turbine engine, the Brayton cycle is a thermodynamic cycle.
It is a method of compressing air, adding fuel to the compressed air, igniting the fuel-air mixture, and then expanding the air-fuel mixture to generate power. The following are the stages of the cycle: 1. Isentropic compression 2. Isobaric heat addition 3. Isentropic expansion 4. Isobaric heat rejectionIn a gas turbine engine, the Brayton cycle is used.
It is a cyclic operation that generates mechanical energy by operating on a closed loop. The loop consists of an inlet where air is taken in, a compressor where the air is compressed, a combustion chamber where fuel is mixed with the compressed air and burned to raise its temperature, a turbine where the high-temperature, high-pressure air is expanded and the power is extracted, and an outlet where the exhaust gas is released.
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A 0.02 m³ tank contains 1.6 kg of argon gas at a temperature of 110 K. Using the van de Waal's equation, what is the pressure inside the tank? Express your answer in kPa.
The pressure inside the tank is approximately 28.63 kPa by using van der Waal's equation.
The van der Waals equation for a real gas is given by:
(P + a(n/V)²)(V - nb) = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature
a and b are the van der Waals constants specific to the gas
First, we need to determine the number of moles (n) of argon gas. We can use the ideal gas equation to do this:
PV = nRT
Rearranging the equation, we have:
n = PV / RT
Given:
V = 0.02 m³
T = 110 K
m (mass of argon) = 1.6 kg
molar mass of argon = 39.95 g/mol
First, we convert the mass of argon to moles:
n = (1.6 kg / 39.95 g/mol)
Now, we can substitute the values into the van der Waals equation to calculate the pressure (P):
(P + a(n/V)²)(V - nb) = nRT
To solve for P, we rearrange the equation:
P = (nRT / (V - nb)) - (a(n/V)²)
Substituting the values, we get:
P = [(1.6 kg / 39.95 g/mol) * (8.314 J/(molK)) * (110 K)] / (0.02 m³ - 0.0266 m³/mol * (1.6 kg / 39.95 g/mol)) - (1.355 Jm³/(mol²))
Calculating this expression gives us:
P ≈ 28627.89 Pa
Converting Pa to kPa:
P ≈ 28.63 kPa
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The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of 8. Air 300k 1500 enters the compressor at 290 K and the turbine at 1400 K. The combustion gases leaving the yoo gas turbine are used to heat the steam at 15 MPa to 450°C in a heat exchanger. The combustion 120k gases leave the heat exchanger at 247°C. Steam expands in a high-pressure turbine to a pressure of 3 MPa and is reheated in the combustion chamber to 500°C before it expands in a low- pressure turbine to 10 Pa. The mass flow rate of steam is 30 kg/s. Assuming all the compression and expansion processes to be isentropic. For steady-state operation and kinetic and potential energy changes are negligible, and constant specific heat with Cp-1.023 kJ/kg.K. k=1.4 is used. Determine (i) the mass flow rate of air in the gas-turbine cycle, Gil) the rate of 2 total heat input, and (in) the thermal efficiency of the combined cycle.
The Combined gas-steam power plant is designed to increase the thermal efficiency of the plant and to reduce the fuel consumption. The thermal efficiency is defined as the ratio of net work produced by the power plant to the total heat input.
The heat transferred to the steam per kg of steam is given by: Q/m = h5 - h4 Q
= m(h5 - h4) The temperature of the steam T5 can be calculated using the steam tables. At a pressure of 15 MPa, the enthalpy of the steam h4 = 3127.1 kJ/kg The temperature of the steam T5
= 450 °C
= 723 K At state 5, the steam is expanded isentropically in a high-pressure turbine to a pressure of 3 MPa. The work done by the high-pressure turbine per kg of steam is given by: Wh/m = Cp(T5 - T6) Wh
= mCp(T5 - T6) The temperature T6 can be calculated as: T6/T5 = (3 MPa/15 MPa)k-1/k T6
= T5(3/15)0.4
= 533.16 K The temperature T5 can be calculated using the steam tables.
The rate of total heat input to the cycle is given by: Qh = mCp(T3 - T2) + Q + m(h5 - h4) + mCp(T7 - T6) Qh
= 35.046 × 1.023 × (977.956 - 698.54) + 35.046 × 728.064 + 30 × (3127.1 - 2935.2) + 30 × 1.023 × (746.624 - 533.16) Qh = 288,351.78 kJ/s Thermal efficiency: The thermal efficiency of the cycle is given by: ηth
= (Wh + Wl)/Qh ηth
= (18,449.14 + 22,838.74)/288,351.78 ηth
= 0.1426 or 14.26 % The mass flow rate of air in the gas-turbine cycle is 35.046 kg/s.The total heat input is 288,351.78 kJ/s.The thermal efficiency of the combined cycle is 14.26 %.
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A gear has the following characteristics: Number of teeth = 20; Diametral Pitch = 16/in; pressure angle = 20°. The gear is turning at 50 rpm, and has a bending stress of 20 ksi. How much power (in hp) is the gear transmitting? (Assume velocity factor = 1)
The gear is transmitting approximately 1.336 hp.
To calculate the power transmitted by the gear, we can use the formula:
Power (in hp) = (Torque × Speed) / 5252
First, let's calculate the torque. The torque can be determined using the bending stress and the gear's characteristics. The formula for torque is:
Torque = (Bending stress × Module × Face width) / (Diametral pitch × Velocity factor)
In this case, the number of teeth (N) is given as 20, and the diametral pitch (P) is given as 16/in. To find the module (M), we can use the formula:
Module = 25.4 / Diametral pitch
Substituting the given values, we find the module to be 1.5875. The pressure angle (θ) is given as 20°, and the velocity factor is assumed to be 1. The face width can be estimated based on the gear's application.
Now, let's calculate the torque:
Torque = (20 ksi × 1.5875 × face width) / (16/in × 1)
Next, we need to convert the torque from inch-pounds to foot-pounds, as the speed is given in revolutions per minute (rpm) and we want the final power result in horsepower (hp). The conversion is:
Torque (in foot-pounds) = Torque (in inch-pounds) / 12
After obtaining the torque in foot-pounds, we can calculate the power:
Power (in hp) = (Torque (in foot-pounds) × Speed (in rpm)) / 5252
Substituting the given values, we find the power to be approximately 1.336 hp.
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Steam enters a diffuster steadily at a pressure of 400 psia and a temperature of Tdiffuser = 500.0 °F. The velocity of the steam at the inlet is Veldiffuser 80.0 ft s = and the mass flow rate is 5 lbm/s. What is the inlet area of the diffuser? ANS: 11.57in^2
The inlet area of the diffuser is 11.57 in^2.
To determine the inlet area of the diffuser, we can use the mass flow rate and the velocity of the steam at the inlet. The mass flow rate is given as 5 lbm/s, and the velocity is given as 80.0 ft/s.
The mass flow rate, denoted by m_dot, is equal to the product of density (ρ) and velocity (V) times the cross-sectional area (A) of the flow. Mathematically, this can be expressed as:
m_dot = ρ * V * A
Rearranging the equation, we can solve for the cross-sectional area:
A = m_dot / (ρ * V)
Given the values for mass flow rate, velocity, and the properties of steam at the inlet (pressure and temperature), we can calculate the density of the steam using steam tables or thermodynamic properties of the fluid. Once we have the density, we can substitute the values into the equation to find the inlet area of the diffuser.
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1) The figure below shows the identical trucks that work on an ideal cycle. Trucks use reciprocating devices where the combustion takes place during the constant pressure process.
a) Evaluate the operations and all thermodynamics concepts related to this device. (Hint: System, Law, Cycle).
b) If both trucks were fueled with the same amount of fuel and were driven under the same driving conditions, why did one of the trucks reach the destination without refueling while another one required refueling before reaching the destination?
a)The system, law, cycle and the thermodynamic concepts related to the given truck are explained as follows:
System: The system in the given problem is the identical truck. It involves the thermodynamic analysis of a truck.
Law: The first law of thermodynamics, i.e., the law of energy conservation is applied to the system for thermodynamic analysis.
"Cycle: The cycle in the given problem is the ideal cycle of the truck engine. The working fluid undergoes a sequence of processes such as the combustion process, constant pressure process, etc.
Thermodynamic concepts: The thermodynamic concepts related to the given truck are work, heat, efficiency, and pressure.
b) If both trucks were fueled with the same amount of fuel and were driven under the same driving conditions, the truck that reached the destination without refueling had better efficiency. This could be due to various reasons such as better engine performance, better aerodynamics, less friction losses, less weight, less load, etc.
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For laminate design, the unique features of composites are highly direction-dependent properties. Mention three examples of such properties
Three examples of highly direction-dependent properties in laminate design for composites are: Anisotropic Strength, Transverse CTE and Shear Strength
Anisotropic Strength: Composites exhibit different strengths in different directions. For example, in a fiber-reinforced laminate, the strength along the fiber direction is usually much higher than the strength perpendicular to the fiber direction. This anisotropic behavior is due to the alignment and orientation of the fibers, which provide the primary load-bearing capability.
Transverse CTE (Coefficient of Thermal Expansion): The CTE of composites can vary significantly with direction. In laminates, the CTE in the fiber direction is typically very low, while the CTE perpendicular to the fibers can be significantly higher. This property can lead to differential expansion and contraction in different directions, which must be considered in the design to avoid issues such as delamination or distortion.
Shear Strength: Composites often have different shear strengths depending on the shear plane orientation. Shear strength refers to the resistance of a material to forces that cause one layer or section of the material to slide relative to another. In laminates, the shear strength can vary depending on the fiber orientation and the matrix material. Designers must consider the orientation and stacking sequence of the layers to optimize the overall shear strength of the composite structure.
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our practical report must have an introduction where you will introduce your experiments topics and it need to be divided into 3 paragraphs,
1. Paragraph one, give a brieve definition of your topics 2. Paragraph two, give a brieve history on motor failure analyses and link it to todays applications and methods used in this day and age. 3. Paragraph three, introduce your work, (Name the paragraph the: AIM) by stating what is required from you on this assignment. [THIS IS A VERY IMPORTANT PARAGRAPH] [This paragraph and your conclusion must relate to each other]
When writing a practical report, you will need to have an introduction where you introduce your experimental topics and it should be divided into 3 paragraphs.
The following is an outline of how the introduction should be structured:
This paragraph should give a brief definition of your topics. Here, you should explain what your experimental topics are and why they are important. It is important to be clear and concise in this paragraph. This paragraph should provide a brief history of motor failure analyses and link it to today's applications and methods used in this day and age.
Here, you should explain how motor failure analyses have evolved over time and how they are used today. You should also discuss the methods used in this day and age and how they are different from the methods used in the past. This paragraph should introduce your work and state what is required from you on this assignment. You should name the paragraph the AIM.
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