The velocity in the $2-\text{cm}$-diameter pipe of Fig. has only one nonzero velocity component given by $u(r, t)=2\left(1-r^2 / r_0^2\right)\left(1-e^{-t / 10}\right)~\mathrm{m} / \mathrm{s}$, where $r_0$ is the radius of the pipe and $t$ is in seconds. Calculate the maximum velocity and the maximum acceleration: (a) Along the centerline of the pipe (b) Along a streamline at $r=0.5 \mathrm{~cm}$ (c) Along a streamline just next to the pipe wall [Hint: Let $v_z=u(r, t), v_r=0$, and $v_\theta=0$ in the appropriate equations in Table.]

Twenty-five samples of size 4 were taken from a production process. The sample means are listed in chronological order below. The mean of the sample means and the pooled standard deviation are:

$$\overline{\bar{x}}=13.3 \quad S=3.8$$

$$\begin{array}{rrrrrrr}14.5 & 10.3 & 17.0 & 9.4 & 13.2 & 9.3 & 17.1 \\ 5.5 & 5.3 & 16.3 & 10.5 & 11.5 & 8.8 & 12.6 \\ 10.5 & 16.3 & 8.7 & 9.4 & 11.4 & 17.6 & 20.5 \\ 21.1 & 16.3 & 18.5 & 20.9 & & & \end{array}$$

Find the centerline and control limits for the $\bar{X}$ chart.

Trees offsetting $\mathbf{C O}_2$. Trees can help offset the buildup of $\mathrm{CO}_2$ due to burning coal and other fossil fuels. $\mathrm{CO}_2$ can be absorbed by tree foliage. Trees use the carbon to grow, and release $\mathrm{O}_2$ into the atmosphere. Suppose a refrigerator uses $600 \mathrm{kWh}$ of electricity per year (about $2 \times 10^9 \mathrm{~J}$ ) from a $33 \%$ efficient coal-fired power plant. Burning $1 \mathrm{~kg}$ of coal releases about $2 \times 10^7 \mathrm{~J}$ of energy. Assume coal is all carbon, which when burned in air becomes $\mathrm{CO}_2$. How much coal is burned per year to run this refrigerator?

Cotner Clothes Inc. is considering the replacement of its old, fully depreciated knitting machine. Two new models are available: (a) Machine $190-3$, which has a cost of $\$ 190,000$, a $3$-year expected life, and after-tax cash flows (labor savings and depreciation) of $\$ 87,000$ per year; and (b) Machine $360-6$, which has a cost of $\$ 360,000$, a $6$-year life, and after-tax cash flows of $\$ 98,300$ per year. Assume that both projects can be repeated. Knitting machine prices are not expected to rise because inflation will be offset by cheaper components (microprocessors) used in the machines. Assume that Cotner's WACC is $14 \%$. Using the replacement chain and EAA approaches, which model should be selected? Why?

The hot water needs of a household are to be met by heating water at $55^{\circ} \mathrm{F}$ to $180^{\circ} \mathrm{F}$ by a parabolic solar collector at a rate of $5 \mathrm{lbm} / \mathrm{s}$. Water flows through a $1.25$-in-diameter thin aluminum tube whose outer surface is black anodized in order to maximize its solar absorption ability. The centerline of the tube coincides with the focal line of the collector, and a glass sleeve is placed outside the tube to minimize heat losses. If solar energy is transferred to water at a net rate of $350 \mathrm{Btu} / \mathrm{h}$ per ft length of the tube, find the necessary length of the parabolic collector to meet the hot water requirements of this house. Also, find the surface temperature of the tube at the exit.

An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an "employee athlete" program, encouraging every employee to devote 5 minutes an hour to physical activity. The company worries that the gains in productivity will be offset by the loss of time on the job. They'd like to know if the program increases or decreases productivity. To calculate it, they monitor a random sample of 145 employees who word process, calculating their hourly keystrokes both before and after the program is instituted. Here are the data:

a) What are the null and alternative hypotheses?

Long cylindrical $AISI$ stainless steel rods $(k=$ $7.74 \mathrm{~Btw} / \mathrm{h} \cdot \mathrm{ft} \cdot{ }^{\circ} \mathrm{F}$ and $\left.\alpha=0.135 \mathrm{~ft}^{2} / \mathrm{h}\right)$ of $4 -\mathrm{in}$-diameter are heat treated by drawing them at a velocity of $7 \mathrm{~ft} / \mathrm{min}$ through a $21-\mathrm{ft}$-long oven maintained at $1700^{\circ} \mathrm{F}$. The heat transfer coefficient in the oven is $20 \mathrm{~Btu} / \mathrm{h} \cdot \mathrm{ft}^{2} \cdot{ }^{\circ} \mathrm{F}$. If the rods enter the oven at $70^{\circ} \mathrm{F}$, Find their centerline temperature when they leave.

A pipe friction experiment for air consists of a smooth brass tube with 63.5 mm inside diameter; the distance between pressure taps is 1.52 m. The pressure drop is indicated by a manometer filled with Meriam red oil. The centerline velocity U is measured with a pitot cylinder. At one flow condition, U = 23 . 1 m/s and the pressure drop is 12.3 mm of oil. For this condition, evaluate the Reynolds number based on average flow velocity. Calculate the friction factor and compare with the value obtained from

$$\frac{1}{\sqrt{f}}=-2.0 \log \left(\frac{e / D}{3.7}+\frac{2.51}{\operatorname{Re} \sqrt{f}}\right) \text { for turbulent flow }(R e \geq 2300)$$

(use n = 7 in the power-law velocity profile).

Which statement is true about what will happen when the example code runs?

1: main PROC
2:     mov eax,40
3:     push offset Here
4:     jmp Ex4Sub
5:   Here:
6:     mov eax,30
7:     INVOKE ExitProcess,0
8: main ENDP
9:
10: Ex4Sub PROC
11:     ret
12: Ex4Sub ENDP

a. EAX will equal 30 on line 7

b. The program will halt with a runtime error on Line 4

c. EAX will equal 30 on line 6

d. The program will halt with a runtime error on Line 11

An incompressible liquid with negligible viscosity and density $\rho=1250 \mathrm{kg} / \mathrm{m}^{3}$ flows steadily through a 5-m-long convergent-divergent section of pipe for which the area varies as $A(x)=A_{0}\left(1+e^{-x / a}-e^{-x / 2 a}\right)$ where $A_{0}=0.25 \mathrm{m}^{2}$ and a=1.5 m. Plot the area for the first 5 m. Develop an expression for and plot the pressure gradient and pressure versus position along the pipe, for the first 5 m, if the inlet centerline velocity is 10 m/s and inlet pressure is 300 kPa. Hint: Use relation $u \frac{\partial u}{\partial x}=\frac{1}{2} \frac{\partial}{\partial x}\left(u^{2}\right)$.

A sawn wood post of rectangular cross section (Figure P16.93) consists of No. I Spruce-Pine-Fir lumber $\left(F_c=1,050 \mathrm{psi}\right.$; $E=1,200,000 \mathrm{psi}$ ). The finished dimensions of the post are $b=$ $5.5 \mathrm{in}$. and $h=7.25 \mathrm{in}$. The post is $12 \mathrm{ft}$ long, and the ends of the post are pinned. Using the interaction method and an allowable bending stress of $850 \mathrm{psi}$, determine the maximum allowable load that can be supported by the post if the load $P$ acts at an eccentricity of $e=6$ in. from the centerline of the post. Use the NFPA NDS column design formula.

A balanced budget amendment would allegedly cause instability, according to a common argument. The fiscal policy variables G and T are thought to be independent of income level. But this is not how things work in the real world. Since taxes are primarily based on income, larger incomes tend to result in higher taxes. In this issue, we look at how taxes react automatically to changes in autonomous spending to help offset their effects on output. Take into account the subsequent behavioural equations:

$$\begin{aligned} C &=c_0+c_1 Y_D \\ T &=t_0+t_1 Y \\ Y_D &=Y-T \end{aligned}$$

G and I are both constant. Assume that t1 is between 0 and 1. Suppose that the government starts with a balanced budget and that there is a drop in c0. What happens to Y? What happens to taxes?

The fiscal policy variables G and T are thought to be independent of income level. But this is not how things work in the real world. Since taxes are primarily based on income, larger incomes tend to result in higher taxes. In this issue, we look at how taxes react automatically to changes in autonomous spending to help offset their effects on output. Take into account the subsequent behavioural equations:

$$\begin{aligned} C &=c_0+c_1 Y_D \\ T &=t_0+t_1 Y \\ Y_D &=Y-T \end{aligned}$$

G and I are both constant. Assume that t1 is between 0 and 1. What is the multiplier? Does the economy respond more to changes in autonomous spending when t1 is 0 or when t1 is positive? Explain.

A hemisphere of radius $R$ is placed in a charge-free region of space where a uniform electric field exists of magnitude $E$ directed perpendicular to the hemisphere's circular base. (a) Using the definition of $\Phi_E$ through an "open" surface, calculate (via explicit integration) the electric flux through the hemisphere. [Hint: assume on the surface of a sphere, the infinitesimal area located between the angles $\theta$ (from the centerline parallel to electric field) and $\theta+d \theta$ is $d A=(2 \pi R \sin \theta)(R d \theta)=2 \pi R^2 \sin \theta d \theta$. ]