The vertical displacement at the center of the loaded shaft is zero. The vertical displacement at the end of the loaded shaft is equal to the length of the shaft multiplied by the slope of the shaft.
What is vertical displacement?
Vertical displacement in tectonics refers to the movement of land inside a vertical direction, which causes uplift and subsidence. Rock layer displacement can reveal information about how and why the lithosphere of Earth evolves over the course of geologic time. Vertical displacement can be caused by a variety of processes, including isostatic adjustments and tectonic activity. When crust is reorganised as a result of a seismic event, tectonic activity causes vertical displacement. Vertical displacement as a result of sinking from an increased load and isostatic rebound from a removed load is the outcome of isostatic corrections. At the margins of convergent and divergent plate boundaries, tectonic activity results in vertical displacement. As the magma begins to rise to protrude weaker lithospheric crust, the movement of the magma in the asthenosphere can cause divergent plate boundaries.
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the relative costs to find and repair an error or defect increase dramatically as we go from prevention to detection to internal failure to external failure costs.:
Prevention costs are the costs incurred to keep errors and defects from happening in the first place. These costs include things like design reviews, process audits, and training.
What is Prevention costs?
As part of the cost of quality, prevention expenditures are incurred in order to avoid product faults. Employee training & supplier certification are typically included in the cost of prevention. Generally speaking, preventing defects is what leads to the biggest increases in product quality. Even while such prevention entails additional expenses, these expenses are typically more than offset by savings linked to a decline in the frequency of defects. In the past, it was frequently thought that at some non-zero amount of defects, overall quality costs would be reduced. However, a belief that supports the objective of zero flaws has largely supplanted that one. This novel idea is supported by the observation that failure costs frequently reduce dramatically in response to tiny increases in prevention cost.
Detection costs are the costs incurred to find errors and defects once they have already occurred.
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How is the national saving in an open economy calculated?
The national savings in an open economy is calculated by adding private savings, public savings, and net capital inflows.
What is economy?
The creation, distribution, and exchange of goods and services, as well as their consumption, constitute the economy. It is broadly defined as a "social realm emphasising actions, discourses, and material expressions associated with the development, use, and management of finite resources." A given economy is a set of activities with primary variables such as culture, values, education, technological evolution, history, social organisation, political structure, legal systems, and natural resources. These factors provide context and content, as well as the conditions and parameters that govern an economy. Alternatively, the economic sphere is a social world of interconnected human activities and transactions that does not exist in isolation.
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13.when circuit breakers are classified as 100a through 2,000a frames, these numbers are normally referred to as the .
These figures are typically referred as the frame size when circuit breakers are categorised as 100a through 2,000a frames.
What is frames?
A frame is a digital data transfer unit used in telecommunication and computer networking. A frame is merely a straightforward container for a single network packet in packet switching systems. A frame is a repeating structure that supports time-division multiplexing in other telecommunications systems. The beginning or end of the payload data inside the stream of symbols and bits that the receiver receives are often indicated by a series of bits or symbols called frame synchronisation characteristics. When a frame is transmitted, a receiver connected to the system ignores the information until it notices a fresh frame synchronisation sequence.
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from the chart, estimate (roughly) the number of transistors per ic in 2018. using your estimate and moore's law, what would you predict the number of transistors per ic to be in 2040?
From the chart, it appears that the number of transistors per IC in 2018 is approximately 10 billion. Using Moore's Law, the number of transistors per IC in 2040 would be approximately 160 billion.
What is Moore's Law?
The observation known as Moore's law states that an integrated circuit's (IC) density doubles roughly every two years. Moore's law is a historical tendency that has been observed and projected. It is an empirical relationship connected to production experience gains rather than a physical law. The finding bears the name of Gordon Moore, a co-founder of Fairchild Semiconductor as well as Intel (and a former CEO of the latter), who predicted in 1965 that the number of components in an integrated circuit would double every year and that this rate of growth would last for at least another ten years. He updated his prediction in 1975, looking ahead to the following ten years, to doubling every two years, or a compound annual growth rate (CAGR) of 41%.
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A 6. 00-m-long, 500 kg steel uniform beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. A 70 kg construction worker stands at the far end of the beam.
18816 Nm is the amount of torque applied to the bolt by the worker and the weight of the beam.
The given parameters;
length of steel, L = 6.00 m
mass of steel, m = 500 kg
mass of work, m = 70 kg
The center of gravity of the beam Equals The torque caused by the worker and the weight of the beam is computed as follows:
= [tex]\frac{6.00}{2}[/tex]= 3 m
[tex]T_{t} = T_{1} + T_{2}\\T_{t} = F_{1} r_{1} + F_{2}r_{2}\\T_{t} = m_{1}gr_{!} + m_{2}gr_{2}\\[/tex]
[tex]T_{t} =[/tex](500 ×9.8×3) + (70×9.8×6.00)
[tex]T_{t} =[/tex]18816 Nm
This results in a torque of 18816 Nm being applied on the bolt by the worker and the weight of the beam.
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When we use gearing or some other power transmission system to reduce speed, the system often _______ torque.
answer choices
has the same
gains
looses
none of these
When we reduce speed by using gearing or another type of power transmission system, the system frequently gains torque.
Gears may appear to be "reduced" in size or quantity at first glance, which is only partially accurate. Gears are frequently utilized to achieve the desired outcome when a rotary machine, such as an engine or electric motor, needs the output speed reduced and/or torque raised.
By dividing the rotational speed of the rotary machine by a gear ratio more than 1:1, the term "gear reduction" explicitly refers to the speed of the rotary machine. A smaller gear (reduced size) with fewer teeth drives a larger gear (increased size) with more teeth, resulting in a gear ratio greater than 1:1.
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A day of the week is chosen and a month is chosen at random. What is the probability of choosing Saturday and a months that begins with the letter J?
The probability of choosing Saturday and a months that begins with the letter J is 1/28 (3.57%).
What is the probability?A day of the week is chosen and a month is chosen at random.the probability of choosing Saturday and a months that begins with the letter J is
3 months (January, June, July that start with J)
12 Months (number of possible outcomes)
Probability of choosing a J month is 3/12 = 1/4 (or 25%). Probabilities are denoted by fractions, decimals, or percentages.
one Saturday
seven days a week
Probability of choosing Saturday is 1/7 = (14.28%).
The likelihood of both events occurring simultaneously is 1/4 X 1/7 = 1/28 (3.57%).
The probability of choosing Saturday and a months that begins with the letter J is 1/28 (3.57%).
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in arizona, photovoltaic (pv) panels can generate an average annual power of 1 mw/acre. if there are 305 sunny days per year in arizona, but only 158 sunny days per year in pennsylvania, how much average power (in mw/acre) could the same pv panels generate in pennsylvania? please include two decimal places in your answer. note: assume that a cloudy day delivers 0 watts/acre of solar power. this is not true, but it simplifies the problem for us.
0.51 MW/acre is the average power (in mw/acre) could the same pv panels generate in pennsylvania.
What is average power?
The average power is the ratio of total effort or activity performed by the body to total time spent by the body. Average power is computed by dividing total energy expended by total time spent.
Given Data :-
Average annual power generation in Arizona =1MW/acre
Number of sunny days in Arizona per year = 311
Number of sunny days in Pennsylvania per year=160
To Find:-
Average annual power generation in Pennsylvania = ?
Solution:- As there is zero power generation on a cloudy day we will only calculate for the sunny days.
Therefore by crossmultiplying the values we get,
X = (160 * 1 ) 311
X = 0.51 MW/acre
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which type of nozzle can be driven through stucco, block, wood, or lightweight steel to access fires in concealed spaces?
To reach flames in hidden locations, a piercing nozzle can be pushed through stucco, brick, wood, or lightweight steel.
A nozzle is a tool used to change the properties of a fluid flow as it leaves (or enters) a closed chamber or conduit, particularly to enhance velocity.
A nozzle is often a pipe or tube with a variable cross sectional area that is used to control, direct, or alter the flow of a fluid (liquid or gas). Nozzles are widely used to regulate the stream that emerges from them in terms of flow rate, speed, direction, mass, form, and/or pressure.
A nozzle designed to propel gas or liquid into the environment in a coherent stream is known as a gas jet, fluid jet, or hydro jet. Gas stoves, ovens, and grills frequently have gas jets. Before the invention of electric light, gas jets were frequently employed as sources of illumination. Other varieties of fluid jets may be seen in spas and jacuzzis, where smooth, calibrated orifices are utilised to control the flow of fuel into an engine.
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which of the following is a windows programming interface that allows computers to communicate across a local area network (lan)? a. Sever Message Block (SMB) b. Null session values. c. SMTP d. NetBIOS e. Stealth Session
NetBIOS , (Network Basic Input or Output System) is just a network service that allows different computers' applications to communicate with one another over a local area network (LAN).
What is NetBIOS?
On local networks, NetBIOS provides communication services. It employs NetBIOS Frames, a software protocol that enables applications and computer systems on a local area network to interact with network hardware and transfer data across the network.
NetBIOS is a networking industry standard that stands for Network Basic Input/Output System. Sytek invented it in 1983, and it is frequently used there NetBIOS over TCP/IP protocol. It is, however, used in Token Ring networks and by Microsoft Windows.
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2. (a) a three-point transverse bending test is conducted on a cylindrical specimen of aluminum oxide having a reported flexural strength of 390 mpa (56,600 psi). if the specimen radius is 2.5 mm (0.10 in.) and the support point separation distance is 30 mm (1.2 in.), predict whether or not you would expect the specimen to fracture when a load of 620 n (140 lbf) is applied. justify your prediction. (b) would you be 100% certain of the prediction in part (a)? why or why not?
Since, Our calculated value of flexural length 373(Mpa) is less than 390(MPa) value therefore fracture is not predicted. Hence, Specimen will not fracture.
What is Flexural Length?
Flexural strength is a measure of concrete tensile strength. It is the ability of an unreinforced concrete beam and slab to withstand bending failure. Loading 6 x 6-inch (150mm x 150 mm) concrete beams with span length at least three times the depth is used to determine it. Flexural strength is measured using standard test methods which is ASTM C 78 (third-point loading) / ASTM C 293 and is expressed as Modulus of Rupture (MR) in psi (MPa) (center-point loading).
Depending on the type, size, and also volume of coarse aggregate used, flexural MR ranges from 10 to 20% of compressive strength. However, laboratory tests of given materials, mix design yield the best co - relation for specific materials. The MR calculated by third-point loading is lower, sometimes by as much as 15%, than the MR ascertained by center-point loading.
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Question 3
You are given a wood beam with the following information:
Base - 6in
Height - 2in
Span Length 7ft
Modulus of Elasticity= 1,820,000 lb/in^2
M
A force is applied to the beam which causes a delta max of 3 inches. The force that would cause this delta max is equal to _____ lbs.
152,880,000 lbs. When forces are stretching an object and producing its elongation, or when the length change L L is positive, tensile stress and strain occur, compressional tension.
How are wood beams calculated?Find the elastic modulus (E) of your wood beam.Find your beam's area moment of inertia (I), which is equal to I = b d3 / 12 = 1.5 in (7.5 in)3 / 12 = 52.73 inches to the fourth power.Let's say our beam must withstand a 15 pound per inch applied load.When calculating the beem force, the piston surface area and fluid pressure are multiplied by 70, where F is the force in Newtons (N). Piston area (A) is measured in square centimeters (cm2). F = A × P ÷ 70,The length and precise cross-sectional measurements of the 2 x 3 lumber beams should be measured and noted. Calculate the bending section modulus.Base: 6 in. 2 in. 7 ft. 18 20 000 delta152,880,000 lbs.To learn more about Wood beam refer to:
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152,880,000 lbs. Tensile stress and strain, as well as compressional tension, occur when forces stretch an object, causing it to elongate, or when the length change L L is positive.
How are wood beams calculated?When calculating the beem force, the piston surface area and fluid pressure are multiplied by 70, where F is the force in Newtons (N). Piston area (A) is measured in square centimeters (cm2).
Find the elastic modulus (E) of your wood beam.
Find your beam's area moment of inertia (I), which is equal to
I = b d3 / 12 = 1.5 in (7.5 in)3 / 12 = 52.73 inches to the fourth power.
Let's say our beam must withstand a 15 pound per inch applied load.
F = A × P ÷ 70,
The length and precise cross-sectional measurements of the 2 x 3 lumber beams should be measured and noted. Calculate the bending section modulus.
Base: 6 in. 2 in. 7 ft. 18 20 000 delta
152,880,000 lbs.
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a person that can use html, css, and javascript to create websites (as well as service the website and manage user accounts) is known as which of the following?
A person who can construct websites using HTML, CSS, and JavaScript (as well as maintain the website and handle user accounts) is referred to as a web developer.
What is website?
A website, often known as a web site, is a collection of web pages or related material that is published on for at least one web server and given a shared domain name. The World Wide Web is the collective name for all publicly accessible websites. A company's internal website because of its employees is an example of a private website that can only be accessed via a private network. Most websites focus on a single subject or objective, including news, education, business, entertainment, and social networking. The navigation of a website, which frequently begins with a home page, is aided by hyperlinks between web pages. On a variety of gadgets, including PCs, laptops, tablets, and smartphones, users can visit websites. A web browser is the name of the application used on these gadgets.
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Using the given section of the MARIE memory space, 10 points
What will be the AC value if Load 004 instruction is executed?
What will be the AC value if LoadI 004 instruction is executed?
What will be the MAR value if Add 004 instruction is executed?
Answer:
answer is B
Explanation:
suppose you are studying an unknown solution based on its precipitation reactions with other solutions, resulting in this data table. na2so4 nacl na2co3
Answer:
Ba ( [tex]No_{3}[/tex])2 and Sr ( NO3))2
A steel which has been rapidly cooled from Austenite to room temperature and then is reheated for a few (2-3) hours at a moderate temperature (-400 C) will be undergoing which process? a. Annealing b. Spheroidizing c. Tempering d. Normalizing e. Carburizing
Tempering rapid cooling is used to make steel hard.
What is steel?
Iron, which has a hardness similar to copper in its pure form, is a key component of steel. With the exception of very rare instances, iron is polycrystalline, like all other metals, which means that its crystals are connected at their boundaries. A well-ordered arrangement of atoms, best represented as contacting spheres, makes up a crystal. They are arranged in planes, referred to as lattices, that pierce one another in particular ways. For iron, a unit cube containing eight iron atoms at its corners serves as the finest representation of the lattice structure. The allotropy of iron, or its existence as two crystalline forms, is significant for the distinctiveness of steel.
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Do you like my drawing??
Answer:
Yes
Explanation:
That is a very nicely done drawing!
procedure in this activity you will identify the centroid location of common and complex shapes using object symmetry, mathematics, and mdsolids software. calculate and label the centroid location calculate, label, and dimension the x and y components. indicate the location of the centroid using the symbol.
It is extremely simple to determine the centroid of a form like a circle or square.The intersection of a triangle's three medians is where the triangle's centroid is found.
Calculate the centroid location ?It is regarded as one of the triangle's three points of concurrency—the incenter, circumcenter, and centroid.Within a triangle is where the centroid is located. The geometric center, however, only serves to indicate the centroid for an object like a beam if the material is uniform or homogeneous.A separate substance is frequently used to strengthen beams and other structures.The centroid's distance from the geometric center is probably altered by this strengthening.Engineers must take this into consideration while creating their designs. Equipment: Card stock, poster board, or a corkboard.- Paper that weighs no more than 20 kg. - Clear tapeScissors, 18 inches of twine, one washer, a thumbtack, a ruler, and MDSolids.To learn more about centroid location refer
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Name in each case two advantages and two disadvantages of the abovementioned( distillation, stripping ) thermal separation processes.
Thermal distillation and stripping are two processes used in substance separation and purification. Both processes of separation and purification have advantages and disadvantages.
What is Thermal distillation?
Thermal distillation involves heating a mixture and condensing the resulting vapors to form a pure product. This method can purify a wide range of substances, including water, alcohol, and other volatile liquids.
What is Stripping?
The stripping process is used to separate metal from scrap or ore in order to obtain pure metal in the form of a pellet or ingot. It is a technique for purifying a substance. The process of removing impurities from metals, ores, or other substances.
Advantages of distillation:
It is possible to use it to purify liquids.It is capable of separating liquid mixtures.Disadvantages of distillation:
It takes a lot of energy.Slowness is possible.Advantages of stripping:
It is capable of removing volatile impurities from liquids.Is a fairly simple procedureDisadvantages of stripping:
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experiment 8: dissociation constant of acetic acid by electrical conductivity measurements lab example
The dissociation constant as well as equivalent conductance at infinite dilution, Ao, of a weak electrolyte are computed using only two conductance measurements at different concentration levels. The iterative procedure used on acetic acid data produced the dissociation constant of 1.80 X 10-5 and, an average (n = 4) value of Ao of 389.5, compared to an expected value of 390.7.
What is Electrical conductivity?
Electrical conductivity is just a standard measure of how easily an electric current can flow through a material. Electrical resistivity, on the other hand, attempts to measure how firmly a material resists this same flow of electric current. Both properties are precise inverses of one another. The Greek letter σ denotes electrical conductivity, while the Greek letter ρ denotes electrical resistivity.
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technician a says that instrument panel warning lamps can indicate faults with various systems on the vehicle. technician b says that instrument panel warning lamps can indicate proper operation of various vehicle systems. who is correct?
Both technicians are correct in saying that warning lamps on the instrument panel can both signal a problem with a vehicle's systems and show that those systems are functioning properly.
Your automobile uses the dashboard warning lights to let you know when something is wrong, whether it's a door that wasn't closed properly or the dreaded check-engine light. They shine briefly when your car or truck warms up each time you start it, checking that all systems are secure and ready to drive. A light appears on the dashboard of the car when one or more sensors detect a part of it that isn't operating according to plan, signaling a problem that needs to be fixed. Comparable to a home's electrical fuse panel. As soon as you can, stop and turn off the engine if these lights start to appear. The check engine light in some vehicles may be red.
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when a function finishes executing, it returns a value back to the part of the program that called it. True or False
It's true that when a function finishes executing, it returns a value back to the part of the program that called the function.
Returning control to the calling function terminates the execution of the function. Immediately after the call, the execution is raised back in the caller's function. The calling function can get a value from the return statement. See Return Type for more details.
The calling function receives the value of the expression if it exists. If the expression is omitted, the return value of the function is undefined. If an expression is given, it is evaluated before being converted to the type returned by the function. The compiler issues a warning and does not evaluate an expression when the return statement in a function with return type void contains an expression.
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one of the differences between high density polyethylene (hdpe) and low density polyethylene (ldpe) is the higher crystallinity of ldpe.
The answer of polythylene is true.
What is polythylene?
Polyethylene or polythene is the most commonly made plastic. It is a polymer that is mostly used for packaging. In 2017, approximately 100 million tonnes of polyethylene resins were manufactured annually, accounting for 34% of the overall plastics market. Eric Fawcett and Reginald Gibson at the Imperial Chemical Industries (ICI) facilities in Northwich, England, unexpectedly found the first industrially feasible polyethylene synthesis (diazomethane is a very unstable compound that is normally avoided in industrial application). When a mixture of ethylene and benzaldehyde was subjected to extremely high pressure (several hundred atmospheres), a white, waxy substance was created.
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the mail theft reporting system aims to identify patterns in mail theft across geographic regions as well as compile ____relating to mail theft victims and monetary losses.
The goal of the mail theft reporting process is to spot trends in mail theft across different geographical areas as well as compile data pertaining to victims of mail theft and financial losses.
What is mail?
A system for physically delivering postcards, letters, and packages is known as the mail or post. Public or private postal services are both available, albeit many governments have limits on the former. National postal services have often been formed as a government monopoly since the middle of the 19th century, with a fee just on article prepaid. A postage metre is also used for bulk mailing, but adhesive postage stamps are typically used as proof of payment. The term "snail mail" was first used when email first became popular. In addition to conveying mail, postal authorities frequently perform other duties. In some nations, a postal, telegraph, & telephone (PTT) service also manages the telephone and telegraph networks in addition to the postal system. Some nations' postal services process passport applications as well as savings account applications.
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Write a game_setup function that does the following: 1. Creates a numpy array representing the 3 doors 2. Creates a numpy array representing the prizes (0 for goat and 1 for car). You should randomly choose one of the elements of the prize array to be a car and the others should be goats. 3. Your function should return the arrays of doors and prizes
A game_setup function,
def game_setup():
doors = np.array([1, 2, 3])
prizes = np.array([0, 0, 1])
np.random.shuffle(prizes)
return doors, prizes
What is function?
The fundamentals of Python functions, including who they are, their syntax, their primary parts, return keywords, the major types, will be covered in this course. Additionally, we'll examine several examples of Python function definitions. A function is a group of connected claims that together carry out a mathematical, analytic, or evaluative activity. Python functions are easy to define and crucial for programming at the intermediate level. The same standards apply to variable names and function names. The objective is to define a function by grouping together a few often performed actions. We can call the function and reuse the code contained within it using different variables rather than repeatedly writing the same code block for different input variables.
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. there are n people, each in possession of a different rumor. they want to share all the rumors with each other by sending electronic messages. assume that a sender includes all the rumors he or she knows at the time the message is sent and that a message may only have one addressee. design a greedy algorithm that always yields the minimum number of messages they need to send to guarantee that everyone of them gets all the rumors. (hint. the minimum number of messages for n
The Greedy Algorithm that always yields the minimum number of messages they (n number of people) need to send to guarantee that every one of them gets all the rumors is given as follows:
Func: (State, n) →
this · max = 1 if ! this · max || this · max > n
this · max_num = 1 if ! this · max _ num ||
this · max_num >n
messages = [ ]
if max_num = = n
for i in [ 1...n]
continue if i = = max_num
messages · push [max_num, i, max-state [i]]
else
messages · push [max_num, max_num + 1, max]
this · max + 1
this · max_num + =1
messages.
What is a Greedy Algorithm?A Greedy Algorithm is one that always selects the best instant, or local, option when searching for an answer.
Greedy algorithms discover the overall, or globally, the best solution to some optimization issues but may provide less-than-optimal solutions to specific cases of other problems.
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usgs stream-gauging stations record water depth, , and channel in order to calculate the discharge of the stream.
USGS stream-gauging stations record water depth and velocity and channel width in order to calculate the discharge of the stream.
Water discharge is used as a support for people's lives in the form of liquid substances. Water has the most important role in human needs. Water discharge is very closely related to time & volume. Water discharge is the velocity of the flow of liquid through the cross-sectional distance per unit time. Water discharge uses volume units per time or ml/second, liters/second, m³/second, liters/hour, m³/hour, and various other units. Discharge units are often used in monitoring the capacity (capacity) of water in rivers or dams so that the existing water can be controlled.
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A) Implement an algorithm to find the shortest path from the start node to the end node using an A* (A-star) heuristic search. Use the straight-line distance to the end node as a heuristic function. Show your pseudo code for this algorithm. Is this an admissible heuristic function? Why or why not?
Hint: Define the necessary functions to implement the search problem. This should include a function that takes a vertex as input and returns the set of vertices that can be reached in a straight line from the given vertex. You may need to implement a function that detects whether two-line segments intersect (the algorithm is attached). The problem can be solved using shortest path algorithms, but you are required to use A*.
B) Present the solutions for the following pair of starting point and ending point using the A* algorithm you implemented. Show the optimal path.
Start: (115, 655) End: (380, 560)
With the finding that g(n) = g*(n) for any expanded n, an A* uses a consistent heuristic to find the optimal routes to all extended nodes.
Is this a heuristic function that is acceptable? An algorithm is a process for executing a program step-by-step.An algorithm (/aelrm/ (listen)) is a finite series of precise instructions used in mathematics and computer science to solve a class of specific problems or perform a computation.Algorithms are used as specifications for carrying out calculations and processing data.Advanced algorithms can reroute the execution of the code along many paths by performing automated deductions (also known as automated reasoning) and using logical and mathematical tests (referred to as automated decision-making).Alan Turing was the first to refer to human characteristics as metaphorical representations of computers using terms like "memory," "search," and "stimulus."On the other hand, a heuristic is a problem-solving method that, particularly in problem domains, may not be completely defined or may not always result in the best or most accurate solutions.To learn more about heuristic function refer
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A sculptor uses a constant volume of modeling clay to form a cylinder with a large height and a relatively small radius. The clay is molded in such a way that the height of the clay increases as the radius decreases, but it retains its cylindrical shape. At time t=c, the height of the clay is 8 inches, the radius of the clay is 3 inches, and the radius of the clay is decreasing at a rate of 12 inch per minute. (a) at time t=c, at what rate is the area of the circular cross section of the clay decreasing with respect to time? show the computations that lead to your answer. Indicate units of measure.
The rate [tex]\frac{dr}{dh} = - \frac{r}{2h}[/tex] iat which the area of the circular cross section of the clay decreasing with respect to time.
Step-by-step explanation of the given problem:
The formula for calculating a cylinder's volume is: V = πr²h,
Where V is the volume, r is the cylinder's radius, and h is the cylinder's height.
The rate of change of the radius of the clay with respect to the height of the clay is to be expressed in terms of height h and radius r.
That is, dr / dh is expressed in terms of height h and radius r. To do so, we must first differentiate the volume from the height, i.e. find dV / dh:
V = πr²h
dV/dh = d/dh(π[tex]r^{2}[/tex]h)
dV/dh = π[tex]r^{2}[/tex] + 2πrh (dr/dh)
The volume is constant, hence dV/dh = 0.
We get,
0 = π[tex]r^{2}[/tex]h
dV/dh = π[tex]r^{2}[/tex] + 2πrh (dr/dh)
-π[tex]r^{2}[/tex] = 2πrh (dr/dh)
dr/dh = - π[tex]r^{2}[/tex]/2πrh
dr/dh = - r/2h
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The water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine–
generator at a location where the depth of the water is 50 m (Fig. below). Water is to be supplied at a rate of
5000 kg/s. If the electric power generated is measured to be 1862 kW and the generator efficiency is 95
percent, determine:
(a) the overall efficiency of the turbine–generator,
(b) the mechanical efficiency of the turbine, and
Energy, Energy Transfer, and General Energy Analysis
Example
c)the shaft power supplied by the turbine to
the generator.
From the prompt above, calculations show that:
the overall efficiency of the turbine–generator is 76%the mechanical efficiency of the turbine is 72%; The power of the shaft supplied by the turbine to the generator is 1, 768.9 kW.What is overall efficiency?The yearly total of electricity and mechanical energy generation and usable heat output divided by the fuel input required for heat produced in a cogeneration process and total electricity and mechanical energy production is referred to as overall efficiency.
To arrive at the above results:
Recall that:
Depth of water h = 50m
The Mass flow rate of water, m = 5000kg/s
Generated electric power, P = 1862
Generator efficiency n = 95%
i) To solve overall efficiency we have the expression:
Overall Efficient (Oe) = P/Power generated due to the potential energy of water that is stored (Pw)
Oe = P/Pw x 100% ...........................1
Recall that Potential Energy is given as:
PE = mgh
Hence, Pw - mgh
Plugging in values from the above expression
Pw = 5000 x 9.81 x 50
Pw = 2452500
Pw = 2452.5 kW
Plugging in the values into (1)
Overall Efficiency (Oe) = [1862/ 2452.5] * 100 %
Oe = 0.75922528032
Hence, Overall Efficiency (Oe) [tex]\approx[/tex] 76%
ii) To solve for mechanical Efficiency the formula is given by:
Mechanical Efficiency (Me) = [ Power of Shaft (Ps)/ Potential Energy of Water (Pw)] x 100% ..............................................(2)
In this case, the formula or expression for power generated (Pg) is:
n = Ps/Pg; Making Ps subject of the expression, we have,
Ps = Pg * n
Inputting the values, we have:
Ps = 1862 x 0.95
Ps = 1768.9 kW
Plugging the above into equation 2, we have:
Me = (1768 / 2452.5) x 100%
Me = 0.72089704383
Me [tex]\approx[/tex] 72%
iii) since the shaft power (Ps) is generated by the turbine to the generated, which is already computed in part ii above,
Power of the Shaft (Ps) = 1768.9kW
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