224 ENGINEERING THERMODYNAMICSdharm
/M-therm/Th4-7.pm5- Steam at 7 bar and 200°C enters an insulated convergent divergent nozzle with a velocity of 60 m/s. It
leaves the nozzle at a pressure of 1.4 bar and enthalpy of 2600 kJ/kg.
Determine the velocity of the steam at exit. [Ans. 701 m/s] - A petrol engine develops 50 kW brake power. The fuel and air-flow rates are 10 kg and 107 kg/h. The
temperature of fuel-air mixture entering the engine is 20°C and temperature of gases leaving the engine
is 500°C. The heat transfer rate from the engine to the jacket cooling water is 50 kJ/s and that to the
surroundings is 10 kJ/s.
Evaluate the increase in the specific enthalpy of the mixture as it flows through the engine.
[Ans. – 110 kJ/s] - A compressor takes air at 100 kN/m^2 and delivers the same at 550 kN/m^2. The compressor discharges 16 m^3
of free air per minute. The densities of air at inlet and exit are 1.25 kg/m^3 and 5 kg/m^3. The power of the
motor driving the compressor is 40 kW. The heat lost to the cooling water circulated around the compressor
is 30 kJ/kg of air passing through the compressor.
Neglecting changes in P.E. and K.E. determine the change in specific internal energy. [Ans. 60 kJ/kg] - A centrifugal pump operating under steady flow conditions delivers 3000 kg of water per minute at 20°C.
The suction pressure is 0.8 bar and delivery pressure is 3 bar. The suction pipe diameter is 15 cm and
discharge pipe diameter is 10 cm. Find the capacity of the drive motor.
Neglect the change in internal energy and assume that the suction and discharge are at same level.
[Ans. 11.8 kW] - 60 kg of water is delivered by a centrifugal pump per second. The inlet and outlet pressures are 1 bar and
4 bar respectively. The suction is 2 m below the centre of the pump and delivery is 8 m above the centre of
the pump. Determine the capacity of the electric motor to run the pump. The suction and delivery pipe
diameters are 20 cm and 10 cm and respectively. [Ans. 27.15 kW] - The air speed of a turbojet engine in flight is 270 m/s. Ambient air temperature is – 15°C. Gas temperature
outlet of the nozzle is 600°C. Corresponding enthalpy values for air and gas are respectively 260 and 912 kJ/kg.
Fuel air ratio is 0.0190. Chemical energy of the fuel is 44.5 MJ/kg. Owing to incomplete combustion 5% of
the chemical energy is not released in the reaction. Heat loss from the engine is 21 kJ/kg of air.
Calculate the velocity of exhaust jet. [Ans. 560 m/s] - Air at a temperature of 15°C passes through a heat exchanger at a velocity of 30 m/s, where its temperature
is raised to 800°C. It then enters a turbine with the same velocity of 30 m/s and expands until the tempera-
ture falls to 650°C. On leaving the turbine, the air is taken at a velocity of 60 m/s to a nozzle where it
expands until the temperature has fallen to 500°C. If the air flow rate is 2 kg/s, calculate (i) the rate of heat
transfer to the air, (ii) the power output from the turbine assuming no heat loss, and (iii) the velocity at exit
from nozzle, assuming no heat loss.
Take the enthalpy of air as h = cpt, where cp is the specific heat equal to 1.005 kJ/kg°C and t the temperature.
[Ans. 1580 kJ/s ; 298.8 kW ; 554 m/s]
Vapour (Steam)
- 0.05 kg of steam is heated at a constant pressure of 2 bar until the volume occupied is 0.0658 m^3. Calculate
the heat supplied and work done. [Ans. 18.25 kJ ; 4.304 kJ] - Steam at 7 bar and dryness fraction 0.9 expands in a cylinder behind a piston isothermally and reversibly to
a pressure of 1.5 bar. Calculate the change of internal energy and the change of enthalpy per kg of steam.
The heat supplied during the process is found to be 400 kJ/kg. Calculate the work done per kg of steam.
[Ans. 217.5 kJ/kg (gain) ; 245.7 kJ/kg ; 182.5 kJ/kg] - 1 kg of steam at 100 bar and 375°C expands reversibly in a perfectly thermally insulated cylinder behind a
piston until pressure is 38 bar and the steam is then saturated.
Calculate the work done by the steam. [Ans. 169.7 kJ/kg] - In a steam engine the steam at the beginning of the expansion process is at 7 bar, dryness fraction 0.95, and
the expansion follows the law pv1.1 = constant, down to a pressure of 0.34 bar. Calculate the work done per
kg of steam during the expansion, and the heat flow per kg of steam to or from the cylinder walls during the
expansion. [Ans. 436 kJ/kg ; 155.6 kJ/kg (heat supplied)] - Steam at 19 bar is throttled to 1 bar and the temperature after throttling is found to be 150°C. Calculate the
initial dryness fraction of the steam. [Ans. 0.989]