Extra problems in the course F0039T
Compressible flow:
Flow in duct of varying area
1.
Gas of temperature 50 °C and pressure 25 bar flows into a convergent
nozzle which has the smallest area 6 cm2. Neglect the inlet velocity. Calculate the
mass flow and the velocity in the most narrow section if the gas flows from the
nozzle into a room where the pressure is
a) 15 bar
b) 12 bar
R=286.7 J/kgK and =1.536.
Answ: a) 3.4 kg/s; 294 m/s
b) 3.5 kg/s; 335 m/s
2.
What is the highest possible velocity, that air of pressure 8 kp/cm2 and
temperature 20 °C would get in a convergent - divergent nozzle, in an adiabatic
expansion to the pressure 1 kp/cm2 ? Determine pressure and temperature in the
smallest section.
Answ:
514 m/s
4.22 at
-29°C ]
3.
Air with the temperature 500 °C and pressure 35 bar enters a
convergent-divergent nozzle from a container. The massflow is 1.3 kg and the
pressure at the outlet is 7 bar. The flow process is considered to be isentropic. R=287
J/kgK and =1.4. Calculate
a)
area of the smallest section.
b)
outlet area.
c)
velocity in the smallest section.
d)
velocity at the outlet
Answ a) 256 mm2
b) 344 mm2
c) 509 m/s d) 757 m/s
4.
Atmospheric air at 101.3 kPa and 15.0°C is accelerated isentropically.
What are its velocity and density when the Mach-number becomes 1.00 and what is
the maximum velocity theoretically obtainable? Will this velocity be achieved in
practice?
Answ:
311 m/s;
0.777 kg/m3;
761 m/s;
No
5.
Air flows isentropically from atmosphere (pressure 101.5 kPa and
temperature 15.0°C ) to a 600 mm square duct where the Mach-number is 1.6.
Calculate the static pressure, the velocity and the mass flow rate in the duct. What is
the minimum cross-sectional area upstream of this section?
Answ:
23.9 kPa;
443 m/s;
69.6 kg/s;
0.288 m2
Fanno-flow
6.
Air flows adiabatically at the rate of 2.7 kg/s through a horizontal 100
mm diameter pipe for which a mean value f = 0.006 may be assumed. Inlet static
pressure and temperature are 180 kPa and 50.0°C.
a) What are the inlet velocity and Mach-number?
b) What is the maximum lenght of the pipe for which choking will not occure?
c) What are then the static temperature and pressure at the exit?
Answ:
a) 177 m/s; 0.49
b) 4.75 m
c) 9.2°C ; 82.7 kPa
Rayleigh flow
7.
Air flows without friction at the rate of 1 kg/s in a pipe. Inlet velocity is
300 m/s and stagnation temperature 500 K. Determine the required heat input to the
air to obtain choking in this pipe.
Answ:
50 kW
Shock
8.
A normal shock wave forms in front of a 'two-dimensional' blunt-nosed
obstacle in a supersonic air stream. The static pressure at the nose of the obstacle is
three times the static pressure upstream of the shock wave. Determine the upstream
Mach number, the density ratio across the shock and the velocity immediately after
the shock if the upstream static temperature is 10.0°C
Answ:
Ma1=1.65;
2/1=2.11; 263 m/s
Turbine theory
9.
In one stage of a reaction turbine of axial type the mean blade velocity is,
U = 60 m/s. Steam enters the rotor blades with pressure 3.6 bar and temperature
175°C (specific volume 0.5607 m3/kg). The steam flow rate is 13.5 kg/s. Blade angles
are 2=60° 3=70°, 2=70° and 3=60°. Calculate
a) height of the rotor blades if this height should be 1/10 of the mean diameter, D, of
the ring of blades.
b) power of this stage
c) The isentropic enthaly drop across these blades if the isentropic efficiency is
s=0.85.
Answ: a) 64 mm
b) 214 kW
c) 19 kJ/kg
10.
In an impuls turbine of axial type the nozzle has an angle of 22° (a2=68°)
to the velocity of the rotor blades, C2 = 680 m/s. Mean diameter of the ring of blades
is D = 1.25 m. Blade angles are 2=54°, 3=54°. Assume isentropic flow. Mass flow
rate is 2500 kg/h. Calculate
a) rotational speed, n (rpm).
b) steam absolute velocity, C3, when the steam leaves the rotor blades.
c) shaft torque
Answ: a) 4276 rpm
b) 264 m/s
c) 304 N m
11
In one stage of an impuls turbine of axial type the mean blade velocity is
U2 = U3 = 215 m/s. 2 = 60°, C2 = 550 m/s. Due to losses in rotor channels the relative
velocity changes so that V3 =0.85 V2. The absolute velocity of the steam when it
leaves the rotor blades has axial direction, that is a3=0°.
Massflow is 700 kg/h. Calculate
a) blade angles 2 and 3
b) absolute velocity for the steam leaving te rotor blades, c3
c) power of this stage
Answ: a) 2=43.5°
b) b3=41.8°
c) P = 19.9 kW