The rectangular gate shown in Fig. is $3 \mathrm{~m}$ wide. The force $P$ needed to hold the gate in the position shown is nearest: (A) $24.5 ~\mathrm{kN}$ (B) $32.7 ~\mathrm{kN}$ (C) $98 ~\mathrm{kN}$ (D) $147 ~\mathrm{kN}$

For the inclined-tube manometer of the figure, the pressure in pipe $A$ is $0.6$ psi. The fluid in both pipes $A$ and $B$ is water, and the gage fluid in the manometer has a specific gravity of 2.6. What is the pressure in pipe $B$ corresponding to the differential reading shown?

The pressure in the foothills of the Rockies near Boulder, Colorado is $84 ~\mathrm{kPa}$. The pressure, assuming a constant density of $1.00 ~\mathrm{~kg} / \mathrm{m}^3$, at the top of a nearby $4000$-$\mathrm{m}$-$\mathrm{high}$ mountain is closest to: (A) $60~ \mathrm{kPa}$ (B) $55 ~\mathrm{kPa}$ (C) $50 ~\mathrm{kPa}$ (D) $45 ~\mathrm{kPa}$

Water at a temperature of $77^{\circ} \mathrm{C}$ is to be evaporated slowly in a vessel. The water is in a low-pressure container surrounded by steam as shown in the sketch below. The steam is condensing at $107^{\circ} \mathrm{C}$. The overall heat transfer coefficient between the water and the steam is $1100 \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}$. Calculate the surface area of the container that would be required to evaporate water at a rate of $0.01 \mathrm{~kg} / \mathrm{s}$.

A jet-propelled airliner flies at an altitude of 15,000 m and a velocity of 265 m/s. What is the stagnation pressure and stagnation temperature of the air entering the engine? If the airliner is stationary on the ground, the engines are running with the same Mach number flow into the engines, and the airflow to each engine is $40 \mathrm{~kg} / \mathrm{s}$. what is the airflow to each engine at the above flight conditions?

Find the horizontal and vertical forces to hold stationary the nozzle. The fluid flowing through it is 10$^{\circ}$ C liquid water; $A_1=1.0 \mathrm{~m}^2, A_2=0.25 \mathrm{~m}^2, V_1=20 \mathrm{~m} / \mathrm{s}, p_2=p_{\text {atm }}$ and $p_1=p_{\text {atm }}+30$ kPa. Neglect gravity.

A large heated steel block $(\rho = 7832 kg/m^3, c_p = 434 J/kg \cdot K, k = 63.9 W/m \cdot K,$ and $\alpha = 18.8 \times 10^{–6} m^2/s)$ is allowed to cool in a room at $25^\circ C.$ The steel block has an initial temperature of $4506\circ C$ and the convection heat transfer coefficient is $25 W/m^2 \cdot K.$ Assuming that the steel block can be treated as a quarter-infinite medium, determine the temperature at the edge of the steel block after 10 minutes of cooling.

The roller coaster car has a mass of 700 kg, including its passenger. If it is released from rest at the top of the hill A, determine the minimum height h of the hill crest so that the car travels around both inside the loops without leaving the track. Neglect friction, the mass of the wheels, and the size of the car. What is the normal reaction on the car when the car is at B and when it is at C? Take $\rho_B = 7.5$ m and $\rho_C = 5$ m.

The roller coaster car has a mass of 700 kg, including its passenger. If it starts from the top of the hill A with a speed $v_A = 3$ m/s, determine the minimum height h of the hill crest so that the car travels around the inside loops without leaving the track. Neglect friction, the mass of the wheels, and the size of the car. What is the normal reaction on the car when the car is at B and when it is at C? Take $\rho_B = 7.5$ m and $\rho_C = 5$ m.

The air velocity in the duct is $750 \mathrm{ft} / \mathrm{s}$. The air static temperature is $100^{\circ} \mathrm{F}$. Use the mercury manometer measurement to calculate the static and stagnation pressures of the flowing air.

The 800-lb roller-coaster car starts from rest on the track having the shape of a cylindrical helix. If the helix descends 8 ft for every one revolution, determine the time required for the car to attain a speed of 60 ft/s. Neglect friction and the size of the car.

The 800-lb roller-coaster car starts from rest on the track having the shape of a cylindrical helix. If the helix descends 8 ft for every one revolution, determine the speed of the car when t = 4 s. Also, how far has the car descended in this time? Neglect friction and the size of the car.

Natural gas having a molar analysis of 60% methane $(CH_4)$ and 40% ethane $(C_2H_6)$ enters a compressor at 340 K, 6 bar and is compressed isothermally without internal irreversibilities to 20 bar. The compressor operates at steady state, and kinetic and potential energy effects are negligible. a. Assuming ideal gas behavior, determine for the compressor the work and heat transfer, each in kJ per kmol of mixture flowing. b. Compare with the values for work and heat transfer, respectively, determined assuming ideal solution behavio. For the pure components at 340 K:

$$\begin{matrix} \quad & \text{h (kJ/kg) } & \quad & s(k J / k g \cdot k)\\ \quad & \text{6 bar} & \text{20 bar} & \text{6 bar} & \text{20 bar}\\ \text{Methane} & \text{715.33} & \text{704.40} & \text{10.9763} & \text{10.3275}\\ \text{Ethane} & \text{462.39} & \text{439.13} & \text{7.3493} & \text{6.9680}\\ \end{matrix}$$

The mechanism used in a marine engine consists of a crank AB and two connecting rods BC and BD. Determine the velocity of the piston at D the instant the crank is in the position shown and has an angular velocity of 5 rad/s.