Water flows through a turbine. Calculate the power (MW) transmitted by the output shaft of the turbine. The water density is $1000 \mathrm{~kg} / \mathrm{m}^3$. The elevation of the upper reservoir surface is $720 \mathrm{~m}$ and that of the lower reservoir is $695 \mathrm{~m}$. The pipeline diameter is $2.2 \mathrm{~m}$, the total length is $50 \mathrm{~m}$, and the mean velocity is $2.4 \mathrm{~m} / \mathrm{s}$. The friction factor is $0.25$. The sum of minor loss coefficients is $4.7$. The turbine efficiency is $80 \%$. Choose the closest answer (MW): (a) $1.6$, (b) $1.7$, (c) $2.0$, (d) $2.1$, (e) $2.5$.

If an automobile tire develops a leak, how does the mass of air and density change inside the tire with time? Assuming the temperature remains constant, how is the change in density related to the tire pressure?

Air with a density of $0.0644\ \mathrm{lbm} / \mathrm{ft}^3$ is flowing upward in the vertical duct, as shown. The velocity at the inlet (station 1 ) is 80 $\mathrm{ft} / \mathrm{s}$, and the area ratio between stations 1 and 2 is $0.5$ $\left(A_2 / A_1=0.5\right)$. Two pressure taps, $10\ \mathrm{ft}$ apart, are connected to a manometer, as shown. The specific weight of the manometer liquid is $120\ \mathrm{lbf} / \mathrm{ft}^3$. Determine the deflection, $\Delta h$, of the manometer.

The heat exchanger consists of $20 \mathrm{~m}$ of drawn tubing $2 \mathrm{~cm}$ in diameter with 19 return bends. The flow rate is $3 \times 10^{-4} \mathrm{~m}^3 / \mathrm{s}$. Water enters at $20^{\circ} \mathrm{C}$ and exits at $80^{\circ} \mathrm{C}$. The elevation difference between the entrance and the exit is $0.8 \mathrm{~m}$. Compute the pump power needed to operate the heat exchanger if the pressure at 1 equals the pressure at 2. Use the viscosity corresponding to the average temperature in the heat exchanger.

Water flows out of a reservoir, through a penstock, and then through a turbine. Calculate the total head loss in units of meters. The mean velocity is $5.3 \mathrm{~m} / \mathrm{s}$. The friction factor is $0.02$. The total penstock length is $30 \mathrm{~m}$ and the diameter is $0.3 \mathrm{~m}$. There are three minor loss coefficients: $0.5$ for the penstock entrance, $0.5$ for the bends in the penstock, and $1.0$ for the exit. Select the closest answer (m): (a) $1.2$, (b) $2.8$, (c) $3.8$, (d) $4.8$, (e) $5.7$.

Air (40$^{\circ}$C, 1 atm) will be transported in a straight horizontal copper tube over a distance of 150 m at a rate of 0.1 m3/s. If the pressure drop in the tube should not exceed 6 in H2O, what is the minimum pipe diameter?

A train travels through a tunnel as shown in the given figure . The train and tunnel are circular in cross-section. Clearance is small, causing all air $\left(60^{\circ} \mathrm{F}\right)$ to be pushed from the front of the train and discharged from the tunnel. The tunnel is $10 \mathrm{ft}$ in diameter and is concrete. The train speed is $50 \mathrm{fps}$. Assume the concrete is very rough $\left(k_s=0.05 \mathrm{ft}\right)$.

a. Determine the change in pressure between the front and rear of the train that is due to pipe friction effects.

b. Sketch the energy and hydraulic grade lines for the train position shown in the given figure.

c. What power is required to produce the airflow in the tunnel?

A fluid flows through a pipe. Calculate the drop in piezometer level $(\Delta h)$ in units of $\mathrm{cm}$. The flow is steady and fully developed. The fluid is Newtonian. The mean velocity is $0.4 \mathrm{~m} / \mathrm{s}$. The Reynolds number is 100,000. The relative roughness is $0.002$.

What is f for the flow of water at 10$^{\circ}C$ through a 10-cm cast-iron pipe with a mean velocity of 4 m/s?

Water is pumped through a heat exchanger consisting of tubes 6 mm in diameter and 6 m long. The velocity in each tube is 12 cm/s. The water temperature increases from 20ºC at the entrance to 30$^{\circ}$C at the exit. Calculate the pressure difference across the heat exchanger, neglecting entrance losses but accounting for the effect of temperature change by using properties at average temperatures.

Velocity measurements are made in a 30-cm pipe. The velocity at the center is found to be 1.5 m/s, and the velocity distribution is observed to be parabolic. If the pressure drop is found to be 1.9 kPa per 100 m of pipe, what is the kinematic viscosity v of the fluid? Assume that the fluid’s specific gravity is 0.80.

Water is flowing through a gate valve $\left(K_v=0.2\right)$. Calculate the value of $b$ in units of $\mathrm{mm}$. The pipe is horizontal. The flow is steady and fully developed. Over a 3-meter pipe length upstream of the valve, the EGL drops by $a=430 \mathrm{~mm}$. The pipe ID is $0.25$ $\mathrm{m}$ and the friction factor in the pipe is $0.03$. Choose the closest answer (mm): (a) 180, (b) 240, (c) 320, (d) 340, (e) 360.

Glycerine $\left(T=20^{\circ} \mathrm{C}\right)$ flows through a funnel with $D=1.3 \mathrm{~cm}$ as shown. Calculate the mean velocity of the glycerine exiting the tube. Assume the only head loss is due to friction in the tube.

Glycerine at $20^{\circ} \mathrm{C}$ flows at $0.6 \mathrm{~m} / \mathrm{s}$ in the $2 \mathrm{~cm}$ commercial steel pipe. Two piezometers are used as shown in the given figure to measure the piezometric head. The distance along the pipe between the standpipes is $1 \mathrm{~m}$. The inclination of the pipe is $20^{\circ}$. What is the height difference $\Delta h$ between the glycerine in the two standpipes?