A 1-m-diameter Pelton wheel rotates at 300 rpm. Which of the following heads (in meters) would be best suited for this turbine: (a) 2, (b) 5, (c) 40, (d) 70, or (e) 140? Explain.

Water at $40^{\circ} \mathrm{C}$ is pumped from an open tank through 200 m of 50-mm-diameter smooth horizontal pipe and discharges into the atmosphere with a velocity of 3 m/s. Minor losses are negligible. (a) If the efficiency of the pump is 70%, how much power is being supplied to the pump? (b) What is the $\mathrm{NPSH}_{A}$ at the pump inlet? Neglect losses in the short section of pipe connecting the pump to the tank. Assume standard atmospheric pressure.

Water flows through the Pelton wheel turbine shown in the figure. For simplicity, we assume that the water is turned $180^{\circ}$ by the blade. Show, based on the energy equation, that the maximum power output occurs when the absolute velocity of the fluid exiting the turbine is zero.

The static pressure to stagnation pressure ratio at a point in a gas flow field is measured with a Pitot-static probe as being equal to 0.6. The stagnation temperature of the gas is $20^{\circ} \mathrm{C}$. Determine the flow speed in m/s and the Mach number if the gas is air. What error would be associated with assuming that the flow is incompressible?

A person is donating blood. The pint bag in which the blood is collected is initially flat and is at atmospheric pressure. Neglect the initial mass of air in the 1/ 8 -in. I.D. 4 ft-long plastic tube carrying blood to the bag. The average blood pressure in the vein is 40 mmHg above atmospheric pressure. Estimate the time required for the person to donate one pint of blood. Assume that blood has a specific gravity of 1.06 and a viscosity of $1.0 \times 10^{-4}\hspace{1mm} \frac{\text{lb}\cdot\text{sec}}{\text{ft}^{2}}$. The needle's I.D. is 1/ 16 inch and the needle length is 2.0 in. The bag is 1.0 ft below the needle inlet and the vein's I.D is 1/ 8 in.

Air flows steadily and isentropically from standard atmospheric conditions to a receiver pipe through a converging duct. The cross-sectional area of the throat of the converging duct is 0.05 ft$^{2}$. Determine the mass flowrate through the duct if the receiver pressure is (a) 10 psia, (b) 5 psia. Sketch temperature–entropy diagrams for situations (a) and (b). Verify results obtained with values from the appropriate graph with calculations involving ideal gas equations. Is condensation of water vapor a concern? Explain.

Supersonic airflow enters an adiabatic, constant area (inside diameter = 1 ft) 30-ft-long pipe with $\mathrm{Ma}_{1}$ = 3.0. The pipe friction factor is estimated to be 0.02. What ratio of pipe exit pressure to pipe inlet stagnation pressure would result in a normal shock wave standing at (a) x = 5 ft, or (b) x = 10 ft, where x is the distance downstream from the pipe entrance? Determine also the duct exit Mach number and sketch the temperature-entropy diagram for each situation.

A 1-m-diameter Pelton wheel rotates at 300 rpm. Which of the following heads (in meters) would be best suited for this turbine: (a) 2, (b) 5, (c) 40, (d) 70, or (e) 140? Explain.

Standard atmospheric air $\left(T_{0}=59^{\circ} \mathrm{F}, p_{0}=14.7 \mathrm{psia}\right)$ is drawn steadily through a frictionless and adiabatic converging nozzle into an adiabatic, constant cross-sectional area duct. The duct is 10 ft long and has an inside diameter of 0.5 ft. The average friction factor for the duct may be estimated as being equal to 0.03. What is the maximum mass flowrate in slugs/s through the duct? For this maximum flowrate, determine the values of static temperature, static pressure, stagnation temperature, stagnation pressure, and velocity at the inlet [section (1)] and exit [section (2)] of the constant area duct. Sketch a temperature-entropy diagram for this flow.

The gas entering a rocket nozzle has a stagnation pressure of 1500 kPa and a stagnation temperature of $3000{ }^{\circ} \mathrm{C}$. The rocket is traveling in the still Standard Atmosphere at $30,000 \mathrm{~m}$. Determine the throat and exit area for a flow rate of $10 \mathrm{~kg} / \mathrm{s}$. Assume $k=135, R=$ $287.0 \mathrm{~N} \cdot \mathrm{m} / \mathrm{kg} \cdot \mathrm{K}$. The gas is perfect, expanded to the ambient pressure.

Often young children drink milk $\left(\rho=1030 \hspace{1mm} \mathrm{kg} / \mathrm{m}^{3}\right)$ through a straw. Determine the maximum length of a vertical straw that a child can use to empty a milk container, assuming that the child can develop 75 mmHg of suction, and use this answer to determine if you think this is a reasonable estimate of the suction that a child can develop.

Water at 20 $^{\circ} \mathrm{C}$ flows down a vertical pipe with no pressure drop. Find the range of pipe diameters D (if any) for which the flow is definite.y laminar.

A convergent-divergent nozzle has an exit throat area ratio of 3.0. It is to be supplied with air. Find: (a) The first, second, and third critical pressure ratios; (b) The exit plane Mach number in each case; $(c)$ The throat Mach number in each case.

The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately 11,000 m below the surface. For a surface density of 1030 $\mathrm{kg} / \mathrm{m}^{3}$ , a constant water temperature, and an isothermal bulk modulus of elasticity of $2.3 \times 10^{9}\hspace{1mm} \mathrm{N} / \mathrm{m}^{2}$, find the pressure at this depth.