Test your level of competency for GATE Mechanical Engineering and UPSC ESE Mechanical Engineering exam for the topic of Unsteady Flow application from First Law of Thermodynamics.
Q1) Consider a hollow core printed circuit board 9 cm high and 18 cm long, dissipating a total of 15 W. The width of the air gap in the middle of the PCB is 0.25 cm. If the cooling air enters the 12 cm wide core at 25oC and 1 atm at a rate of 0.8 L/s, determine the average temperature at which the air leaves the hollow core.
Q2) Hot water at 90oC enters a 22 m section of a cast iron pipe whose inner diameter is 2.5 cm at an average velocity of 0.6 m/s. The outer surface of the pipe is exposed to the cold air at 10oC in a basement. If water leaves the basement (at 88oC), determine the rate of heat loss from the water.
Q3) A 5m x 6m x 8m room is to be heated by an electric resistance heater placed in a short duct in the room. Initially, the room is at 15oC and the local atmospheric pressure is 98 kPa. The room is losing heat steadily to the outside at a rate of 200 kJ/min. A 200 W fan circulates the air steadily through the duct and the electric heater at an average mass flow rate of 50 kg/min. The duct can be assumed to be adiabatic, and there is no air leaking in or out of the room. If it takes 15 min for the room air to reach an average temperature of 25oC, find (a) the power rating of the electric heater, and (b) the temperature rise that the air experiences each time it passes through the heater.
Q4) Air at 300 K and 100 kPa steadily flows into a hair dryer having electrical work input of 1500 W. Because of the size of the air intake, the inlet velocity of the air is negligible. The air temperature and velocity at the hair dryer exit are 353 K and 21 m/s. The flow process is both constant pressure and adiabatic. (a) Determine the air mass flow rate into the hair dryer, in kg/s, (b) determine the air volume flow rate at the hair dryer exit in m3/s.
Q5) An insulated rigid tank is initially evacuated. A valve is opened, and atmospheric air at 95 kPa and 290 K enters the tank until the pressure in the tank reaches 95 kPa, at which point the valve is closed. Determine the final temperature of the air in the tank.
Q6) A rigid, insulated tank that is initially evacuated is connected through a valve to a supply line that carries helium at 200 kPa and 393 K. Now the valve is opened, and helium is allowed to flow into the tank until the pressure reaches 200 kPa, at which point the valve is closed. Determine the flow work of the helium in the supply line and the final temperature of the helium in the tank.
Q7) Underground water is being pumped into a pool whose cross section is 6 m x 9 m while water is discharged through a 7 cm diameter orifice at a constant average velocity of 4 m/s. If the water level in the pool rises at a rate of 2.5 cm/min, determine the rate at which water is supplied to the pool, in m3/s.
Q8) Water is boiled at 100oC electrically by a 3 kW resistance wire. Determine the rate of evaporation of water.
Q9) The air flow in a compressed air line is divided into two equal streams by a T-fitting in the line. The compressed air enters this 2.5 cm diameter fitting at 1.6 MPa and 313 K with a velocity of 50 m/s. Each outlet has the same diameter as the inlet, and the air at these outlets has a pressure of 1.4 Mpa and a temperature of 309 K. Determine the velocity of the air outlets and the rate of change of flow energy (flow power) across T-fitting.
Q10) Air enters a pipe at 338 K and 200 kPa and leaves at 333 K and 175 kPa. It is estimated that heat is lost from the pipe in the amount of 3.3 kJ per kg of air flowing in the pipe. The diameter ratio for the pipe is . Determine the inlet and exit velocities of the air.