TUTORIAL PROBLEMS

TUTORIAL1

1 An air jet at 300K has sonic velocity. Determine the following a. velocity of sound at 300K b. velocity of sound at stagnation conditions c. maximum velocity of the jet d. stagnation enthalpy e. Crocco numberTake γ=1.4 , R=287J/KgK

2. The pressure, temperature, and fluid velocity of air at entry of the flow passage are 3bar, 280K, and 140m/s.The pressure, temperature, and velocity at exit of a flow passage are 2bar, 260K, and 250m/s.the area of cross section at entry is 600cm2 . Determine for adiabatic flow. a. stagnation temperature. b. maximum velocity. c. mass flow rate. d. area of cross section at exit.

TUTORIAL-2

1. Steam at a section of a pipe has a pressure of 10 bar, temperature of 550K, velocity of 125m/s and datum height of 10m. Calculate the following. a. Mach number. b. stagnation pressure. c. stagnation temperature. d. compare the stagnation pressure value with that obtained from Bernoulli equation and comment on the difference.

2. The pressure, temperature, and Mach no at the entry of a flow passage are 2.45 bar, 26.5°C is 1.4 respectively. If the exit Mach no is 2.5, determine the following for adiabatic flow of a perfect gas (γ=1.3, R=.469KJ/KgK). a. stagnation temperature. b. Temperature and velocity of gas at exit. c. The flow rate per square meter of the inlet cross section.

TUTORIAL-3

1. Air (γ=1.4, R=287J/KgK) enters a straight axis symmetric duct at 300K, 3.45bar and 150m/s and it at 277K,2.058 bar and 260m/s. The area of cross section at entry is 500cm2 . Assuming adiabatic flow determine a. stagnation temperature. b. maximum velocity. c. mass flow rate. d. Area of cross section at exit.

2. Gas (γ=1.3, and Cp=1.1 KJ/Kg K) flows through a duct of diameter 69.5mm. At a section static pressure 150KPa, and static temperature is 48.5°C. The flow rate is 30Kg/min.Find the Mach number and velocity of gas.

TUTORIAL-4

1. The pressure, temperature, and Mach no at the entry of a nozzle are 2 bar, 300K and 1.4 respectively. The exit Mach number is 2.4. Determine the following for isentropic flow a. velocity of sound at stagnation condition. b. the maximum velocity c. the mach number M1

* and M2* .

d. temperature and pressure at exit. Take γ=1.3, R=0.52KJ/KgK.

2. The pressure, temperature, and Mach no at the entry of a diffuser 0.7 bar, 345K and 190m/s respectively. The entry diameter of diffuser is 15cm and exit diameter is 35cm. Determine the following. a. exit pressure. b. exit velocity. c. force exerted on the diffuser walls. Assuming isentropic flow and take γ=1.4, and Cp=1005 J/Kg K .

TUTORIAL-5.

1. A diffuser has exit to throat area ratio of 1.5 to 1 the inlet Mach number is 0initial pressure and temperature are 1 bar and 15°C . Assuming the flow to be isentropic. Calculate the following for exit air. a. exit pressure b. exit temperature c. exit Mach number.

2. Air is discharged from a receiver at Po=6.91 bar and To= 325°C through a nozzle to an exit pressure of 0.98 bar. If the flow rate is 3600Kg/hr.Determine for isentropic flow a. Area, pressure and velocity at throat. b. Area and Mach number at exit. c. Maximum possible velocity.

TUTORIAL-6.

1. A convergent divergent diffuser has an exit area to throat area of 2. Air enter the diffuser with stagnation properties Po=1MPa bar and To= 400K.The throat area is 6cm2

Determine the mass flow rate of flow and exit properties.

2. The stagnation properties of air entering a convergent nozzle are 200KPa and 400K.The throat area is 5cm2 .Find the mass the flow rate for the following back pressures a. 105.6 KPa b. 95 KPa c.130KPa.

TUTORIAL-7.

1. Air at a pressure of 25 bar, -223°C and velocity of 125m/s flows through a constant area duct diabatically and leaves with a velocity of 25m/s. Find the heat transferred and the properties of air at exit. Take γ=1.4, R=287J/KgK.

2. A constant area combustion chamber receives air at 77°C, 0.55bar and 75m/s. If the air leaves the combustion chamber at a Mach no of 0.85, determine conditions of air and the amount of heat transferred and also find change in entropy.

TUTORIAL-8.

1. Air is heated in a constant area duct from a Mach no of 0.2 to 0.8. The inlet stagnation conditions are 2bar and 93°C. Determine the stagnation conditions of air at exit, the amount of heat transferred per unit flow and change in entropy.

2. Ina heat exchanger the stagnation temperature of air is raised from 27°C to 177°C. The inlet pressure is 1.03bar and the inlet Mach number is 0.07.Neglecting the effect of wall friction. Determine the final Mach no.

TUTORIAL-9.

1. Air is flowing into an insulated duct with a velocity of 150m/s. The temperature and pressure at the inlet are 280°C and 28barrespectively. Find the temperature at a section in the duct where the pressure is 15.7bar. If the duct diameter is 15cm and friction factor is 0.005, find the distance between the two sections.

2. The friction factor for a 50mm diameter steel pipe is 0.005.At the inlet to the pipe the velocity is 70m/s, temperature is 80°C and the pressure is 10bar. Find the temperature, pressure and Mach no at exit if the pipe is 25m long .Also determine the maximum possible length.

TUTORIAL-10.

1. Air at a mach no of 1.6 pressure of 0.9bar, and temperature of 370K passes through a normal shock. Calculate the density after the shock. Compare this value with isentropic compression through the same pressure ratio.

2.Air is enter to super sonic wind tunnel at nozzle throat area of 200 cm2 and test cross sectional area of 330 cm2 .If the normal shock is located in the test section, find the following a. Test section Mach no. b. Diffuser throat area.

TUTORIAL-11.

1. A convergent divergent nozzle is designed to expand air from a reservoir in which the pressure is 700KPa and temperature is 5°C and the nozzle inlet Mach no is 0.2. The nozzle throat area is 46 cm2 and the exit area is 230 cm2. A normal shock appears at a section where the area is 175 cm2.Find the exit pressure and temperature. Also find the increase in entropy across the shock.

2. A convergent divergent air nozzle has to throat area ratio of 3. A normal shock appears at the divergent section where the existing area ratio is 2.2. Find the Mach number, before and after the shock. If the inlet stagnation properties are 500KPa and 450KPa, find the properties of air at exit and entropy increase across the shock.

TUTORIAL-12.

1. A convergent divergent duct is operating under off designed conditions as it conducts air from a high pressure tank where Po=210KPa and To=37°C. A normal shock is present in the divergent section of nozzle. Find the exit pressure, loss in stagnation pressure, and increase in entropy for the following areas.

2. Air enters a convergent divergent nozzle with a stagnation pressure of 29bar and temperature of 50°C. In the diverging part at a section just before a normal shock, the pressure just behind the shock ? Find the air flow rate per unit area at the throat.

TUTORIAL-13.

1. A rocket has the following data: Propellant flow rate =5Kg/s;ambient pressure=1.103bar;nozzle exit diameter=10cm;nozzle exit pressure=1.02bar;thrust chamber pressure=20bar;thrust=7KN.Determine the effective jet velocity ,actual jet velocity , specific impulse and specific propellant consumption.

2.A rocket nozzle has a throat area of 20 cm2 , combustion chamber pressure of 24bar and weight flow rate is 45N/s.If the specific impulse is 120s,determine

a. thrust coefficientb. propellant weight flow coefficientc. specific propellant consumptiond. characteristic velocity

TUTORIAL-14

1. A rocket operating at an altitude of 19km with the following data: Propellant flow rate =1Kg/s Thrust chamber pressure=28bar Thrust chamber temperature=2500K Nozzle area ratio=10.12

Calculate a. thrust b effective jet velocity c. specific impulseTake γ=1.3 , R=355J/KgK

2. A rocket nozzle has a throat area of 18 cm2 , combustion chamber pressure of 25bar and rate of flow of propellant is 44.145N/s.If the specific impulse is 127.42s,determine

a. thrust coefficientb. propellant weight flow coefficientc. specific propellant consumptiond. characteristic velocity

TUTORIAL-15

1.Calculate the thrust , specific impulse, propulsive efficiency, thermal and overall efficiencies of a rocket engine from the following data

a. effective jet velocity=1250m/sb. flight to jet speed ratio=.8c. oxidizer flow rate=3.5 Kg/sd. fuel flow rate=1 Kg/se. heat of reaction of exhaust gases=2500KJ/Kg

2.The effective jet velocity from a rocket is 2700 m/s. The forward flight velocity is 1350m/s and the propellant consumption is 78.6Kg/s. Calculate thrust, thrust power, propulsive efficiency.