Numericals on Thermodynamics:
1. Mass enters an open system with one inlet and one exit at a constant rate of 50 kg/min. At the exit, the mass flow rate is 60 kg/min. If the system initially contains 1000 kg of working fluid, determine the time when the system mass becomes 500 kg.
2. Mass leaves an open system with a mass flow rate of c*m, where c is a constant and m is the system mass. If the mass of the system at t = 0 is m0, derive an expression for the mass of the system at time t.
3. Water enters a vertical cylindrical tank of cross-sectional area 0.01 m2 at a constant mass flow rate of 5 kg/s. It leaves the tank through an exit near the base with a mass flow rate given by the formula 0.2h kg/s, where h is the instantaneous height in m. If the tank is empty initially, develop an expression for the liquid height h as a function of time t. Assume density of water to remain constant at 1000 kg/m3.
4. A conical tank of base diameter D and height H is suspended in an inverted position to hold water. A leak at the apex of the cone causes water to leave with a mass flow rate of c*sqrt(h), where c is a constant and h is the height of the water level from the leak at the bottom. (a) Determine the rate of change of height h. (b) Express h as a function of time t and other known constants, rho (constant density of water), D, H, and c if the tank was completely full at t=0.
5. Steam enters a mixing chamber at 100 kPa, 20 m/s, with a specific volume of 0.4 m3/kg. Liquid water at 100 kPa and 25oC enters the chamber through a separate duct with a flow rate of 50 kg/s and a velocity of 5 m/s. If liquid water leaves the chamber at 100 kPa and 43oC with a volumetric flow rate of 3.357 m3/min and a velocity of 5.58 m/s, determine the port areas at the inlets and exit. Assume liquid water density to be 1000 kg/m3 and steady state operation.
6. Air is pumped into and withdrawn from a 10 m3 rigid tank as shown in the accompanying figure. The inlet and exit conditions are as follows. Inlet: v1= 2 m3/kg, V1= 10 m/s, A1= 0.01 m2; Exit: v2= 5 m3/kg, V2= 5m/s, A2= 0.015 m2. Assuming the tank to be uniform at all time with the specific volume and pressure related through p*v=9.0 (kPa.m3), determine the rate of change of pressure in the tank.
7. A gas flows steadily through a circular duct of varying cross-section area with a mass flow rate of 10 kg/s. The inlet and exit conditions are as follows. Inlet: V1= 400 m/s, A1= 179.36 cm2; Exit: V2= 584 m/s, v2= 1.1827 m/kg. (a) Determine the exit area. (b) Do you find the increase in velocity of the gas accompanied by an increase in flow area counter intuitive? Why?
8. Steam enters a turbine with a mass flow rate of 10 kg/s at 10 MPa, 600oC, 30 m/s, it exits the turbine at 45 kPa, 30 m/s with a quality of 0.9. Assuming steady-state operation, determine (a) the inlet area, and (b) the exit area.
Answers: (a) 0.01279 m2 (b) 1.075 m2