Steam expands isentropically through a converging nozzle operating at steady state from a large tank at $1.83\ \text{bar}$, $280^{\circ} \mathrm{C}$. The mass flow rate is $2 \mathrm{~kg} / \mathrm{s}$, the flow is choked, and the exit plane pressure is $1\ \text{bar}$. Determine the diameter of the nozzle, in $\mathrm{cm}$, at locations where the pressure is $1.5\ \text{bar}$, and $1\ \text{bar}$, respectively.

The seismic instrument is mounted on a structure which has a vertical vibration with a frequency of 5 Hz and a double amplitude of 18 mm. The sensing element has a mass m = 2 kg, and the spring stiffness is k = 1.5 kN/m. The motion of the mass relative to the instrument base is recorded on a revolving drum and shows a double amplitude of 24 mm during the steady-state condition. Calculate the viscous damping constant c.

A tank of Refrigerant 12 is at $150\ \mathrm{kPa}$ gage and $20^{\circ} \mathrm{C}$. Compute the weight flow rate through the nozzle for tank gage pressures of $125 \mathrm{kPa}, 100 \mathrm{kPa}, 75 \mathrm{kPa}, 50 \mathrm{kPa}$, and $25 \mathrm{kPa}$. Suppose that the temperature in the tank is $20^{\circ} \mathrm{C}$ for all cases. Plot the weight flow rate versus tank pressure.

Oxygen $\left(\mathrm{O}_{2}\right) \text { at } 25^{\circ} \mathrm{C},$ 100 kPa enters a compressor operating at steady state and exits at $260^\circ C,$ 650 kPa. Stray heat transfer and kinetic and potential energy effects are negligible. Modeling the oxygen as an ideal gas with k = 1.379, determine the isentropic compressor efficiency and the work in kJ per kg of oxygen flowing.

Consider a cross-sectional slice through an array of heat exchanger tubes. For each desired piece of information, choose which kind of flow visualization plot (vector plot or contour plot) would be most appropriate, and explain why. (a) The location of maximum fluid speed is to be visualized. (b) Flow separation at the rear of the tubes is to be visualized. $(c)$ The temperature field throughout the plane is to be visualized. (d) The distribution of the vorticity component normal to the plane is to be visualized.

Air flows at $1.42 \mathrm{~kg} / \mathrm{s}$ through a $100-\mathrm{mm}$ diameter duct. At the inlet section, the temperature and absolute pressure are $52^{\circ} \mathrm{C}$ and $60.0 \mathrm{kPa}$. At the section downstream where the flow is choked, $T_2=45^{\circ} \mathrm{C}$. Determine the heat addition per unit mass, the entropy change, and the change in stagnation pressure for the process, assuming frictionless flow.

In a dairy, milk at $100^{\circ} \mathrm{F}$ is reported to have a kinematic viscosity of $1.30$ centistokes. Calculate the Reynolds number for the flow of the milk at $45 \mathrm{gal} / \mathrm{min}$ through a $11/4$-in steel tube with a wall thickness of $0.065 \mathrm{in}$.

Determine to six decimal places the steady state vector corresponding to the given initial state vector. Also find the smallest integer k such that $\mathbf{x}_{k}=\mathbf{x}_{k+1}$ to 6 decimal places for all entries. (NOTE: Even if it is less computationally efficient, it may be easier to compute state vectors using powers of A instead of the recursive formula.)

$$A=\left[\begin{array}{cccc} 0.2 & 0.3 & 0.1 & 0.4 \\ 0.3 & 0.5 & 0.6 & 0.2 \\ 0.1 & 0.1 & 0.2 & 0.2 \\ 0.4 & 0.1 & 0.1 & 0.2 \end{array}\right], \ \mathbf{x}_{0}=\left[\begin{array}{c} 0.25 \\ 0.25 \\ 0.25 \\ 0.25 \end{array}\right]$$

A piezometer and a manometer containing mercury are connected to the venturi meter. If the levels are indicated, find the volumetric flow of water through the meter. Draw the energy and hydraulic grade lines. Take $\gamma_{\mathrm{Hg}}=846 \mathrm{lb} / \mathrm{ft}^3$

An ideal gas expands isentropically through a converging nozzle from a large tank at $120\ \mathrm{lbf} / \mathrm{in}^2, 600^{\circ} \mathrm{R}$, and discharges into a region at $60\ \mathrm{lbf} /$ in.$^2$ Find the mass flow rate, in $\mathrm{lb} / \mathrm{s}$, for an exit flow area of $1\ \mathrm{in.}^2$, , if the gas is (a) air, with $k=1.4$. (b) carbon dioxide, with $k=1.26$. (c) argon, with $k=1.667$.

A gearbox operating at steady state receives $25\ \mathrm{hp}$ along its input shaft, delivers power along its output shaft, and is cooled on its outer surface according to $\mathrm{hA}\left(T_{\mathrm{b}}-T_0\right)$, where $T_{\mathrm{b}}=130^{\circ} \mathrm{F}$ is the temperature of the outer surface and $T_0$ $=40^{\circ} \mathrm{F}$ is the temperature of the surroundings far from the gearbox. The product of the heat transfer coefficient $\mathrm{h}$ and outer surface area A is $40\ \mathrm{Btu} / \mathrm{h} \cdot{ }^{\circ} \mathrm{R}$. For the gearbox, determine, in hp, a full exergy accounting of the input power. Let $T_0=40^{\circ} \mathrm{F}$.

An electronic package with a surface area of $1 m^2$ placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1 kW of its power to the space through its exposed surface. The exposed surface has an emissivity of 1.0 and an absorptivity of 0.25. Determine the steady state exposed surface temperature of the electronic package (a) if the surface is exposed to a solar flux of $750 W/m^2,$ and (b) if the surface is not exposed to the sun.

(a) Calculate the heat flux through a sheet of brass 7.5 mm (0.30 in.) thick if the temperatures at the two faces are $150^{\circ} \mathrm{C}$ and $50^{\circ} \mathrm{C}$ $302^{\circ} \mathrm{F}$ and $122^{\circ} \mathrm{F}$); assume steady-state heat flow. (b) What is the heat loss per hour if the area of the sheet is $0.5 \mathrm{m}^{2}\left(5.4 \mathrm{ft}^{2}\right)$? (c) What is the heat loss per hour if soda–lime glass is used instead of brass? (d) Calculate the heat loss per hour if brass is used and the thickness is increased to 15 mm (0.59 in.).

Compare the work required at steady state to compress water vapor isentropically to $3\ \mathrm{MPa}$ from the saturated vapor state at $0.1\ \mathrm{MPa}$ to the work required to pump liquid water isentropically to $3\ \mathrm{MPa}$ from the saturated liquid state at $0.1\ \mathrm{MPa}$, each in $\mathrm{kJ}$ per $\mathrm{kg}$ of water flowing through the device. Kinetic and potential energy effects can be neglected.