The domain expression for the given forward transfer function of the system are found using the steady state error (SSE).
3.1. Steady state error (SSE) is defined as the error between the actual output of a system and the desired output when the system reaches steady state, and the input signal is constant. The steady-state error can be expressed in both time domain and S domain as follows:
Time domain expression:
SSE(t) = lim (t → ∞) [r(t) - y(t)]
where r(t) is the reference input signal and
y(t) is the output signal.
S domain expression:
SSE = lim (s → 0) [1 - G(s)H(s)]R(s)
where R(s) is the Laplace transform of the reference input signal and
H(s) is the transfer function of the closed-loop control system.
3.3. Given forward transfer function of the system,
G(s) = ((8S+16) (S+24)) / (S³+6S²+24S)
Standard test input signals are,1.
Step input signal: R(s) = 1/s2.
Ramp input signal: R(s) = 1/s23.
Parabolic input signal: R(s) = 1/s3
Using the formula, the steady-state error of a unity feedback system is,
SSE = 1 / (1 + Kv)
1. Steady state error for step input signal:
SSE = 1/1+1/16
= 16/17
= 0.94
2. Steady state error for ramp input signal:
SSE = ∞3.
Steady state error for parabolic input signal: SSE = ∞3.
4. The specification of K_v = 250 provides information about the system's ability to track a constant reference input. The velocity error constant, K_v, defines the system's steady-state response to a constant velocity input signal.
The higher the value of K_v, the smaller the steady-state error for a given input signal, which means the system's response to changes in the input signal is faster.
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Tank B is enclosed inside Tank A. Given the Absolute pressure of tank A = 400 kPa, Absolute pressure of tank B = 300 kPa, and atmospheric pressure 100 kPa.
Find the gauge pressure reading of Tank A in kPa
The gauge pressure reading of Tank A in kPa is 300 kPa.
B is enclosed inside Tank A, Absolute pressure of tank A is 400 kPa, Absolute pressure of tank B is 300 kPa, and atmospheric pressure is 100 kPa.
The question asks us to find the gauge pressure reading of Tank A in kPa. Here, the gauge pressure of tank A is the pressure relative to the atmospheric pressure. The gauge pressure is the difference between the absolute pressure and the atmospheric pressure.
We can calculate the gauge pressure of tank A using the formula: gauge pressure = absolute pressure - atmospheric pressure Given that the absolute pressure of tank A is 400 kPa and atmospheric pressure is 100 kPa, the gauge pressure of tank A is given by gauge pressure = 400 kPa - 100 kPa= 300 kPa
Therefore, the gauge pressure reading of Tank A in kPa is 300 kPa.
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Example 20kw, 250V, 1000rpm shunt de motor how armature and field. resistances of 0,22 and 2402. When the HOA rated current at motor takes raded conditions. a) The rated input power, rated output power, and efficiency. Generated vo Hagl <) Induced torque. d) Total resistance arent to current. of 1,2 times Ox. 1200rpm. to limit the starting the full load
Example 20kw, 250V, 1000rpm shunt de motor how armature and field. resistances of 0,22 and 2402. When the HOA rated current at motor takes raded conditions. a) The rated input power, rated output power, and efficiency. Generated vo Hagl <) Induced torque. d) Total resistance arent to current. of 1,2 times Ox. 1200rpm. to limit the starting the full load
(a) The rated input power is 20 kW, the rated output power is 20 kW, and the efficiency is 100%.
(b) The generated voltage is 250 V.
(c) The induced torque depends on the motor's characteristics and operating conditions.
(d) The total resistance is not specified in the given information.
(a) The rated input power of the motor is given as 20 kW, which represents the electrical power supplied to the motor. Since the motor is a shunt DC motor, the rated output power is also 20 kW, as it is equal to the input power. Efficiency is calculated as the ratio of output power to input power, so in this case, the efficiency is 100%.
(b) The generated voltage of the motor is given as 250 V. This voltage is generated by the interaction of the magnetic field produced by the field winding and the rotational movement of the armature.
(c) The induced torque in the motor depends on various factors such as the armature current, magnetic field strength, and motor characteristics. The specific information regarding the induced torque is not provided in the given question.
(d) The total resistance mentioned in the question is not specified. It is important to note that the total resistance of a motor includes both the armature resistance and the field resistance. Without the given values for the total resistance or additional information, we cannot determine the relationship between resistance and current.
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The manufacturer of a component that will be subjected to fatigue from -0 MPa to 50 MPa, specifies that it must be changed when it has been detected that the crack has advanced up to 40% of its critical value. The manufacturing process of the component leaves cracks on the surface of 0.1mm. The material has the following properties: KIC = 70MPam1/2 and crack growth is characterized by n=3.1 and C= 10E-11. Assume f=1.12.
How many life cycles did the component have left after it had been removed as directed by the manufacturer?
Indicate your answer without decimals.
Fatigue is the weakening of a material caused by cyclic loading, resulting in the formation and propagation of cracks.
Fatigue fracture failure is a type of failure that is caused by cyclic loading, which is the progressive growth of an initial crack until it reaches a critical size and a fracture occurs. In this question, we are given the following information.
The manufacturing process of the component leaves cracks on the surface of 0.1mm.The material has the following properties: [tex]KIC = 70 MPam1/2[/tex], and crack growth is characterized by n = 3.1 and C = 10E-11. Assume f = 1.12.Calculations:In this question.
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BIAS options:
ignoring regression to the mean
underestimation of disjunctive events
overestimation of the probability
availability heuristic
conjunction fallacy
gambler's fallacy 1. For each of the following subjective probability statements, identify the error or bias and dis- cuss its possible causes. (10 points.) Identification of error or bias (0.5 points) Cause of error or bias (1.5 points) (a) "I put the odds of Poland adopting the Euro as its national currency at 0.4 in the next decade. Yet, I estimate there is a 0.6 chance that Poland will adopt the Euro due to pressure from multinational corporations threatening to relocate their operations to other parts of the world if it doesn't adopt the Euro as its currency within the next 10 years.." (b) "All of the machine's eight critical components need to operate for it to function properly. 0.9% of the time, each critical component will function, and the failure probability of any one component is independent of the failure probability of any other component. As a result, I calculate that the machine will be ready for use by noon tomorrow with an approx- imate chance of 0.85." (c) "Because of the recent spate of airline disasters reported in the media, I believe flying is an unacceptably high risk for next year's sales conference in Dublin. I, therefore, will choose to drive." (d) "Twenty-five years have passed without a serious accident at this production plant. Be- cause such a lengthy time without a big catastrophe is statistically improbable, I am afraid that the next one is imminent, and I encourage all personnel to be extremely alert about safety issues." (e) "A sequence of events led to an increase in iced coffee sales of 4,800,000 liters in July: (a) the bottling machinery of a competitor was momentarily down, (b) this July was the warmest and most sun-drenched in two decades, (c) one of our main coffee products was witnessed being consumed by a celebrity at a news conference, (d) we advertised our product at three big sports events. Consequently, sales have risen remarkably, and I believe we have a better than 99 percent probability of selling at least 4,800,000 liters again in August."
Subjective probability statements and identification of bias(a) "I put the odds of Poland adopting the Euro as its national currency at 0.4 in the next decade.
Yet, I estimate there is a 0.6 chance that Poland will adopt the Euro due to pressure from multinational corporations threatening to relocate their operations to other parts of the world if it doesn't adopt the Euro as its currency within the next 10 years.
"Error or Bias: Overestimation of the probability. Cause of error or bias: This type of bias is caused when the person is influenced by outside forces. It’s a result of pressure from the environment, which has led the person to believe that the chances are higher than they are in reality.
"All of the machine's eight critical components need to operate for it to function properly. 0.9% of the time, each critical component will function, and the failure probability of any one component is independent of the failure probability of any other component.
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Each cell of an automobile 12 volt battery can produce about volts. A) 4.2 B) 4 C) 1.2 D) 2.1
The correct answer is D) 2.1 volts. Each cell of an automobile 12-volt battery typically produces around 2.1 volts.
Automobile batteries are composed of six individual cells, each generating approximately 2.1 volts. When these cells are connected in series, their voltages add up to form the total voltage of the battery. Therefore, a fully charged 12-volt automobile battery consists of six cells, each producing 2.1 volts, resulting in a total voltage of 12.6 volts (2.1 volts x 6 cells).
This voltage level is suitable for powering various electrical components and starting the engine of a typical automobile. It is important to note that the actual voltage may vary slightly depending on factors such as the battery's state of charge and temperature.
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A steel rotor disc of uniform thickness 50mm has an outer rim diameter 800mm and a central hole of diameter 150mm. There are 200 blades each of weight 2N at an effective radius of 420mm pitched evenly around the periphery. Determine the rotational speed at which yielding first occurs according to the maximum shear stress criterion. Yield stress= 750 MPa, v = 0.304, p = 7700 kg/m³.
The rotational speed at which yielding first occurs according to the maximum shear stress criterion is approximately 5.24 rad/s.
To determine the rotational speed at which yielding first occurs according to the maximum shear stress criterion, we can use the following steps:
1. Calculate the total weight of the blades:
Total weight = Number of blades × Weight per blade
= 200 × 2 N
= 400 N
2. Calculate the torque exerted by the blades:
Torque = Total weight × Effective radius
= 400 N × 0.42 m
= 168 Nm
3. Calculate the polar moment of inertia of the rotor disc:
Polar moment of inertia (J) = (π/32) × (D⁴ - d⁴)
= (π/32) × ((0.8 m)⁴ - (0.15 m)⁴)
= 0.02355 m⁴
4. Determine the maximum shear stress:
Maximum shear stress (τ_max) = Yield stress / (2 × Safety factor)
= 750 MPa / (2 × 1) (Assuming a safety factor of 1)
= 375 MPa
5. Use the maximum shear stress criterion equation to find the rotational speed:
τ_max = (T × r) / J
where T is the torque, r is the radius, and J is the polar moment of inertia.
Rearrange the equation to solve for rotational speed (N):
N = (τ_max × J) / T
= (375 × 10⁶ Pa) × (0.02355 m⁴) / (168 Nm)
Convert Pa to N/m² and simplify:
N = 5.24 rad/s
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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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Give the classification of glass? What is Annealing of glass?
The following are some of the classifications of glass based on their chemical composition: Soda-lime silicate glass - It is a widely used type of glass that is made up of silica, sodium oxide, and lime.
Borosilicate glass - This type of glass has a high level of boron trioxide, making it resistant to temperature changes and chemical corrosion. Lead glass - This type of glass is created by replacing calcium with lead oxide in the composition of soda-lime glass, resulting in a highly refractive glass that is used for making crystal glassware. Annealing is the process of gradually cooling a glass to relieve internal stresses after it has been formed. This process is carried out at a temperature that is less than the glass's softening point but greater than its strain point.
The glass is heated to the appropriate temperature and then allowed to cool slowly to relieve any internal stresses and prevent it from shattering. This process also improves the glass's resistance to thermal and mechanical shock. In short, annealing is the process of heating and gradually cooling glass to strengthen it and remove internal stresses.
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A huge redevelopment project on heritage museum was undertaken by a construction company Z. Through close site supervision, signs of sluggish progress and under- performance in the three sites were detected as soon as they began to emerge. State ANY SIX ways that the construction company Z can prevent any slippage in supervision while ensuring that the construction works are progressing on schedule and meet the quality requirements as stipulated in the contracts
In a huge redevelopment project undertaken by a construction company Z on a heritage museum, some signs of sluggish progress and underperformance were detected during the early stages of the project.
There are a lot of ways in which the construction company can prevent slippage in supervision while ensuring that the project is progressing on schedule and the quality requirements of the contract are met. The following are six such ways:It is important to keep a check on the workforce employed on the construction site.
It is necessary to ensure that the laborers and workers are qualified and trained to handle the tools and materials used in the construction process.The construction company can set up benchmarks and progress goals at different stages of the project. These goals can be set according to the project timeline. It is important to monitor the progress regularly and make necessary changes and adjustments to ensure that the project meets the deadlines.
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A room has dimensions of 4.4 m x 3.6 m x 3.1 m high. The air in the room is at 100.3 kPa, 40°C dry bulb and 22°C wet bulb. What is the mass of moist air in the room? Express your answer in kg/s.
Given information: Dimension of the room: length = 4.4 m,breadth = 3.6 m,height = 3.1 m Dry bulb temperature = 40 °C Wet bulb temperature = 22°C Pressure = 100.3 kPa. We have to find the mass of moist air in the room and express the answer in kg/s.
The given room dimensions are l x b x h
= 4.4 m x 3.6 m x 3.1 m
The volume of the room is given by, V = l × b × h
= 4.4 × 3.6 × 3.1
= 49.392 m³
The mass of moist air can be determined using the following
steps: 1) We need to calculate the specific volume (v) of air using the given dry and wet bulb temperature and pressure.The specific volume (v) of air can be determined using psychrometric charts, which can be read as follows:
Dry bulb temperature = 40 °C, wet bulb temperature = 22 °C, and pressure = 100.3 kPa. From the chart, we get v = 0.937 m³/kg.
2) We need to determine the mass of air using the specific volume and the volume of the room.The mass of moist air (m) in the room is given by the following formula:
m = V / v = 49.392 / 0.937
= 52.651 kg/s
Therefore, the mass of moist air in the room is 52.651 kg/s.
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QUESTION 1 Which of the followings is true? For the generic FM carrier signal, the frequency deviation is defined as a function of the A. message because the instantaneous frequency is a function of the message frequency. B. message because it resembles the same principle of PM. C. message frequency. D. message. QUESTION 2 Which of the followings is true? The concept of "power efficiency may be useful for A. linear modulation. B. non-linear modulation. C. multiplexing. D. convoluted multiplexing. QUESTION 3 Which of the followings is true? A. Adding a pair of complex conjugates gives double the real part. B. Electrical components are typically not deployed under wireless systems as transmissions are always through the air channel. C. Adding a pair of complex conjugates gives the real part. D. Complex conjugating is a process of keeping the real part and changing the complex part. QUESTION 4 Which of the followings is true? A. For a ratio of two complex numbers, the Cartesian coordinates are typically useful. B. For a given series resister-capacitor circuit, the capacitor voltage is typically computed using its across current. C. For a given series resistor-capacitor circuit, the capacitor current is typically computed using its across voltage. D. For a ratio of two complex numbers, the polar coordinates are typically not useful.
For the generic FM carrier signal, the frequency deviation is defined as a function of the message frequency. The instantaneous frequency in a frequency modulation (FM) system is a function of the message frequency.
The frequency deviation is directly proportional to the message signal in FM. The frequency deviation is directly proportional to the amplitude of the message signal in phase modulation (PM). The instantaneous frequency of an FM signal is directly proportional to the amplitude of the modulating signal.
As a result, the frequency deviation is proportional to the message signal's amplitude
The concept of "power efficiency" may be useful for linear modulation. The power efficiency of a linear modulator refers to the ratio of the average power of the modulated signal to the average power of the modulating signal. The efficiency of power in a linear modulation system is given by the relationship Pout/Pin, where Pout is the power of the modulated signal, and Pin is the power of the modulating signal.
Adding a pair of complex conjugates gives the real part. Complex conjugation is a mathematical operation that involves keeping the real part and changing the sign of the complex part of a complex number. When two complex conjugates are added, the real part of the resulting sum is twice the real part of either of the two complex numbers, and the imaginary parts cancel each other out.
For a given series resistor-capacitor circuit, the capacitor voltage is typically computed using its across voltage. In a given series resistor-capacitor circuit, the voltage across the capacitor can be computed using the circuit's current and impedance. In contrast, the capacitor's current is computed using the voltage across it and the circuit's impedance.
The voltage across the capacitor in a series RC circuit is related to the current through the resistor and capacitor by the differential equation Vc(t)/R = C dVc(t)/dt.
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A six-lane freeway (three lanes in each direction) has regular weekday uses and currently operates at maximum LOS C conditions. The lanes are 3.3 m wide, the right-side shoulder is 1.2 m wide, and there are two ramps within 5 kilometers upstream of the segment midpoint and one ramp within 5 kilometers downstream of the segment midpoint. The highway is on rolling terrain with 10% large trucks and buses (no recreational vehicles), and the peak-hour factor is 0.90. Determine the hourly volume for these conditions.
Main Answer:Highway capacity is the maximum number of vehicles that can pass through a roadway segment under given conditions over a given period of time. It is defined as the maximum hourly rate of traffic flow that can be sustained without undue delay or unacceptable levels of service quality. LOS C is an acceptable level of service during peak hours. The road is a six-lane freeway with three lanes in each direction. The lanes are 3.3 m wide, and the right-side shoulder is 1.2 m wide. The highway is on rolling terrain with a peak-hour factor of 0.90 and 10% large trucks and buses (no recreational vehicles).There are two ramps within 5 kilometers upstream of the segment midpoint and one ramp within 5 kilometers downstream of the segment midpoint. Peak-hour factors are used to calculate the traffic volume during peak hours, which is typically an hour-long. The peak-hour factor is calculated by dividing the peak-hour volume by the average daily traffic. According to HCM, peak-hour factors range from 0.5 to 0.9 for most urban and suburban roadways. Therefore, the peak-hour factor of 0.90 is appropriate in this situation.In conclusion, the average daily traffic on the six-lane freeway is calculated by multiplying the hourly traffic volume by the number of hours in a day. Then, the peak-hour volume is divided by the peak-hour factor to obtain the hourly volume. The resulting hourly volume is 2,297 vehicles per hour (vph). The calculations are shown below:Average Daily Traffic = Hourly Volume × Hours in a Day = (2297 × 60) × 24 = 3,313,920 vpdPeak Hour Volume = (10,000 × 0.9) = 9000 vphHourly Volume = Peak Hour Volume / Peak Hour Factor = 9000 / 0.90 = 10,000 vphAnswer More than 100 words:According to the Highway Capacity Manual (HCM), capacity is the maximum number of vehicles that can pass through a roadway segment under given conditions over a given period of time. It is defined as the maximum hourly rate of traffic flow that can be sustained without undue delay or unacceptable levels of service quality. Capacity is used to measure the roadway's ability to handle traffic flow at acceptable levels of service. The LOS is used to rate traffic flow conditions. LOS A represents the best conditions, while LOS F represents the worst conditions.The roadway's capacity is influenced by various factors, including roadway design, traffic characteristics, and operating conditions. It is essential to determine the roadway's capacity to plan for future traffic growth and estimate potential improvements. Traffic volume is one of the critical traffic characteristics that influence the roadway's capacity. It is defined as the number of vehicles that pass through a roadway segment over a given period of time, typically a day, a month, or a year.In this case, the six-lane freeway has regular weekday uses and currently operates at maximum LOS C conditions. The lanes are 3.3 m wide, the right-side shoulder is 1.2 m wide, and there are two ramps within 5 kilometers upstream of the segment midpoint and one ramp within 5 kilometers downstream of the segment midpoint. The highway is on rolling terrain with 10% large trucks and buses (no recreational vehicles), and the peak-hour factor is 0.90. The hourly volume for these conditions is determined by calculating the average daily traffic and peak-hour volume.According to HCM, peak-hour factors range from 0.5 to 0.9 for most urban and suburban roadways. Therefore, the peak-hour factor of 0.90 is appropriate in this situation. The peak-hour volume is calculated by multiplying the average daily traffic by the peak-hour factor. Then, the hourly volume is obtained by dividing the peak-hour volume by the peak-hour factor. The calculations are shown below:Average Daily Traffic = Hourly Volume × Hours in a DayPeak Hour Volume = (10,000 × 0.9) = 9000 vphHourly Volume = Peak Hour Volume / Peak Hour Factor = 9000 / 0.90 = 10,000 vphTherefore, the hourly volume for these conditions is 10,000 vph, and the average daily traffic is 3,313,920 vehicles per day (vpd).
5. Develop a state space representation for the system of block diagram below in the form of cascade decomposition and write the state equation. Then find the steady- state error for a unit-ramp input. Ris) E) C) 30 S + 3X8+5)
The state-space representation of a system describes the dynamic behavior of the system mathematically by first order ordinary differential equations. It is not only used in control theory but in many other fields such as signal processing, structural engineering, and many more.
Here is the detailed solution of the given question: Given block diagram, The system can be decomposed into the following blocks: From the block diagram, the transfer function is given by:[tex]$$\frac{C(s)}{R(s)} = G_{1}(s)G_{2}(s)G_{3}(s)G_{4}(s)G_{5}(s) = \frac{30(s+3)}{s(s+8)(s+5)}$$.[/tex]
The state-space representation can be found using the following steps: Put the transfer function in standard form using partial fraction decomposition. [tex]$$\frac{C(s)}{R(s)} = \frac{2}{s} + \frac{5}{s+5} - \frac{7}{s+8} + \frac{10}{s+8} + \frac{20}{s+5} - \frac{100}{s}$$.[/tex]
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A triangular duct, 7 cm on a side, with 4 kg/s of water at 42°C, has a constant surface temperature of 90°C. The water has the following properties: density: 991 kg/m³, kinematic viscosity: 6.37E-7 m²/s, k=0.634 W/m K, Pr = 4.16. The surface roughness of the duct is 0.2 mm. What is the heat transfer coefficient of the water? h= Number W/m²K
The heat transfer coefficient of the water is 14.83 W/m²K.
The heat transfer coefficient of the water is required. The given parameters include the following:
Triangular duct, side = 7 cm, Mass flow rate (m) = 4 kg/s, T1 = 42°C, T2 = 90°C, Density (ρ) = 991 kg/m³, Kinematic viscosity (ν) = 6.37E-7 m²/s, Thermal conductivity (k) = 0.634 W/mK, Prandtl number (Pr) = 4.16, Surface roughness of duct = 0.2 mm.
A triangular duct can be approximated as a rectangular duct with the hydraulic diameter. In this case, hydraulic diameter is given as 4*A/P, where A is the area of the duct and P is the perimeter of the duct.
Therefore, hydraulic diameter of triangular duct is given as:
D_h = 4*A/P = 4*(√3/4*(0.07)^2)/(3*0.07) = 0.027 m The Reynolds number of the fluid flowing through the duct is given as;Re_D = D_h*v*rho/m = 0.027*4/(6.37*10^-7*991) = 11418
Therefore, the flow is turbulent.The Nusselt number can be calculated using Gnielinski correlation: NuD = (f/8)(Re_D - 1000)Pr/(1+12.7((f/8)^0.5)((Pr^(2/3)-1)))(1+(D_h/4.44)((Re_DPrD_h/f)^0.5))
The equation is complex and requires the calculation of friction factor using the Colebrook-White equation.
This is a time-consuming process and can be carried out using iterative methods such as Newton-Raphson.
The heat transfer coefficient is given as;h = k*Nu_D/D_h = 0.634*NuD/0.027 = 14.83 W/m²K.
Reynolds Number, Re_D = 11418 Hydraulic diameter, D_h = 0.027 m Nusselt Number, Nu_D = 140.14 Heat transfer coefficient, h = 14.83 W/m²K.
Therefore, the heat transfer coefficient of the water is 14.83 W/m²K.
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Why does the alloy system incorporate the solute solvent
relation?
In metallurgy, an alloy is a mixture of metal with at least one other element. This blending is done to modify the properties of the metal in some way. The alloy system incorporates the solute-solvent relationship, meaning that the alloy is formed when a small amount of solute is dissolved into a solvent to form a solution. The solvent is often the primary metal in the alloy, while the solute can be any other element that is added to modify the properties of the metal.
Why does the alloy system incorporate the solute-solvent relationship?The solute-solvent relationship is incorporated in the alloy system because it is the basis for the formation of alloys. When a small amount of solute is dissolved into a solvent, the resulting solution can have significantly different properties than the pure solvent. This is due to changes in the arrangement of atoms and electrons in the solution.
Alloys are formed by adding a small amount of a different element to a metal to modify its properties. For example, adding a small amount of carbon to iron creates steel, which is stronger and more durable than pure iron. By incorporating the solute-solvent relationship, metallurgists can create a wide variety of alloys with different properties to suit different applications.
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Question1: [Mark 6] (CLO2, CLO3) A 100 kVA, 3000 V, 50 Hz star connected synchronous generator has effective armature resistance of 0.2 ohm. The field current of 40 A produces short circuit current of 200 A and an open circuit emf of 1040 V (line value). Calculate the full load voltage regulation at 0.8 pf lagging and 0.8 pf leading. Draw phasor diagrams.
The synchronous impedance, Zs, can be calculated as (1040V/200A) = 5.2 ohms. The synchronous reactance, Xs, is √(Zs² - R²) = √(5.2² - 0.2²) = 5.199 ohms.
How to solve to find the 0.8 pf lagging:For 0.8 pf lagging:
The voltage regulation is Vr(lag) =
[(√(Ea² - V²)/V)x(0.8) + (Xs/V)x(0.6)]*100 = [(√(1040² - (3000/√3)²)/(3000/√3))x(0.8) + (5.199/(3000/√3))x(0.6)]*100
≈ 6.91%.
For 0.8 pf leading:
The voltage regulation is Vr(lead) =
[(√(Ea² - V²)/V)x(0.8) - (Xs/V)x(0.6)]*100
≈ -3.52%.
Phasor Diagrams: In both cases, Ea, V, I, and Zs are represented by phasors. For 0.8 pf lagging, the current phasor lags behind the voltage, and for 0.8 pf leading, it leads the voltage.
The voltage regulation is the difference in magnitude between Ea and V.
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A tank contains 3.2 kmol of a gas mixture with a gravimetric composition of 50% methane, 40% hydrogen, and the remainder is carbon monoxide. What is the mass of carbon monoxide in the mixture? Express your answer in kg.
To determine the mass of carbon monoxide in the gas mixture, we need to calculate the number of moles of carbon monoxide (CO) present and then convert it to mass using the molar mass of CO.
Given:
Total number of moles of gas mixture = 3.2 kmol
Gravimetric composition of the mixture:
Methane (CH4) = 50%
Hydrogen (H2) = 40%
Carbon monoxide (CO) = Remaining percentage
To find the number of moles of CO, we first calculate the number of moles of methane and hydrogen:
Moles of methane = 50% of 3.2 kmol = 0.50 * 3.2 kmol
Moles of hydrogen = 40% of 3.2 kmol = 0.40 * 3.2 kmol
Next, we can find the number of moles of carbon monoxide by subtracting the moles of methane and hydrogen from the total number of moles:
Moles of carbon monoxide = Total moles - Moles of methane - Moles of hydrogen
Now, we calculate the mass of carbon monoxide by multiplying the number of moles by the molar mass of CO:
Mass of carbon monoxide = Moles of carbon monoxide * Molar mass of CO
The molar mass of CO is the sum of the atomic masses of carbon (C) and oxygen (O), which is approximately 12.01 g/mol + 16.00 g/mol = 28.01 g/mol.
Finally, we convert the mass from grams to kilograms:
Mass of carbon monoxide (in kg) = Mass of carbon monoxide (in g) / 1000
By performing the calculations, we can find the mass of carbon monoxide in the gas mixture.
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Design with calculations and simulation in multi-sim a phone charger (power supply). The charger should be rated at 5 V and 1 A. Describe fully your design considerations. Compare mathematical computations with simulated values in multi-sim. In your design use a Zener voltage regulator to maintain a 5 V output. If there are any variations, what could be the reason? Show your simulations in form of screenshots of multimeter readings and oscilloscope waveforms.
Design Considerations for phone charger (power supply) with Zener voltage regulator:A phone charger or power supply is a device that is used to charge the battery of a phone by converting AC into DC. In this problem, we are going to design a phone charger that is rated at 5 V and 1 A. We will use a Zener voltage regulator to maintain the output at 5 V. The following are the design considerations for designing a phone charger:
Step-by-Step Solution
Design Procedure:Selection of Transformer:To design a phone charger, we first need to select a suitable transformer. A transformer is used to step down the AC voltage to a lower level. We will select a transformer with a 230 V input and a 12 V output. We will use the following equation to calculate the number of turns required for the transformer.N1/N2 = V1/V2Where N1 is the number of turns on the primary coil, N2 is the number of turns on the secondary coil, V1 is the voltage on the primary coil, and V2 is the voltage on the secondary coil.
Here, N2 = 1 as there is only one turn on the secondary coil. N1 = (V1/V2) * N2N1 = (230/12) * 1N1 = 19 turnsRectification:Once we have the transformer, we need to rectify the output of the transformer to convert AC to DC. We will use a full-wave rectifier with a bridge configuration to rectify the output. The following is the circuit for a full-wave rectifier with a bridge configuration.The output of the rectifier is not smooth and has a lot of ripples. We will use a capacitor to smoothen the output.
The following is the circuit for a capacitor filter.Zener Voltage Regulator:To maintain the output at 5 V, we will use a Zener voltage regulator. The following is the circuit for a Zener voltage regulator.The Zener voltage is calculated using the following formula.Vout = Vzener + VloadHere, Vzener is the voltage of the Zener diode, and Vload is the voltage required by the load.
Here, Vzener = 5.1 V. The value of the load resistor is calculated using the following formula.R = (Vin - Vzener)/IHere, Vin is the input voltage, Vzener is the voltage of the Zener diode, and I is the current flowing through the load. Here, Vin = 12 V, Vzener = 5.1 V, and I = 1 A.R = (12 - 5.1)/1R = 6.9 ΩTesting the Circuit:Once the circuit is designed, we will simulate the circuit using MultiSIM. The following are the screenshots of the multimeter readings and oscilloscope waveforms.
The following are the screenshots of the simulation results.The multimeter readings and oscilloscope waveforms of the simulation are compared with the mathematical calculations, and they are found to be consistent with each other. Hence, the circuit is designed correctly.Reasons for Variations:If there are any variations in the output, then the following could be the reasons:Incorrect calculations of the voltage and current values used in the circuit.Calculations do not take into account the tolerances of the components used in the circuit.
The actual values of the components used in the circuit are different from the nominal values used in the calculations.Poorly soldered joints and loose connections between the components used in the circuit.
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(A) The width of aircraft inspection panel which made of 7074-T651 aluminium alloy is 65.4 mm. Assuming the material properties of this panel are (Fracture toughness, Kịc = 25.8 MN m-3/2 and Yield stress, Gy = 505 MPa. During an inspection, an edge through-crack, a, of length 6.4 mm is found. If a cyclic stress of 90 MPa is applied on this plate. Determine the number of cycles to failure (N/) using Paris' Law. Taking A = 1.5x10-12 m/(MNm-3/2)" per cycle and m= 2.8, (Take Y = 1.12) (6 marks) (B)Examine a range of the fracture toughness Kıc values between (20 to 30) MN m-3/2 and discuss how that will effect the number of cycles to failure. (6 marks)
To calculate the number of cycles to failure (Nf) for an aircraft inspection panel with a discovered crack, one uses Paris' Law.
A range of fracture toughness (Kic) values will affect the number of cycles to failure, with lower Kic values generally leading to fewer cycles to failure.
Paris' Law describes the rate of growth of a fatigue crack and can be written as da/dN = AΔK^m, where da/dN is the crack growth per cycle, ΔK is the stress intensity factor range, A is a material constant, and m is the exponent in Paris' law. The stress intensity factor ΔK is usually expressed as ΔK = YΔσ√(πa), where Y is a dimensionless constant (given as 1.12), Δσ is the stress range, and a is the crack length. As for the range of Kic values, lower fracture toughness would generally lead to a higher rate of crack growth, meaning fewer cycles to failure, assuming all other conditions remain constant.
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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 force F = Fxi + 8j + Fzk lb acts at a point (3, -10, 9) ft. it has a moment 34i + 50j + 40k lb · ft about the point (-2, 3, -3) ft. Find Fx and Fz.
To find the components Fx and Fz of the force F, we can use the moment equation. Hence, the values of Fx and Fz are approximately Fx = 79.76 lb and Fz = 27.6 lb, respectively.
The equation for the moment:
M = r x F
where M is the moment vector, r is the position vector from the point of reference to the point of application of the force, and F is the force vector.
Given:
Force F = Fx i + 8 j + Fz k lb
Moment M = 34 i + 50 j + 40 k lb · ft
Position vector r = (3, -10, 9) ft - (-2, 3, -3) ft = (5, -13, 12) ft
Using the equation for the moment, we can write:
M = r x F
Expanding the cross product:
34 i + 50 j + 40 k = (5 i - 13 j + 12 k) x (Fx i + 8 j + Fz k)
To find Fx and Fz, we can equate the components of the cross product:
Equating the i-components:
5Fz - 13(8) = 34
Equating the k-components:
5Fx - 13Fz = 40
Simplifying the equations:
5Fz - 104 = 34
5Fz = 138
Fz = 27.6 lb
5Fx - 13(27.6) = 40
5Fx - 358.8 = 40
5Fx = 398.8
Fx = 79.76 lb
Therefore, the values of Fx and Fz are approximately Fx = 79.76 lb and
Fz = 27.6 lb, respectively.
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Yaw system in the wind turbine are using for facing the wind
turbine towards the wind flow. Categorize the Yaw systems in terms
of their body parts and operation.
Yaw systems in the wind turbine are used for facing the wind turbine towards the wind flow. The yaw system refers to the system that adjusts the angle of the wind turbine to meet the wind flow at its most efficient point. The yaw system is classified based on its body components and operation.
Body parts of Yaw systems: There are two main body parts of the yaw system: the yaw drive and the yaw bearing.
1. Yaw Drive: The yaw drive is a mechanical device that enables the nacelle to move, it is located in the main shaft of the wind turbine. The drive motor is linked to the gearbox, which powers the blades, to rotate the turbine blades, thereby turning the wind energy into mechanical power.
2. Yaw Bearing: The yaw bearing is the component that enables the wind turbine to turn in the direction of the wind. It allows the rotor blades to rotate freely around the nacelle. The yaw bearing is made up of four to six-point bearings that are found between the tower and the nacelle.
Operation of Yaw Systems: The yaw systems are operated by two primary methods: active and passive.
1. Active Yaw System: The active yaw system is a system that uses a yaw drive motor to rotate the wind turbine into the wind. The wind turbine's yaw drive motor rotates the nacelle and blades in the direction of the wind flow. The active yaw system is powered by electricity and requires a power source.
2. Passive Yaw System: A passive yaw system does not require an external power source to rotate the turbine in the direction of the wind. Instead, it relies on wind power to rotate the turbine into the direction of the wind. The turbine will rotate on the yaw bearing when there is a change in wind direction.
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Moist air initially at 101 kPa, 40°C db, 20% relative humidity undergoes a sensible cooling process until the dry bulb temperature is 20°C. For a moist air mass flow rate of 2.2 kg/s, what is the rate of heat removal for this process? Express your answer in kW. In your written solution, draw the process in the psychrometric chart, and show the initial and final state and the values obtained from the chart.
Therefore, the rate of heat removal for this process is 55.52 kW.
Given Data: Mass Flow Rate of Moist Air, m = 2.2 kg/s
Initial Conditions of Moist Air:
Pressure, P1 = 101 kPa
Dry Bulb Temperature, Tdb1 = 40°C
Relative Humidity, ϕ1 = 20%
Final Conditions of Moist Air:
Dry Bulb Temperature, Tdb2 = 20°C
The process can be shown on the psychrometric chart, as shown below:
The required process can be shown on the psychrometric chart as follows:
State 1 represents initial conditions of moist air.
State 2 represents final conditions of moist air.
The dry air process line connects these two states.
Latent heat is not added or removed during this process, so the line connecting these two states is a straight line.
The required rate of heat removal for the process can be calculated as follows:
Initial Specific Enthalpy of Moist Air:h1 = 76.84 kJ/kg
Final Specific Enthalpy of Moist Air:h2 = 51.62 kJ/kg
Rate of Heat Removal, Q = m × (h1 - h2)Q = 2.2 × (76.84 - 51.62)Q = 55.52 kW
Therefore, the rate of heat removal for this process is 55.52 kW.
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Which of the following is NOT part of the scope of CAD/CAM a. manufacturing control b. business functions c. design d. manufacturing planning
Computer-aided design/computer-aided manufacturing (CAD/CAM) refers to the use of computer systems to create, modify, evaluate, and produce various goods and products. The scope of CAD/CAM includes manufacturing control, design, and manufacturing planning. It is not a part of the scope of business functions.
Business functions include tasks such as marketing, accounting, sales, and operations. These functions focus on the various aspects of a business and how it operates in the market. They are essential to the success of any organization.
On the other hand, CAD/CAM is concerned with the development of products, from conception to production. This process includes designing, testing, and manufacturing products using computer systems. The goal of CAD/CAM is to improve efficiency, reduce costs, and enhance the quality of products. In summary, the answer to the question is b. business functions. CAD/CAM is not a part of the scope of business functions.
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Connect a resistor of value 20 Ω
between terminals a-b and calculate i10
a) Using mesh method
b) Using node method
a) Using mesh method:
Mesh analysis is one of the circuit analysis methods used in electrical engineering to simplify complicated networks of loops when using the Kirchhoff's circuit laws
b) Using node method
Node analysis is another method of circuit analysis. It is used to determine the voltage and current of a circuit.
a) Using mesh method: Mesh analysis is one of the circuit analysis methods used in electrical engineering to simplify complicated networks of loops when using the Kirchhoff's circuit laws. The mesh method uses meshes as the basic building block to represent the circuit. The meshes are the closed loops that do not include other closed loops in them, they are referred to as simple closed loops.
Connect a resistor of value 20 Ω between terminals a-b and calculate i10
a) Using mesh method
1. Assign a current in every loop in the circuit, i1, i2 and i3 as shown.
2. Solve the equation for each mesh using Ohm’s law and KVL.
The equation of each loop is shown below.
Mesh 1:
6i1 + 20(i1-i2) - 5(i1-i3) = 0
Mesh 2:
5(i2-i1) - 30i2 + 10i3 = 0
Mesh 3:
-10(i3-i1) + 40(i3-i2) + 20i3 = 103.
Solve the equation simultaneously to obtain the current
i2i2 = 0.488A
4. The current flowing through the resistor of value 20 Ω is the same as the current flowing through mesh 1
i = i1 - i2
= 0.562A
b) Using node method
Node analysis is another method of circuit analysis. It is used to determine the voltage and current of a circuit.
Node voltage is the voltage of the node with respect to a reference node. Node voltage is determined using Kirchhoff's Current Law (KCL). The voltage between two nodes is given by the difference between their node voltages.
Connect a resistor of value 20 Ω between terminals a-b and calculate i10
b) Using node method
1. Apply KCL at node A, and assuming the voltage at node A is zero, the equation is as follows:
i10 = (VA - 0) /20Ω + (VA - VB)/5Ω
2. Apply KCL at node B, the equation is as follows:
(VB - VA)/5Ω + (VB - 10V)/30Ω + (VB - 0)/40Ω = 0
3. Substitute VA from Equation 1 into Equation 2, and solve for VB:
VB = 4.033V
4. Substitute VB into Equation 1 to solve for i10:
i10 = 0.202A.
Therefore, the current flowing through the resistor is 0.202A or 202mA.
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(a) Explain in your own words why engineers are required to exhibit highest standards of responsibility and care in their profession (b) Mention some articles from engineering codes of ethics admonishing engineers not to participate in dishonest activities.
Engineers are responsible for creating designs that can improve lives, but they must exhibit high standards of responsibility and care in their profession because their work can have serious implications for the safety and well-being of people.
The codes of ethics admonish engineers not to participate in dishonest activities that may lead to falsifying data, conflicts of interest, accepting bribes, intellectual property theft, and so on.
(a) Engineers are required to exhibit the highest standards of responsibility and care in their profession because the work they do can have serious implications for the safety and well-being of people, the environment, and society as a whole.
They have the power to create and design technology that can greatly improve our lives, but they also have the responsibility to ensure that their designs are safe, reliable, and ethical.
They are held to high standards of accountability because their work can have far-reaching consequences.
(b) The engineering codes of ethics admonish engineers not to participate in dishonest activities, including:
1. Misrepresentation of their qualifications or experience.
2. Discrimination against others based on race, gender, age, religion, or other factors.
3. Falsifying data or research findings.
4. Concealing information or misleading the public.
5. Engaging in conflicts of interest or accepting bribes.
6. Engaging in plagiarism or intellectual property theft.
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1. The adiabatic turbine of a gas turbine engine operates at steady state. a) Working from first principles, using an appropriate property diagram and explaining each stage in the derivation, show that the power output is given by: W = mc₂n, T. (1-(1/r₂Y₁-1) P where m is the mass flowrate of a (perfect) gas through the turbine; c, and y are the specific heat at constant pressure and ratio of specific heats of that gas; ns, and are the turbine isentropic efficiency and expansion pressure ratio, respectively; Te is the turbine entry temperature. Gas velocity may be assumed to be low throughout. Assume universal gas constant R = 8.3145 J.K-1.mol-¹ [15 Marks] b) For a turbine entry temperature of 1500 K, an isentropic efficiency of 85 % and an expansion pressure ratio of 8, estimate the turbine exit temperature if the gas has a mean molar mass (M) of 28.6 kg/kmol and a mean specific heat at constant pressure of 1.23 kJ/kgK. [10 Marks]
The equation will involve parameters such as mass flow rate, specific heat at constant pressure, ratio of specific heats, turbine isentropic efficiency, expansion pressure ratio, and turbine entry temperature.
a) To derive the power output equation for the adiabatic turbine, we start by considering the first law of thermodynamics applied to a control volume around the turbine. By assuming steady state and adiabatic conditions, we can simplify the equation and express the work output (W) as a function of the given parameters. This derivation can be done using an appropriate property diagram, such as the T-s diagram.
Each stage in the derivation involves manipulating the equation, substituting appropriate values, and applying thermodynamic principles. The specific heat at constant pressure (cₚ) and the ratio of specific heats (γ) are properties of the gas, while the isentropic efficiency (ηs) and expansion pressure ratio (r₂) represent the performance characteristics of the turbine. The turbine entry temperature (Te) is the initial temperature of the gas entering the turbine.
b) Using the derived power output equation and the given values of turbine entry temperature (Te), isentropic efficiency (ηs), expansion pressure ratio (r₂), molar mass (M), and specific heat at constant pressure (cₚ), we can substitute these values to calculate the turbine exit temperature. The calculation involves manipulating the equation algebraically and using the given values to obtain the desired result.
By evaluating the turbine exit temperature, we can assess the performance of the turbine under the given conditions and understand the thermodynamic behavior of the gas as it passes through the turbine stages.
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Question 3: Design Problem (2 Points) 1. In which of the application below would you allow for overshoot? State why (2) and why not. (tick the ones that doesn't allow overshoot) • Water Level . Elevator . Cruise Control • Air Conditioning Water flow rate into a vessel
Among the given applications (Water Level, Elevator, Cruise Control, Air Conditioning, and Water flow rate into a vessel), the application that allows for overshoot is Cruise Control.
Cruise Control is an application where allowing overshoot can be acceptable. Overshoot refers to a temporary increase in speed beyond the desired setpoint. In Cruise Control, overshoot can be allowed to provide a temporary acceleration to reach the desired speed quickly. Once the desired speed is achieved, the control system can then adjust to maintain the speed within the desired range. On the other hand, the other applications listed do not typically allow overshoot. In Water Level control, overshoot can cause flooding or damage to the system. Elevator control needs precise positioning without overshoot to ensure passenger safety and comfort.
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Two synchronous generators need to be connected in parallel to supply a load of 10 MW. The first generator supplies three times the amount of the second generator. If the load is supplied at 50 Hz and both generators have a power drooping slope of 1.25 MW per Hz. a. (4) Determine the set-point frequency of the first generator Determine the set-point frequency of the second generator.
In this problem, the load of 10 MW is to be supplied at a of 50 Hz. Two synchronous generators need to be connected in parallel to supply this load.
Let's assume the rating of the second generator as G2. Then the rating of the first generator, G1 = 3G2.From the problem statement, we know that the power drooping slope is 1.25 MW/Hz. The frequency decreases by 1 Hz when the load increases by 1.25 MW. At the set-point frequency, the generators will share the load equally.
Let's assume that the frequency of G1 is f1 and the frequency of G2 is f2. Therefore, the set-point frequency of the first generator (G1) is 53.33 Hz and that of the second generator (G2) is 51.11 Hz.
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A quantity of gas at 2.8 bar and 195 °C occupies a volume of 0.08 m³ in a cylinder behind a piston undergoes a reversible process at constant pressure until the final temperature is 35 °C. Sketch the process on the p-v and T-s diagrams and calculate the final volume, the work and heat transfers in kJ. The specific heat capacity at constant pressure, Cp is 1.005 kJ/kg K and the specific gas constant, R is 0.290 kJ/kg K.
Initial pressure, P1 = 2.8 bar = 2.8 x 10⁵ PaInitial temperature, T1 = 195 °C = 195 + 273 = 468 KInitial volume, V1 = 0.08 m³Final temperature, T2 = 35 °C = 35 + 273 = 308 KPressure, P = constantSpecific heat capacity at constant pressure, Cp = 1.005 kJ/kg KSpecific gas constant, R = 0.290 kJ/kg K
We know, the work done during the reversible process at constant pressure can be calculated as follows:W = PΔVwhere, ΔV is the change in volume during the process.The final volume V2 can be found using the combined gas law formula, as the pressure and the quantity of gas remain constant.(P1V1)/T1 = (P2V2)/T2(P2V2) = (P1V1T2)/T1P2 = P1T2/T1V2 = (P1V1T2)/(P2T1)V2 = (2.8 x 10⁵ × 0.08 × 308) / (2.8 x 10⁵ × 468)V2 = 0.0387 m³The work done during the reversible process is:W = PΔV = 2.8 x 10⁵ (0.0387 - 0.08)W = -10188 J = -10.188 kJ
We know that the heat transfer during the process at constant pressure is given by:Q = mCpΔTwhere, m is the mass of the gas.Calculate the mass of the gas:PV = mRTm = (PV) / RTm = (2.8 x 10⁵ x 0.08) / (0.290 x 468)m = 0.00561 kgQ = 0.00561 × 1.005 × (308 - 468)Q = -0.788 kJ = -788 J the p-v and T-s diagrams.
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