Consider a unity-feedback control system with the open-loop transfer function G(s) = K/ (s(s^2+s+4)
A) Determine the value of the gain K such that the phase margin is 50∘?
B) What is the gain margin for this case?

Answers

Answer 1

A) The phase margin is defined as the angle between the open-loop gain and the -180 degree line on the Bode plot.

To find the required value of K, we first need to find the gain (magnitude) at the frequency which corresponds to the phase margin angle.

At 50 degrees, the frequency is calculated as:

f_pm = 1 / (2π tan(50)) = 0.637 rad/s

The magnitude at this frequency can be determined by substituting s = j f_pm into the transfer function.

G(jf_pm) = K / (jf_pm (f_pm^2 + jf_pm + 4))

Simplifying, the magnitude of G(jf_pm) is:

|G(jf_pm)| = K / |f_pm (f_pm^2 + jf_pm + 4)| = K / 4.839

Therefore, the required value of K is:

K = 4.839 * |G(jf_pm)|

B) The gain margin is the minimum amount of gain needed to make the system stable. It can be determined by calculating the magnitude at the frequency which corresponds to the -180 degree angle on the Bode plot.

At -180 degrees, the frequency is calculated as:

f_gm = 1 / (2π tan(-180)) = 0

The magnitude at 0 frequency can be determined by substituting s = 0 into the transfer function.

G(0) = K / (0(0^2 + 0 + 4)) = K/4

Therefore, the gain margin is:

GM = 4/K

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Related Questions

An air-conditioning system is used to maintain a house at a constant temperature of 20 °C. The house is gaining heat from outdoors at a rate of 20000 kJ/h, and the heat generated in the house from the people, lights, and appliances amounts to 8000 kJ/h. For a COP of 2.5, determine the required power input to this air-conditioning system.

Answers

The required power input to this air-conditioning system is 3.11kW

How to solve for the  required power input

We would have to calculate the cooling load of the airconditioner first

This is given as

Q outdoors + Q house

In the question

Q outdoors = 20000

Q house = 8000 kJ/h

Cooling load = 20000 kJ/h + 8000 kJ/h

= 28000 kJ/h

Next we have to solve for the power input into the house

28000 / 2.5

= 11200 kJ/h

11200 kJ/h ÷ 1 / 3600

= 3.11kW

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what is the driving force for flow in an open channel? how is the flow rate in an open channel established?

Answers

Gravity acts as the primary factor causing flow in an open channel. An open channel's flow rate is determined. Open-channel flow is implied by flow in a channel that is open to the atmosphere.

What controls the flow in an open channel?

On the other hand, in an open channel flow, the flowing liquid has a free surface at atmospheric pressure and is propelled by gravity.

What determines the flow rate in an open channel?

The standard technique is to construct a weir or flume across the flow, monitor the flow velocity, and using a radar or ultrasonic level sensor, measure the height of the liquid just before the weir or flume. This measured height can subsequently be used to compute the volume flow rate.

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Entrapment and transfer of hear from the sun to a building without use of machinery
passive solar system

Answers

Solar system that is active. a device that stores solar energy as heat energy and transports it somewhere else through mechanical means.

What is a system that stores solar energy as heat energy and uses machinery to transport it?Solar system that is active. a device that stores solar energy as heat energy and transports it somewhere else through mechanical means.Renewable energy is created by natural processes that are constantly renewed.This includes the sun, geothermal heat, wind, tides, water, and other biomasses. This energy is endlessly replenished.The term "renewable" is typically used to describe energy sources and technological advancements that share the trait of being naturally replenishable or non-depletable.  

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we want to replace a 119 mw coal-fired power plant with a geothermal power plant. the geothermal recovery rate at the location is 5.6 w/m2 and we can assume that the geothermal plant runs at 100% capacity with a 17% total conversion efficiency. how much area (at a minimum) does the geothermal plant need to extend pipes to achieve 119 mw production?

Answers

Area the geothermal plant need to extend pipes to achieve 119 mw production is 99.1926 km²

What is a geothermal plant?

Electrical energy derived from geothermal energy is known as geothermal power. Dry steam, flash steam, and binary cycle power plants are among the technologies currently in use. Currently, 26 countries use geothermal energy for the production of electricity, and 70 countries use it for heating.

In 2019, there were 15.4 gigawatts (GW) of geothermal power installed in the world, with 3.68 GW, or 23.9 percent, installed in the United States. Global geothermal power capacity is anticipated to reach 14.5–17.6 GW by 2020, with international markets expanding at an average annual rate of 5% over the three years leading up to 2015.

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sediment transported on top of a glacier is being transported , whereas sediment being transported within the glacier is being transported

Answers

Supraglacially - Sediment is transported on top of the glacier. Subglacially - Sediment is transported at the base of the glacier.

How do glaciers move sediments?Deformed glacier beds can also move a lot of sediment, especially in marginal areas. By regelation into subglacial materials and by freeze-on from rising supercooled waters, rapid sediment entrainment that results in thick debris-rich basal zones is possible.Similar to a river, water running down the glacier's base carries and deposits detritus. The movement of a meltwater stream beneath the ice creates an esker, which is a sinuous ridge comprised of sediment.Through the process of erosion, sediment is transferred from one location to another. The removal and transportation of rock or soil is erosion. Sediment can be transported by erosion through water, ice, or wind. Water can carry debris from a creek, like gravel or stones, into a body of water.

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technician a says that crankshaft end play is controlled by the fillet radius of the crankshaft journals. technician b says that the main bearings limit crankshaft end play. who is correct?

Answers

The camshaft moves in the engine block from back to front is referred to as end play. It is also known as how far the camera will "walk."

Only Roller Camshafts are subject to end play. Tapered lobes on flat tappet cams push the camshaft toward the rear of the engine block. Mechanism of the Valve and Gear Train The movement of the crankshaft is synchronized with the movement of the camshaft and the valves using a gear train or valve timing device. A thin calibrated plastic strip serves as a plastic gauge. It can be used to measure gaps and check bearing clearance. It is utilized at locations on crank or connecting rod bearings where a micrometer measurement cannot be made quickly.

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identify the number returned by the dequeue operation on the following priority queue. array containing 7 elements: 21, 36, 45, 54, 60, 73, 90. group of answer choices 54 36 21 90

Answers

90 is the number returned by the dequeue operation on the priority queue.

What is meant by priority queue with example?The highest number in a queue with priorities arranged in descending order is given the highest priority. The priority queue, for instance, has six numbers in it:21, 36, 45, 54, 60, 73, 90. . Ascending order is the first order in which you should organize these numbers. According to the updated list:90,73,60,54,45,36.In contrast to a standard queue or stack data structure, a priority queue is an abstract data type in which each element also has a priority assigned to it. In a priority queue, a high-priority element receives service before a low-priority element.90 is the number returned by the dequeue operation on the priority queue.

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Draw a circuit that computes the function described by the input/output table. You may want to use the laws of Boolean algebra to simplify your Boolean expression before you draw the circuit. x y f(x,y) (a) 0 x y z f(x y,z) 0 1 0 0 (b) 0 1 0 10 0 1 0 1 0 0

Answers

B is a non-empty set, + and. are binary operations in B,'is a unary operation in B, and 0 and 1 are special elements of B. This is known as a Boolean Algebra.

A Boolean algebra is a mathematical construction with the notation (B,+,., ', 0,1) where B is a non-empty set, + and. are binary operations in B,'is a unary operation in B, and 0 and 1 are special elements of B,

such that:

a) + and. are communative: for all x and y in B,

b) x+y=y+x, and x.y=y.

c) Both x.(y+z) and x+(y.z) are equal to (x+y).(x+z).

d) Identity laws: 0+x=x+0=x for any x in B and 1.x=x.1=x

e) Complementation laws: for all x in B, x+x'=1 and x.x'=0.

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which type of furnace can operate to produce either full heat output or produce at a fixed level that is less than full heat?

Answers

A two-stage furnace can run at a predetermined output level that is either less than full heat or at maximum heat output.

What kinds of furnaces have AFUE ratings over 90% and are considered high efficiency?

Condensing furnaces are those that run with an AFUE of greater than 90%. This indicates that the furnace turns escaping water vapour back into energy and heat by condensing them. The furnace is therefore more effective than a noncondensing furnace.

What two factors affect the efficiency of a furnace and a boiler?

The ability of a burner to burn fuel is indicated by the boiler's combustion efficiency. The amount of unburned fuel in the exhaust and the amount of extra oxygen in the exhaust are the two factors that influence the burner efficiency.

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water emerges from under a gate into a trapezoidal, concrete channel. the gate opening is 0.55m, and the flow rate is 12.6 m3/s. the entry channel has a 1.5m bottom width, side slopes of 1:1 (h:v), and a bottom slope of 0.015. determine the channel and flow classification (e.g., m-1, s-2) and explain your supporting logic.

Answers

The channels and flow classification is M-1, S-2.

M-1 stands for "Minor Stream", which is a small stream with a low amount of flow. S-2 stands for "Secondary Stream", which is a medium-sized stream with moderate flow.

Channel Classification: M-1

Flow Classification: S-2

Supporting Logic:

The channel is trapezoidal with a bottom width of 1.5m, side slopes of 1:1 (h:v), and a bottom slope of 0.015, which is considered to be a wide, shallow channel. This would classify the channel as an M-1 channel.

The flow rate of 12.6 m3/s is considered to be an S-2 flow, which is a moderate flow.

Therefore, the channel and flow classification is M-1, S-2.

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qam (quadrature amplitude modulation) uses phase and amplitude to indicate different signals so that multiple bits can be sent in a clock cycle. more generally, there is a relationship between the number of bits per second (bps) and the number of different signal combinations (states) and the baud rate (signal changes per second). if i want a data rate of 30,000 bps and the baud rate is 10,000 how many states do i need.

Answers

8 states are required to achieve a data rate of 30,000 bps and a baud rate of 10,000.

How do clock cycles work?

Your CPU's clock speed, expressed in GHz, tracks how many cycles it completes each second (gigahertz). Technically speaking, a "cycle" is a pulse timed by an internal oscillator, however for our purposes, they serve as a foundational measure of a CPU's speed. The CPU contains billions of transistors that open and close during each cycle. In certain circumstances, one instruction may be processed over several clock cycles, whereas in other cases, numerous instructions may be finished in a single cycle.

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question at position 6 a three-phase transformer connection has a delta-connected primary and a wye-connected secondary. the center tap of the wye is used as a neutral conductor. if the line-to-line voltage is 480 v, what is the voltage between any one phase conductor and the neutral conductor?

Answers

207.84 V is the voltage between any one phase conductor and the neutral conductor.

What is phase conductor?

Line conductor that is used in an AC electric circuit as a phase conductor. It transmits electrical energy and is, therefore, a live conductor under normal circumstances. The more accurate term "phase conductor" is not always used, especially in the United States and some other nations. Instead, the phrase "line conductor in AC system" is frequently used.

Phase conductors and neutral conductors are used in electrical installations of buildings to supply power for the AC electrical equipment used in them.

A phase conductor is a current-carrying conductor that is included when calculating the total number of electrical conductors used in a circuit, network, or system of electrical devices.

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A large number of compromised computers are infected with malware that allows an attacker (herder) to control them to spread email spam and launch denial-of-service attacks.
Which of the following dose this security threat describe?

Answers

The dose of this security threat describes is Zombie/botnet. The correct option is d.

What is a Zombie/botnet?

A "zombie" or "bot" is a compromised computer under the control of an attacker, who frequently manages a botnet of other compromised devices.

A bot, short for "robot," is a sort of software application or script that executes automatic tasks when given a command. Malicious bots carry out malicious actions that allow an attacker to remotely manipulate an afflicted computer. These infected machines may be referred to as zombies once infected.

Therefore, the correct option is d, Zombie/botnet.

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The question is incomplete. Your most probably complete question is given below:

Phishing

Man-in-the-middle

Spoofing

Zombie/botnet

g determine the transfer function of the system (b) determine the modal form of the system (c) find the transfer function of the system from its modal form. is it the same as the one you found in (a)?

Answers

If you rotate a sample with two strain gauges attached to it by 90 degrees and apply a point load, you should expect to see a change in the readings on the strain gauges. When a load is applied to a material, it will cause the material to deform, which can be measured using strain gauges. In this case, the rotation of the sample would change the orientation of the strain gauges relative to the applied load, which would affect the readings.

A strain gauge is a device that is used to measure the strain or deformation of a material. It consists of a thin strip of conductive material, such as a metallic foil, which is attached to the surface of the material. When the material is subjected to a load, the strain gauge will experience a change in electrical resistance, which can be measured using a meter or other device. This change in resistance is proportional to the strain on the material, and can be used to calculate the amount of deformation that has occurred. Strain gauges are commonly used in engineering and materials science to measure the response of materials to different loads and conditions.

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Calculate the buoyancy force acting on a partially immersed boat (V=5.0 m³). The density of water is 1000 kg/m³. Express your answer in both SI and U.S. Customary units.

Answers

CALCULATION :

SI units:
Buoyancy force = (Volume of water displaced) x (Density of water) x (Acceleration due to gravity)
Buoyancy force = (5.0 m³) x (1000 kg/m³) x (9.81 m/s²)
Buoyancy force = 49,050 N

U.S. Customary units:
Buoyancy force = (Volume of water displaced) x (Density of water) x (Acceleration due to gravity)
Buoyancy Force = (5.0 m³) x (62.4 lb/ft³) x (32.17 ft/s²)
Buoyancy Force = 11,230 lb

What is force ?

A force is anything that pushes or it pulls an object. The objects' interactions with one another are also what causes push and pull. Pressure can also be represented using terms like extend and compress.

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ote: this is a multi-part question. once an answer is submitted, you will be unable to return to this part.consider the given figure. knowing that the radius of each pulley is 200 mm, p

Answers

The calculated torque is 91.55 KN-mm. Yes, the radius of the pulley has an effect on the belt tensions.

For a given frictional torque at the axle, the tension difference between the pull side and the load side is smaller because a larger radius produces a greater moment.

Each pulley's radius is 50 mm;

R1 = R2 = 50 mm.

R1 = 50 mm for the driver's radius

50mm for the radius of the driven,

1800 for the angle of contact (in radians), and

0.3 for the coefficient of friction. T1 = 3KN of permissible stresses Always, T1 is bigger than T2.

Utilizing the formula T1/T2 = e After adding together all the values,

T2 = 1.169KN and 3/T2 = e(0.3)().

Because both pulleys' radiuses are the same, they both experience the same amount of torque (T1–T2). R1

= (T1–T2) (T1–T2). R2

When we add up everything,

(3 - 1.169) X 50

= 91.55 KN-mm.

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several project managers at area 51 are impressed with your recent efforts that successfully characterized the static stability and trim characteristics of the blackstar configuration. your understanding of the fundamentals related to static concepts are clearly quite strong. as such, you are being now tasked on a new project to assist with dynamic concepts of another next-generation aircraft.

Answers

If a first order system's characteristic value, 8, is smaller than zero, we may say that it is dynamically stable. Rolling convergence is the term used to describe the motion, which is a damped roll rate.

Explain the aircraft dynamic modes ?Two parameters can be used to define oscillating motions: the duration of one full oscillation and the duration needed to damp to half-amplitude, or the duration needed to double the amplitude for a dynamically unstable motion. A long-period oscillation known as a phugoid mode and a short-period oscillation known as the short-period mode make up the two different oscillations that make up the longitudinal motion.The "phugoid mode," which has a longer period, is characterised by large amplitude variations in air speed, pitch angle, and altitude but almost no variations in angle of attack.As the aircraft tries to return to the equilibrium level-flight condition from which it had been disturbed, the phugoid oscillation is a slow exchange of kinetic energy (velocity) and potential energy (height) around some equilibrium energy level.

Find the attachment answer

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Adding deductive reasoning to traditional DBMS functions is a benefit of integrating an expert system into the database component of a(n) _____

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Adding deductive reasoning to traditional DBMS functions is a benefit of integrating an expert system into the database component of a(n) DSS (Decision Support System)

What is DBMS?

A computer software known as an expert system use artificial intelligence (AI) techniques to mimic the decision-making and actions of a person or group of people who have knowledge and experience in a certain field. Expert systems are often designed to support human experts rather than to replace them.

Recognizing distinct consumer demographics, such as devoted, new, or prospective customers. Prospects are categorized based on their demographics and other possible demographics, such as potential hobbies. gives significant accounts top priority. tailors marketing messaging to certain targets.

Many information systems strive to convert data into information so that knowledge may be created that can be applied to making decisions.

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he gas storage tank has a longitudinal welded seam on its cylindrical section. the tank has an inner diameter of 1.40 m and a wall thickness of 5.0 mm. determine the magnitude of normal stress on the horizontal weld if the internal tank pressure is 1.2 mpa.

Answers

The magnitude of Normal stress on the weld  = 168 MPa, if the internal tank pressure is 1.2 mpa.

What is stress?

Stress is defined as a force per unit area within a material that results from externally applied forces, uneven heating, or permanent deformation and that enables an accurate description and prediction of elastic, plastic, and fluid behavior in physical sciences and engineering. By dividing a force by an area, a stress is expressed.

Shear stress is caused by forces that are parallel to and lie in the plane of a cross-sectional area of the material, as opposed to normal stress, which is caused by forces that are perpendicular to the area. Tensile stress is the name given to the specific type of normal stress that arises from tension.

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nolan is considering the use of several different types of alternate processing facility for his organization's data center. which one of the following alternative processing sites takes the longest time to activate but has the lowest cost to implement?

Answers

Since all hardware, software, and data must be loaded at the new site, a cold site is the least expensive choice, but it also has the longest switchover time.

Virtualization pioneer VMware offers DR through its vSphere Replication and Site Recovery Manager products, among others. The most crucial element in company continuity and catastrophe recovery planning is employee safety. A DRP's goal is to make sure that an organization is prepared to respond to a disaster or other event that affects information systems while minimizing the impact on daily operations. A backup location known as a "cold site" has little to no hardware installed.

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the shear strength of each of ten test spot welds is determined, yielding the following data (psi): 392 376 401 367 389 362 409 415 358 375 a. assuming that shear strength is normally distributed, estimate the true average shear strength and standard deviation of shear strength using the method of maximum likelihood. b. again assuming a normal distribution, estimate the strength value below which 95% of all welds will have their strengths. [hint: what is the 95th percentile in terms of m and s? now use the invariance principle.] c. suppose we decide to examine another test spot weld. let x 5 shear strength of the weld. use the given data to obtain the mle of p(x

Answers

(a) The sample mean is calculated as 382.3 psi and sample standard deviation is calculated as 19.76 psi.

(b) The 95th percentile is calculated as 414.80 psi that is below 414.80 psi, the 95% of all the welds have their strengths.

(c) There are 81.5% chances that the shear strength of the welds is less than or equal to 400 psi.

What is standard deviation?

A statistic known as the standard deviation, which is calculated as the square root of variance, gauges a dataset's dispersion from its mean. By figuring out how far off from the mean each data point is, the standard deviation can be calculated as the square root of variance.

A higher deviation exists within a data set if the data points are further from the mean; consequently, the higher the standard deviation, the more dispersed the data.

By comparing the annual rate of return of an investment to the standard deviation, a statistical measurement used in finance, one can learn more about the historical volatility of that investment.

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You just posted new photographs to Shutterfly, and the site asks you to review the metadata. Metadata includes the following information EXCEPT _____.
A. The date a photo was taken
B. The file size
C. The GPS location coordinates
D. The HTML coding

Answers

You just posted new photographs to Shutterfly, and the site asks you to review the metadata. Metadata includes the following information EXCEPT The HTML coding.

What is HTML coding?Hyper Text Markup Language is what HTML is. The preferred markup language for building Web pages is HTML. A Web page's structure is described in HTML. A number of elements make up HTML. The content's presentation in the browser is controlled by HTML elements.The term "HTML" stands for "Hypertext Markup Language." Specifically created for digital consumption, HTML files are text-only documents with highly interactive information. This implies that rather than being printed, they work best as an on-screen viewing file.The preferred markup language for Web pages is HTML. You may build your own website using HTML. HTML is simple to learn, and you'll like it.

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the principle that the rate of corrosion is controlled by one of two reduction mechanisms is referred to as

Answers

Answer:

1) Metal type

2) Protective coatings

3) Environmental measures

4) Sacrificial coating

5) Corrosion inhibitor

6) Design modification

a. By selecting NA and ND, the acceptor and donor densities introduced in the semiconductor, a device engineer can control: 1. The values ofn0andp0for the semiconductor used in devices. 2. The group number on the periodic chart for silicon and different dopants. 3. The intrinsic carrier concentration of a semiconductor for operating temperatures of a device. 4. All of the above.

Answers

Option 3 is correct. The semiconductor's intrinsic carrier concentration at a device's operational temperature.

Any member of the family of crystalline solids known as a semiconductor falls into the range of conductors and insulators in terms of electrical conductivity. Diodes, transistors, and integrated circuits are just a few of the electrical devices that use semiconductors in their production. Due to their portability, dependability, energy efficiency, and affordability, these gadgets are widely used. They have been utilized as discrete components in solid-state lasers, optical sensors, and power devices. They are capable of handling a wide range of current and voltage, and more importantly, they are well suited for integration into intricate but easily fabricated microelectronic circuits.

They currently serve as, and will continue to serve as, the primary components of the majority of electronic systems, supporting computing, communications, signal processing, and control applications for both consumer and industrial markets.

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a neural network using a perceptron to distinguish between apples and oranges, based on three sensor measurements (shape, texture and weight). now you are to design a perceptron to distinguish between bananas and pineapples:

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Neural networks are a set of algorithms that simulate how an animal brain works in order to find connections among enormous amounts of data.

A neural network is a collection of algorithms that aims to identify underlying links in a set of data using a method that imitates how the human brain functions. In this context, neural networks are systems of neurons that can be either organic or synthetic in origin.

Since neural networks are capable of adapting to changing input, they can produce the best results without having to change the output criteria. The artificial intelligence-based concept of neural networks is quickly gaining popularity in the design of trading systems.

Neural networks are a set of algorithms that simulate how an animal brain works in order to find connections among enormous amounts of data.

As a result, they frequently resemble the synapses and connections between neurons in the brain.

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Suppose a Vestas 112-m wind turbine rated at 3.075 MW is installed at a site having Rayleigh wind statistics with an average wind speed of 8 m/s at the hub height. The cut-out speed VF is 25 m/s.
Estimate the annual electricity generation.
How many hours per year will the turbine be shutdown due to excessive winds

Answers

The annual electricity generation of the year, E = 8755.88 MWh/year.

Hours per year the turbine will be shutdown due to excessive winds,          T = 4.0883 hours/year

What is electricity?

Electricity is a group of physical phenomena that are connected to the presence and movement of matter that possesses an electric charge. In accordance with Maxwell's equations, magnetism and electricity are both components of the phenomenon known as electromagnetism.

Electricity is a factor in many everyday occurrences, including lightning, static electricity, electric heating, electric discharges, and a host of others.

An electric field is created when there is a charge present, which could be positive or negative. Electric current, which also creates a magnetic field, is created when electric charges move. An electric field that is not zero will exert a force on a charge when it is placed there.

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Hole filling fasteners (for example, MS20470 rivets) should not be used in composite structures primarily because of the
A. Possibility of causing delamination
B. Difficulty in forming a proper shop head.
C. Increased possibility of fretting corrosion in the fastener

Answers

Option c is correct. Hole filling fasteners (for example, MS20470 rivets) should not be used in composite structures primarily because of the  increased possibility of fretting corrosion in the fastener.

Fretting corrosion is the outcome of simultaneous physicochemical and mechanical surface interaction in a tribological contact, and it is the irreversible change of a material. A specific load and cyclic displacement with a limited amplitude must be applied to the contact between the surfaces of two materials for fretting corrosion to take place.

Small gaps develop between the surfaces in contact as a result of cyclic tension. Either material is lost or cracks start to appear as a result. Fretting corrosion's side effect of contact corrosion almost always causes a blockage because the lack of functional movement makes it impossible to remove debris. When debris is still trapped, there is blockage because the oxide takes up more space than the original material.

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the engine in problem 9-7 operating at 2500 rpm has an indicated thermal efficiency of 61%, combustion efficiency of 98%, and mechanical efficiency of 71%. calculate: (a) brake specific fuel consumption. [gm/kw-hr] (b) specific emissions of soot particulates. [gm/kw-hr] (c) emissions index of soot particulates. [gm/kg]

Answers

The engine operating at 2500 rpm has an indicated thermal efficiency of 61%, combustion efficiency of 98%, and mechanical efficiency of 71%, then its:

a) Brake specific fuel consumption is 0.0445 kg/hr

b) Specific emissions of soot particulates is 0.42 kW

c) Emissions index of soot particulates is 3.79 × 10¹⁵

What is mechanical efficiency?

Mechanical efficiency is a dimensionless number in mechanical engineering that quantifies how well a machine or mechanism converts the power input into the device's output. A machine is a mechanical linkage that uses applied force to move a load from one point to another.

A machine's power input is always equal to its input force times the velocity of its input point, and its power output is always equal to the force applied to its load times the velocity of the load.

The mechanical efficiency of a machine is a dimensionless number between 0 and 1 that measures the relationship between the machine's power output and power input. It is frequently represented by the Greek letter 'η'.

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isotropic point sources each emitting s neutrons/sec are placed in an infinite moderator at the four comers of a square of side a. compute the flux and current at the midpoint of any side of the square and at its center.

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Add the two numbers together and divide by two to determine the middle of any range. In this case, 0 + 5 equals 5, 5 / 2 equals 2.5.

A line segment's exact midpoint is the point that lies halfway between its two endpoints. It is therefore the average of the two endpoints, which is the average of the two x- and y-coordinates. Discover the endpoints' coordinates. As a result, the electric field along OB at midpoint O is 5.4 106 N C1. (b) At mid-point O, a test charge in the amount of 1.5 109 C is positioned. Line OA is the direction of the force. This is due to the fact that the charge applied at point B repels the negative test charge whereas point A attracts it.

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prob 3 knief 6-6) based on the 0.025-ev cross sections and the decay constants in fig. 2-16 and a thermal-neutron flux of 5 x 1013 /cm2s: (4 points total) a. estimate the fractional depletion of 235u during 1 year of operation. b. estimate the fraction of 238u that would be converted to 239u in 1 year. c. calculate the instantaneous decay and neutron absorption rates for 239u nuclei and determine their fraction of the combined loss rate. d. repeat (c) for 239np. e. estimate the fraction of 238u absorptions that result in the production of 239pu.

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A radioactive nuclide's decay constant (symbol: and units: s1 or a1) is its probability of decay per unit time. As a result, the number of parent nuclides P decreases with time t, as dP/P dt = −λ.

What is Radioactivity?

Radioactivity, as the name implies, is the act of emitting radiation spontaneously. This is accomplished by an atomic nucleus that is unstable for some reason; it "wants" to give up some energy in order to shift to a more stable configuration.

Much of modern physics was devoted to understanding why this happens during the first half of the twentieth century, with the result that nuclear decay was fairly well understood by 1960. When a nucleus has too many neutrons, it emits a negative beta particle, which converts one of the neutrons into a proton.

When there are too many protons in a nucleus, it emits a positron (positively charged electron), converting a proton into a neutron. When a nucleus has too much energy, it emits a gamma ray, which discards a large amount of energy without changing any of the particles in the nucleus. When a nucleus has too much mass, it emits an alpha particle, discarding four heavy particles (two protons and two neutrons).

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