An axial fan $2 \mathrm{~m}$ in diameter is used in a wind tunnel as shown (test section $1.2 \mathrm{~m}$ in diameter; test section velocity of $60 \mathrm{~m} / \mathrm{s}$ ). The rotational speed of the fan is $1800 \mathrm{rpm}$. Assume the density of the air is constant at $1.2 \mathrm{~kg} / \mathrm{m}^3$. There are negligible losses in the tunnel. The performance curve of the fan is identical to that shown in the mentioned figure. Compute the power needed to operate the fan.

Refrigerant 134 a enters the compressor of a vapor compression heat pump at $30 \mathrm{lbf} /$ in. $^2, 20^{\circ} \mathrm{F}$ and is compressed adiabatically to $200\ \mathrm{lbf} / \mathrm{in}^2, 160^{\circ} \mathrm{F}$. Liquid enters the expansion valve at $200\ \mathrm{lbf} / \mathrm{in}^2, 120^{\circ} \mathrm{F}$. At the valve exit, the pressure is $30 \mathrm{lbf/in.}^2$ Find

(a) the isentropic compressor efficiency.

(b) the coefficient of performance.

Refrigerant 134a is the working fluid in an ideal vaporcompression refrigeration cycle operating at steady state. Refrigerant enters the compressor at 1 .4 bar, $-12^{\circ} \mathrm{C},$ and the condenser pressure is 9 bar. Liquid exits the condenser at $32^\circ C.$ The mass flow rate of refrigerant is 7 kg/min. Determine a. the compressor power, in kW. b. the refrigeration capacity, in tons. c. the coefficient of performance.

An office building requires a heat transfer rate of $20\ \mathrm{kW}$ to maintain the inside temperature at $21^{\circ} \mathrm{C}$ when the outside temperature is $0^{\circ} \mathrm{C}$. A vapor-compression heat pump with Refrigerant $22\mathrm{a}$ as the working fluid is to be used to provide the necessary heating. The compressor operates adiabatically with an isentropic efficiency of $82 \%$. Specify appropriate evaporator and condenser pressures of a cycle for this purpose assuming $\Delta T_{\text {cond }}=\Delta T_{\text {cvap }}=10^{\circ} \mathrm{C}$, as shown in figure. The states are numbered as in figure. The refrigerant exits the evaporator as saturated vapor and exits the condenser as saturated liquid at the respective pressures. Determine the (a) mass flow rate of refrigerant, in $\mathrm{kg} / \mathrm{s}$. (b) compressor power, in $\mathrm{kW}$. (c) coefficient of performance and compare with the coefficient of performance for a Carnot heat pump cycle operating between reservoirs at the inside and outside temperatures, respectively.. Compare the results with those of previous problem and discuss.

The following selected accounts appear in Shaw Company's unadjusted trial balance at December 31, 2018, the end of its fiscal year (all accounts have normal balances).

$$\begin{array}{lrlr} \text{ Prepaid advertising }& \$ 1,200 &\text{ Performance obligations }& \$ 5,400 \\ \text{ Wages expense }& 43,800 &\text{ Service fees revenue }& 87,000 \\ \text{ Prepaid insurance }& 3,420 &\text{ Rental income }& 4,900 \\ \end{array}$$

Prepare its adjusting entries at December 3 I. 2018. (1) using the financial statement effects template. and (2) in journal entry form using the following additional information.

1. Prepaid advertising at December 31 is $800.
2. Unpaid and unrecorded wages earned by employees in December are$1,300.
3. Prepaid insurance at December 31 is $2,280.
4. Perfomance obligations represent service fees collected in advance of when the services are provided to customers. Performance obligations at December 31 are$3,000.
5. Rent revenue of$ 1,000 owed by a tenant is not recorded at December 31 .

A residential heat pump system operating at a steady state is shown schematically in the given figure. Refrigerant 22 circulates through the components of the system, and property data at the numbered states are given in the figure. The compressor operates adiabatically. Kinetic and potential energy changes are negligible as changes in the pressure of the streams pass through the condenser and evaporator. Find

(a) the power required by the compressor, in $\mathrm{kW}$, and the isentropic compressor efficiency.

(b) the coefficient of performance.

A new surgical procedure is said to be successful 80% of the time. Suppose the operation is performed five times and the results are assumed to be independent of one another. a. What is the probability that all five operations are successful? b. What is the probability that exactly four are successful? c. What is the probability that less than two are successful? d. If less than two operations were successful, how would you feel about the performance of the surgical team?

Suppose that you have n values to put into an empty binary search tree.

1. In how many different orders can you add the n values to the tree? This is not the same as the number of possible binary search trees for n values. Explain why.
2. What is the probability that a randomly constructed binary search tree has worst-case performance? Hint: Compute the fraction of the total number of possible orders that results in the worst case.

A refrigerator is operated by a $0.25-\mathrm{hp}(1 \mathrm{hp}$= $746\ watts)$ motor. If the interior is to be maintained at $4.50^{\circ} \mathrm{C}$ and the room temperature on a hot day is $38^{\circ} \mathrm{C}$, what is the maximum heat leak (in $watts$) that can be tolerated? Assume that the coefficient of performance is $50 \%$ of the maximum theoretical value. What happens if the leak is greater than your calculated maximum value?

Determine the optimal control signal u for the system $\dot{\mathbf{x}}=\mathbf{A x}+\mathbf{B} u$ defined by

$$\mathbf{A}=\left[\begin{array}{rr}{0} & {1} \\ {0} & {-1}\end{array}\right], \quad \mathbf{B}=\left[\begin{array}{l}{0} \\ {1}\end{array}\right]$$

. Where such that the following performance index is minimized: $J=\int_{0}^{\infty}\left(\mathbf{x}^{T} \mathbf{x}+u^{2}\right) d t$

A one-sided confidence interval for p can be expressed as $p<\hat{p}+E \text { or } p>\hat{p}-E$, where the margin of error E is modified by replacing $z_{\alpha / 2}$ with $z_{\alpha}$. If Air America wants to report an on-time performance of at least x percent with 95% confidence, construct the appropriate one-sided confidence interval and then find the percent in question. Assume that a simple random sample of 750 flights results in 630 that are on time.

One yardstick for measuring how steadily-if slowly-athletic performance has improved is the mile run. In 1954, Roger Bannister of Britain cracked the 4-minute mark, setting the record for running a mile in 3 minutes, 59.4 seconds, or 239.4 seconds. In the half-century since then, the record has decreased by 0.3 second per year. If this trend continues, in which year will someone run a 3-minute, or 180-second, mile?

Consider a Carnot-cycle heat pump with R22 as the working fluid; Heat is rejected from the R-22 at 100 F: during which process the R-22 changes from saturated vapor to saturated liquid. The heat is transferred to the R-22 at 30 F. a. Show the cycle on a T-diagram. b. Find the quality of the R-22 at the beginning and end of the isothermal heat addition process at 30 F. c. Determine the coefficient of performance for the cycle.

In the 2008 baseball season, first baseman Ryan Howard of the Philadelphia Phillies led the Major Leagues with 48 home runs (HR) and 146 runs batted in (RBI). Overall, using all players with at least 300 plate appearances, the mean number of HR was $14.9$ with a standard deviation of $9.8$, whereas the mean number of RBI was $62.5$ with a standard deviation of $25.5$. Which was the more impressive PERFORMANCE? Explain, using the methods of this chapter.