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Show that, if the solution possesses a boundary layer character, from the behaviour of the solution at large values of η the following relation can be derived: 2 22w wf ” = f 

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Similar expansion boundary layer for β = –1


The Falkner–Skan equation describes the self–similar boundary layer solutions that are obtained for
pressure distributions that correspond to an external flow with me xxu ~)(, and reads: 2”’ ” (1 ‘ )f + f f + f = 0

where 1
2
m+
mβ = and where the following scaling has been used: ‘
e
u = f ( )u
1
2
eu xy m+η = x

In addition to the common boundary conditions, the case of a similar solution with non–zero normal velocity at the wall (suction or injection) has wf(0) = f; where: 2
1
w e
w
e
v u xf = u m


For suction vw is negative, hence fw positive. For fw = 0 separation will occur for a certain negative
vale of β.
A result of the non–linear character of the Falkner–Skan equation is that for negative β not every combination of β and fw allows a solution which possesses a boundary layer character (i.e. with u asymptotically approaching ue), whereas other combinations may display multiple solutions.
This is illustrated here for the case β = –1.

a. Determine which (inviscid) expansion geometry corresponds to the case β = –1.

b. Show that for this special case β = –1 the Falkner–Skan equation can be analytically integrated twice. Express the integration constants in the values which characterise the solution at the wall (i.e. wf and ”wf).

c. Show that, if the solution possesses a boundary layer character, from the behaviour of the solution at large values of η the following relation can be derived: 2 22w wf “ = f 

Hint: use the results of both integration steps!
Which values of fw allow boundary layer solutions?
Derive that the displacement thickness can be expressed in wf and ”wf.

d. The above shows that for certain values of wf two different solutions are possible. For one of them ”wf is positive and for the other negative (the latter hence shows flow reversal near the wall).
Determine both values of ”wf when wf = 2.25 and calculate the two corresponding velocity profiles by a numerical integration (choose any method).

Note: in this case no iteration is required, as all boundary conditions at the wall are known!

What are these ideals and values? Why were they important? How do different writers incorporate them into their works? Did certain values or ideals seem to become more or less important over time? If so, why?

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Early American writers

Consider the ideals, values, and themes that early American writers considered to be important and worthy of inclusion in their journals, sermons, and poems. What are these ideals and values? Why were they important? How do different writers incorporate them into their works? Did certain values or ideals seem to become more or less important over time? If so, why? Cite specific examples from the writings of Bradford, Winthrop, Bradstreet, and Edwards in your response.

Provide information on a musculoskeletal disorder for college-age. This information should be geared toward adults to inform them about musculoskeletal disorders and signs and symptoms of musculoskeletal disorders.

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Musculoskeletal Systems

View these articles:
https://www.nbcnews.com/health/kids-health/remote-learning-can-be-pain-kids-more-ways-one-n1243175
https://www.livescience.com/59637-tech-use-tied-to-carpal-tunnel-syndrome.html

Are Your Tech Habits Causing Carpal Tunnel Syndrome?

Provide information on a musculoskeletal disorder for college-age. This information should be geared toward adults to inform them about musculoskeletal disorders and signs and symptoms of musculoskeletal disorders. You can focus on any number of topics related to musculoskeletal disorders or causes including repetitive motions, ergonomics, or muscles, tendons, and ligaments among others.
You should include at least 4 citations total from a referred publication using APA style.

Derive the general expression for the cross-flow angle at the wall, as function of the ratio we/ue. Determine at which we/ue the maximum value of occurs, and what its value is.

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Stagnation flow on an infinite swept wing

For the flow near the stagnation line of an infinite swept wing the numerical solution is given (see table below) in the form of the nondimensional velocity profiles for the directions respectively perpendicular and parallel to the stagnation line, with:

a. Calculate the velocity profiles us/use and un/use, where the velocity vector has been decomposed w.r.t. the flow direction just outside the boundary layer, for the case that we/ue = 0.5. Scale the components with the outer flow velocity use:
w+u = u eese 22


Calculate in addition for this case the cross–flow angle )( = )( e

Give a graphical representation of the results as profiles of η; also, plot the velocity distributions in the form of a hodograph, i.e. us versus un.

b. Derive the general expression for the cross–flow angle at the wall, as function of the ratio we/ue. Determine at which we/ue the maximum value of occurs, and what its value is.


Numerical solution:

η u/ue w/we η u/ue w/we η u/ue w/we
0.0 0.00000 0.00000
0.1 0.11826 0.05704
0.2 0.22661 0.11405
0.3 0.32524 0.17091
0.4 0.41446 0.22749
0.5 0.49465 0.28356
0.6 0.56628 0.33889
0.7 0.62986 0.39319
0.8 0.68594 0.44616
0.9 0.73508 0.49751
1.0 0.77786 0.54692

1.1 0.81487 0.59411
1.2 0.84667 0.63883
1.3 0.87381 0.68085
1.4 0.89681 0.72000
1.5 0.91617 0.75616
1.6 0.93235 0.78924
1.7 0.94577 0.81925
1.8 0.95683 0.84619
1.9 0.96588 0.87017
2.0 0.97322 0.89130

2.5 0.99285 0.96058
3.0 0.99842 0.98851
3.5 0.99972 0.99733
4.0 0.99996 0.99951
4.5 1.00000 0.99993

(0)F” = 1.23259 (0)g = 0.57047
)g(

Is it covered by the UCC? What are the implied warranties?  What are the express warranties? What services does the company provide and under what circumstances. Do you think the consumer is properly protected? Why or why not?

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Product Warranty

Submit Reaction Paper III.
Look at a warranty for an iPod, a cell phone, or computer.
Consider the following questions:

Identify the parties to the warranty.
Is it covered by the UCC?
What are the implied warranties?  What are the express warranties?
What services does the company provide and under what circumstances.
Do you think the consumer is properly protected? Why or why not?

REMEMBER a limited warranty IS NOT the same as a implied warranty!!!!!
Write a 2-3 page reaction paper in MLA formatting and style. Make sure to utilize both legal arguments and your opinion in your analysis. See MLA Formatting and Style Guide. (Links to an external site.)
Save your document in rich-text format (rtf).

What is achieved by selecting the quantity of an activity at which marginal benefit equals marginal cost? Suppose the marginal benefit of an activity exceeds the marginal cost. What does the marginal decision rule say a maximizing decision maker will do?

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PRINCIPLES OF MICROECONOMICS


1. What is achieved by selecting the quantity of an activity at which marginal benefit equals marginal cost?
2. Suppose the marginal benefit of an activity exceeds the marginal cost. What does the marginal decision rule say a maximizing decision maker will do?
3. Suppose you are a discus hurler and your goal is to maximize the distance you achieve. You “produce” discus hurls by practicing. The total benefit of practice is distance achieved, and the input that achieves this distance is hours of practice. Describe the total benefit curve of practice. What point on the curve would you select?
4. This chapter argues that consumers maximize utility and firms maximize profits. What do you suppose each of the following might be presumed to maximize?
a. A minister or rabbi
b. A United States Senator
c. The manager of a major league baseball team
d. The owner of a major league baseball team
e. The director of a charitable organization
5. For each of the following goods, indicate whether exclusive, transferable property rights exist and whether the good poses a problem for public policy. If it does, does the problem relate to a problem of property rights?
a. Clean air
b. Tomatoes
c. Housing
d. Blue whales
6. The dry-cleaning industry is a major source of air pollution. What can you conclude about the price and output of dry-cleaning services?
7. Economists often recommend that polluters such as dry-cleaning establishments be charged fees for the pollution they emit. Critics of this idea respond that the establishments would simply respond by passing these charges on to their customers, leaving the level of pollution unchanged. Comment on this objection.
8. Government agencies often require that children be inoculated against communicable diseases such as polio and measles. From the standpoint of economic efficiency, is there any justification for such a requirement?
9. Which of the following goods or services are public? Why or why not?
a. Libraries
b. Fire protection
c. Television programs
d. Health care
e. Water for household consumption
10. If a village in Botswana is granted several licenses to kill elephants, how does this give it an incentive to preserve elephants and increase the size of the herd? How does the international ban on ivory sales affect the incentive in Botswana to preserve the elephant?
11. The number of fish caught in the ocean has fallen in recent years partly as a result of more intensive
fishing efforts and the use of more sophisticated equipment. Fish in the ocean are a common property
resource. How might this fact be related to declining fish catches? How do you think this drop in the catch
affects the price of seafood?

What would be your tax liability under the current system? What would be the effective tax rate under the current system? What would be your tax liability under this new 18% flat tax system? Would you vote in favor of this flat tax system? Explain your position.

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ACC 261 Online – Discussion Problem 2

Every year during the tax filing season, people complain about how complex the tax system has become. Assume that Congress is considering passing legislation to do away with the current tax system and impose a 18% flat tax on all income. This means there is no longer tax free provisions such as the gain exclusion on the sale of your home, social security income, tax-exempt interest, life insurance proceeds, and child support. This also means that there are no special loopholes, no longer an Alternative Minimum Tax (see Ch. 13), no filing status distinctions, no tax credits, and no graduated tax rates.
1. What would be your tax liability under the current system?
2. What would be the effective tax rate under the current system?
3. What would be your tax liability under this new 18% flat tax system?
4. Would you vote in favor of this flat tax system? Explain your position.
5. Would the government have a budget surplus or deficit under this new system with respect to these two taxpayers (assume all other factors remain constant)? Is this system fair?

Distinguish between private goods and public goods and relate them to the free rider problem and the role of government. Explain why a common property resource is unlikely to be allocated efficiently in the marketplace.

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MARKET FAILURE


1. Explain what is meant by market failure and the conditions that may lead to it.
2. Distinguish between private goods and public goods and relate them to the free rider problem and the role of government.
3. Explain the concepts of external costs and benefits and the role of government intervention when they are present.
4. Explain why a common property resource is unlikely to be allocated efficiently in the marketplace.

After evaluating the characteristic of perfect competition and monopoly, which market structure do you believe is close to the hotel industry in the U.S.?

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Perfect competition and monopoly

Based on the assigned readings, what is your understanding of perfect competition and monopoly? What the main characteristic of each market structure?

After evaluating the characteristic of perfect competition and monopoly, which market structure do you believe is close to the hotel industry in the U.S.?

Address each of the following based on your knowledge of how firms operate in different markets:

Why might a profitable motel shut down in the long run if the land on which it is located becomes extremely valuable due to surrounding economic development? What kinds of costs are involved in making a decision to shut down? – your textbook identifies a specific rule a business needs to follow top make a shutdown decision.

Who will benefit from the service you’re providing? What percentage of the population of your city will benefit? What is the criteria for participating?

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Percentages and Budgets

Report on an actual percentage of people (or animals) benefiting from the current program, a new percentage of volunteers needed for the program in the future, and new budget percentages for the program for the upcoming fiscal year.

Paragraph 1: Introduction – What is the program?

Paragraph 2: Budget Information – What’s the budget? List percentages and actual amounts for each category in your budget.

Paragraph 3: Volunteers – How many do you need and what percentage of the population is that? Do they need any special training? Where might you find volunteers?

Paragraph 4: Beneficiaries – Who will benefit from the service you’re providing? What percentage of the population of your city will benefit? What is the criteria for participating?

Paragraph 5: Conclusion – What are the goals for the project? What is the overall effect on the community?