OpenSeas, Inc. is evaluating the purchase of a new cruise ship. The ship would cost $\$ 497$ million, and would operate for $20$ years. OpenSeas expects annual cash flows from operating the ship to be $\$ 71.1$ million (at the end of each year) and its cost of capital is $12.5 \%$.

a. Prepare an NPV profile of the purchase.

b. Estimate the IRR (to the nearest $1 \%$ ) from the graph.

c. Is the purchase attractive based on these estimates?

d. How far off could OpenSeas' cost of capital be (to the nearest $1\%$) before your purchase decision would change?

Circumferential fins of the rectangular profile are constructed of aluminum and attached to a copper tube having a diameter of $25 \mathrm{~mm}$ and maintained at $100^{\circ} \mathrm{C}$. The length of the fins is $2 \mathrm{~cm}$ and thickness is $2 \mathrm{~mm}$. The arrangement is exposed to a convection environment at $30^{\circ} \mathrm{C}$ with $h=15 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Assume that a number of fins are installed such that the total fin surface area equals that of the total surface fine area in the previous problem. Compute the total heat lost by the fins.

Calculate the viscous and turbulent shear stress components within the SAE $10 \mathrm{~W}$-$30$ oil $2$ in. from the wall of the smooth pipe. The volumetric flow is $1.85\ \mathrm{ft}^3 / \mathrm{s}$ and the pressure drop throughout the pipe length is $0.12\ \mathrm{psi} / \mathrm{ft}$. Use the power law velocity profile, to find the result. Take $\rho_o=1.78\ \mathrm{slug} / \mathrm{ft}^3$ and $\mu_o=2.09\left(10^{-3}\right) \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^2$.

A small fan moves air at a mass flowrate of 0.004 lbm/s. Upstream of the fan, the pipe diameter is 2.5 in., the flow is laminar, the velocity distribution is parabolic, and the kinetic energy coefficient, $\alpha_{1}$, is equal to 2.0. Downstream of the fan, the pipe diameter is 1 in., the flow is turbulent, the velocity profile is quite flat, and the kinetic energy coefficient, $\alpha_{2}$, is equal to 1.08. If the rise in static pressure across the fan is 0.015 psi and the fan shaft draws 0.00024 hp, compare the value of loss calculated: (a) assuming uniform velocity distributions, (b) considering actual velocity distributions.

Two liquids with different densities and viscosities fill the gap between parallel plates as shown in the given figure. The top plate moves to the left with a speed of $5 \mathrm{ft/s}$; the bottom plate moves to the right with a speed of 2 ft/s. The velocity profile consists of two linear segments as indicated. The fixed control volume $A B C D$ coincides with the system at time $t=0$. Make a sketch to indicate (a) the system at time $t=0.1 \mathrm{~s}$ and $(b)$ the fluid that has entered and exited the control volume in that time period.

A long rectangular channel has normal flow conditions at locations $\mathrm{A}$ and $\mathrm{D}$, respectively, far upstream and downstream of location $\mathrm{C}$. At $\mathrm{C}$ a change in slope occurs as shown. (a) Classify the water surface, and sketch the water surface and the energy grade line between A and D. (b) Determine the height $h$ of a transition such that normal flow conditions occur between $\mathrm{A}$ and $\mathrm{B}$, which is a short distance upstream of $\mathrm{A}$. (c) Explain what type of profile now exists downstream of $\mathrm{B}$.

Complete Yasmine’s profile on her favorite social networking site. Then create your own.

Nom : Yasmine

Age : J`ai 16 __________________.

Tout sur moi :Je suis ("génial, strict, sérieux") ____________________________.

Nationalité : Je suis (“fran$\c[c]$ais”) __________________ et (“algérien) ____________________________.

Musique préférée :J’aime bien la musique (“canadien”) __________________ et les films (“américain”) _____________________________________.

Cours préférée : J’aime les arts plastiques, mais les sciences physiques sont (“intéressant”) _________________________________________.

Nom _____________________________________________________.

Age _______________________________________________________.

Tout sur moi _______________________________________________________.

Netionalité ________________________________________________________.

Musique préférée _______________________________________________________.

Cours préférée ______________________________________________________.

A $2.5$-cm-diameter tube has circumferential fins of rectangular profile spaced at 9.5-mm increments along its length. The fins are constructed of aluminum and are $0.8 \mathrm{~mm}$ thick and $12.5 \mathrm{~mm}$ long. The tube wall temperature is maintained at $200^{\circ} \mathrm{C}$, and the environment temperature is $93^{\circ} \mathrm{C}$. The heat-transfer coefficient is $110 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$. Calculate the heat loss from the tube per meter of length.

Water flows from under a sluice gate into a horizontal rectangular channel at a rate of $3 \mathrm{~m}^3$ /s per meter of width. The channel is concrete, and the initial depth is $20 \mathrm{~cm}$. Apply the mentioned equation to construct the water-surface profile up to a depth of $60 \mathrm{~cm}$. In your solution, compute reaches for adjacent pairs of depths given in the following sequence: $d=20 \mathrm{~cm}, 30 \mathrm{~cm}, 40 \mathrm{~cm}, 50 \mathrm{~cm}$, and $60 \mathrm{~cm}$. Suppose that $f$ is constant with a value of $0.02$. Plot your results.

A circumferential fin of the rectangular profile is constructed of a material having $k=55 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$ and is installed on a tube having a diameter of $3 \mathrm{~cm}$. The length of fin is $3 \mathrm{~cm}$ and the thickness is $2 \mathrm{~mm}$. If the fin is exposed to a convection environment at $20^{\circ} \mathrm{C}$ with a convection coefficient of $68 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$ and the tube wall temperature is $100^{\circ} \mathrm{C}$, calculate the heat lost by the fin.

Air flows in a horizontal cylindrical duct of diameter D = 100 mm. At a section a few meters from the entrance, the turbulent boundary layer is of thickness $\delta_{1}$ = 5.25 mm, and the velocity in the inviscid central core is U$_{1}$ = 12.5 m/s. Farther downstream the boundary layer is of thickness $\delta_{2}$ = 24 mm. The velocity profile in the boundary layer is approximated well by the $\frac{1}{7}$-power expression. Find the velocity, U$_{2}$, in the inviscid central core at the second section, and the pressure drop between the two sections.

The velocity profile for fully developed flow of water between parallel plates with the upper plate moving is given by Eq. Assume $U=2 \mathrm{~m} / \mathrm{s}$ and $a=2.5 \mathrm{~mm}$. Determine the volume flow rate per unit depth for zero pressure gradient. Evaluate the shear stress on the lower plate and sketch the shear stress distribution across the channel. Would the volume flow rate increase or decrease with a mild adverse pressure gradient? Estimate the pressure gradient that will give zero shear stress at $y / a=0.25$. Sketch the shear stress distribution for this case.

MagicLand Carnival has a roller coaster with one section that has a profile similar to the diagram at the right. LandPlus, a local real estate company, would like to drape the side of the roller coaster with canvas and paint an advertisement on it. The MagicLand roller coaster operator provides the measurements (in feet) in the following table to the advertising agent of LandPlus. Approximate the amount of canvas required to cover the whole side.

A solid cylindrical specimen, made of perfectly plastic material, is being upset between flat dies with no friction. The process is carried out by a falling weight, as in a drop hammer. The downward velocity of the hammer is at a maximum when it first contacts the workpiece and becomes zero when the hammer stops at a certain height of the specimen. Establish quantitative relationships between workpiece height and velocity, and make a qualitative sketch of the velocity profile of the hammer. (Hint: The loss in the kinetic energy of the hammer is the plastic work of deformation; thus, there is a direct relationship between workpiece height and velocity.)