**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 m

_{0}, 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 m

^{2}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/m^{3}.
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 m

^{3}/kg. Liquid water at 100 kPa and 25^{o}C 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 m^{3}/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/m^{3}and steady state operation.
6.
Air
is pumped into and withdrawn from a 10 m

^{3}rigid tank as shown in the accompanying figure. The inlet and exit conditions are as follows. Inlet: v_{1}= 2 m^{3}/kg, V_{1}= 10 m/s, A_{1}= 0.01 m^{2}; Exit: v_{2}= 5 m^{3}/kg, V_{2}= 5m/s, A_{2}= 0.015 m^{2}. Assuming the tank to be uniform at all time with the specific volume and pressure related through p*v=9.0 (kPa.m^{3}), 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:
V

_{1}= 400 m/s, A_{1}= 179.36 cm^{2}; Exit: V_{2}= 584 m/s, v_{2}= 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, 600

^{o}C, 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 m

^{2}(b) 1.075 m^{2}
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