Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates (Figure \(3(a))\). The top plate is moving at speed \(V\), and the bottom plate is stationary. The distance between these two plates is \(h .\) The gravity acts in the \(z\) direction so the flow can be considered essentially two dimensional in \(x-y\) plane. Assume there acts an applied pressure gradient in the \(x\) -direction with its gradient given by, \(\partial P / \partial x=\) \(\left(P_{2}-P_{1}\right) /\left(x_{2}-x_{1}\right)=\) constant, where \(x_{1}\) and \(x_{2}\) are two arbitrary locations along the \(x\) -axis, and \(P_{1}\) and \(P_{2}\) are the pressures at those two locations.

(i) Prove that the streamwise velocity field \(u\) is given by the following expression.

$$ u=\frac{V y}{h}+\frac{1}{2 \mu} \frac{\partial P}{\partial x}\left(y^{2}-h y\right) $$

(ii) An engineer claims that the, as the gap between walls continues to widen, the applied pressure gradient will eventually determines the drag force the two walls experience. Is his/her claim true? Justify your answer with reason(s).

In: Other

The force applied at the handle of the rigid lever causes the lever to rotate clockwise about the pin B through an angle of 2 degrees. Determine the average normal strain developed in each wire. The wires are unstretched when the lever is in the horizontal position. Please show work.

In: Other

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:

Constraint | Television | Radio | Online |
---|---|---|---|

Audience per advertisement | 150,000 | 17,000 | 35,000 |

Cost per advertisement | $1,500 | $250 | $500 |

Maximum media usage | 12 | 18 | 11 |

To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 10% of the Television Radio Online $1,500 $250 $500 18 total number of advertisements authorized

(a) If the promotional budget is limited to $24,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter "0"

What is the allocation of the budget among the three media?

What is the total audience reached?

(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.

In: Other

**PA 3-3 (Static) Consider a process consisting of three... **

Consider a process consisting of three resources. Assume there exists unlimited demand for the product.

• Resource 1 has a processing time of 6 minutes per unit.

• Resource 2 has a processing time of 3 minutes per unit.

• Resource 3 has a processing time of 5 minutes per unit.

**The three resources are staffed by different workers individually. The flow diagram is shown above. **

Round "Capacity of resource" to 3 decimal places.

a. What is the capacity of resource 2?

b. What is the bottleneck in the process?

c. What is the utilization of resource 2?

d How long does it take the process to produce 200 units starting with an empty system, assuming this is a worker-paced process?

In: Other

The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows:

Year | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Mileage | 3,100 | 4,050 | 3.400 | 3,800 | 3,700 |

a) Using a 2-year moving average, the forecast for year 6 = _______ miles (round your response to one decimal place).

b) If a 2-year moving average is used to make the forecast, the MAD based on this = _______ miles

c) The forecast for year 6 using a weighted 2-year moving average with weights of 0.35 and 0.65 (the weight of 0.65 is for the most recent period) =_______ (round your response to the nearest whole number).

The MAD for the forecast developed using a weighted 2-year moving average with weights of 0.35 and 0.65= _______ miles

d) Using exponential smoothing with α = 0.40 and the forecast for year 1 being 3.100, the forecast for year 6 = _______ miles

In: Other

Consider the following schema:

Suppliers (sid, sname, address)

Parts (pid, pname, colour)

Catalog(sid, pid, cost)

The key for Suppliers is sid, for Parts is pid, and for Catalog is sid and pid The Catalog relation associates prices charged for parts by suppliers.

Write the following queries using relational algebra. For items (a) through (e), use the "sequences of assignments" form. For items (f) and (g), use the "expression tree" form. List all assumptions. (Some marks will be given for the quality of your answers.)

(a) Find the names of suppliers who supply some blue part.

(b) Find the ids of suppliers who supply some blue or magenta part.

(c) Find the ids of suppliers who supply every magenta part.

(d) Find the ids of suppliers who supply every part.

(e) Find the ids of parts supplied by at least two different suppliers

(f) Find the ids of the most expensive parts supplied by company name named "Screw-2-You Limited".

(g) Find the ids of parts supplied by every supplier at less than or equal to $50. (If any supplier either does not supply the part or charges more than $50 for it, then that part should not be in the final relation.)

In: Other

The following table gives the number of pints of type A blood used at Damascus Hospital in the past 6 weeks

Week Of | Pints Used |
---|---|

August 31 | 360 |

September 7 | 370 |

September 14 | 410 |

September 21 | 381 |

September 28 | 366 |

October 5 | 378 |

a) The forecasted demand for the week of October 12 using a 3-week moving average = _______ pints .

b) Using a 3-week weighted moving average, with weights of 0.15, 0.30, and 0.55, using 0.55 for the most recent week, the forecasted demand for the week of October 12 = _______ points. (round your response to two decimal places and remember to use the weights in appropriate order the largest weight applies to most recent period and smallest weight applies to oldest period.)

c) lf the forecasted demand for the week of August 31 is 360 and α = 0.20, using exponential smoothing develop the forecast for each of the weeks with the known demand and the forecast for the week of October 12 .

Week Of | Pints Used | Forecast for this Date |
---|---|---|

August 31 | 360 | 360 |

September 7 | 370 | 360.00 |

September 14 | 410 | 362.00 |

September 21 | 381 | ◻ |

September 28 | 366 | ◻ |

October 5 | 378 | ◻ |

October 12 | - | ◻ |

In: Other

What exercise should be performed FIRST?

A.Broad jump

B.Back squat

C.Split squat

D.Power clean

In: Other

Given an array of numbers, find the index of the smallest array element (the pivot), for which the sums of all elements to the left and to the right are equal. The array may not be reordered.

Example arr=[1,2,3,4,6]

the sum of the first three elements, 1+2+3=6. The value of the last element is 6.

Using zero based indexing, arr[3]=4 is the pivot between the two subarrays.

The index of the pivot is 3.

Function Description

Complete the function balancedSum in the editor below.

balanced Sum has the following

parameter(s):

int arr(n): an array of integers

Returns:

int: an integer representing the index of the pivot

Constraints

3≤n≤10

^{5}1≤ arr[i]≤ 2 * 10

^{4}, where 0≤iIt is guaranteed that a solution always exists.

In: Other

Even Subarray A subarray is a contiguous portion of an array. Given an array of integers, determine the number of distinct subarrays that can be formed having at most a given number of odd elements Two subarrays are distinct if they differ at even one position their contents. For example, if numbers [1, 2, 3, 4] and the maximum number of odd elements allowed, k 1, the following is a list of the 8 distinct valid subarrays: [[1], [21, [3], [4], [1,2], [2, 31, [3, 4], [2, :

In: Other

Write out of the syllogistic forms AEE -1, using S and P as the subject and predicate terms of the conclusion, and M as the middle term. Then test the validity of each syllogistic form using a Venn diagram.

In: Other

State factors that differentiate between a manager and an entrepreneur?

In: Other

The monthly linear trend equation for the Hoopes ABC Beverage Store is:

ŷ = 5.50 + 1.25t

The equation is based on 4 years of monthly data and is reported in thousands of dollars. The index for January is 105.0 and for February it is 98.3. Determine the seasonally adjusted forecast for January and February of the fifth year.

In: Other

This chapter is filled with examples of statutes that have been struck down by the courts. A Texas law banning flag burning was rejected by the Supreme Court, as was a Louisiana death penalty statute. The Affordable Healthcare Act has been voided by two lower court judges, and the Supreme Court may or may not agree with the action.

Do you like the fact that courts can void laws that they determine to be in violation of the Constitution? Or is it wrong for appointed judges to overrule “the will of the majority” as expressed by elected members of Congress and state legislatures?

In: Other

Halmar the Great has boasted to his hordes of followers that many a notorious villain has fallen to his awesome sword: His total of 650 victims consists of evil sorcerers, trolls, and orcs. These he has slain with a total of 700 mighty thrusts of his sword; evil sorcerers and trolls each requiring two thrusts (to the chest) and orcs each requiring one thrust (to the neck). When asked about the number of trolls he has slain, he replies, "I, the mighty Halmar, despise trolls four times as much as I despise evil sorcerers. Accordingly, four times as many trolls as evil sorcerers have fallen to my sword!" How many of each type of villain has he slain?

In: Other