A 2-ft3 tank, initially evacuated, develops a small hole ...



CHE 302: Problem set 51) A 2-ft3 tank, initially evacuated, develops a small hole, and air leaks in from the surroundings at a constant mass flow rate of 0.004 lb/s. Using the ideal gas model for air, determine the pressure, in lbf/in.2, in the tank after 30 s if the temperature is 70°F.2) A 0.5-m3 tank contains ammonia, initially at +40°C, 8 bar. A leak develops, and refrigerant flows out of the tank at a constant mass flow rate of 0.04 kg/s. The process occurs slowly enough that heat transfer from the surroundings maintains a constant temperature in the tank. Determine (a) the time, in s, at which half of the mass has leaked out, and (b) the pressure in the tank at that time, in bar.3) A water storage tank initially contains 100,000 gal of water. The average daily usage is 10,000 gal. If water is added to the tank at an average rate of 5000[exp(–t/20)] gallons per day, where t is time in days, for how many days will the tank contain water?4) Air enters a one-inlet, one-exit control volume at 8 bar, 600 K, and 40 m/s through a flow area of 20 cm2. At the exit, the pressure is 2 bar, the temperature is 400 K, and the velocity is 350 m/s. The air behaves as an ideal gas. For steady-state operation, determine (a) the mass flow rate, in kg/s, (b) the exit flow area, in cm2.5) Air enters a compressor operating at steady state with a pressure of 14.7 lbf/in.2, a temperature of 70°F, and a volumetric flow rate of 500 ft3/min. The air velocity in the exit pipe is 700 ft/s and the exit pressure is 120 lbf/in.2 If each unit mass of air passing from inlet to exit undergoes a process described by pv1.34 = constant, determine (a) the exit temperature, in °F, and (b) the diameter of the exit pipe, in inches.6) The Figure shows a cooling tower operating at steady state. Warm water from an air conditioning unit enters at 120°F with a mass flow rate of 4000 lb/h. Dry air enters the tower at 70°F, 1 atm with a volumetric flow rate of 3000 ft3/min. Because of evaporation within the tower, humid air exits at the top of the tower with a mass flow rate of 14000 lb/h. Cooled liquid water is collected at the bottom of the tower for return to the air conditioning unit together with makeup water. Determine the mass flow rate of the makeup water, in lb/h.7) Carbon dioxide gas is heated as it flows steadily through a 2.5-cm-diameter pipe. At the inlet, the pressure is 2 bar, the temperature is 300 K, and the velocity is 100 m /s. At the exit, the pressure and velocity are 0.9413 bar and 400 m /s, respectively. The gas can be treated as an ideal gas with constant specific heat cp = 0.94 kJ/kg · K. Neglecting potential energy effects, determine the rate of heat transfer to the carbon dioxide, in kW.8) Steam enters a well-insulated nozzle at 300 lbf/in.2, 600°F, with a velocity of 100 ft/s and exits at 40 lbf/in.2 with a velocity of 1800 ft/s. For steady-state operation, and neglecting potential energy effects, determine the exit temperature, in °F.9) Air enters an uninsulated nozzle operating at steady state at 760°R with negligible velocity and exits the nozzle at 520°R with a velocity of 1500 ft/s. Assuming ideal gas behavior and neglecting potential energy effects, determine the heat transfer per unit mass of air flowing, in Btu/lb.10) Helium gas flows through a well-insulated nozzle at steady state. The temperature and velocity at the inlet are 600°R and 175 ft/s, respectively. At the exit, the temperature is 460°R and the pressure is 50 lbf/in.2 The mass flow rate is 1 lb/s. Using the ideal gas model, and neglecting potential energy effects, determine the exit area, in ft2. ................
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