Mechanics of Fluids

552 Compressible flow of gases
throat and exit areas of the nozzle, the pressures in the reservoir
and the nozzle throat and the temperature and velocity of
the air at exit.
11.12 A convergent-divergent nozzle originally designed to give an
exit Mach number of 1.8 with air is used with argon (γ = 5/3).
What is the ratio of the entry stagnation pressure to the exit
pressure when a normal shock is formed just inside the nozzle
exit?
11.13 The mass flow rate of superheated steam (γ = 1.3) is to be
measured by a venturi-meter having inlet and throat diameters
100 mm and 50 mm respectively. If the upstream stagnation
pressure and stagnation temperature are respectively 200 kPa
(absolute) and 150 ◦ C, what is the maximum mass flow rate
that can be measured reliably in this way? Effects of friction
and heat transfer may be neglected. (Thermodynamic tables
will be needed.)
11.14 Superheated steam from a large reservoir in which the pressure
is 1 MPa flows adiabatically through a convergent-divergent
nozzle for which the cross-sectional area at exit is twice that at
the throat. The pressure beyond the exit is 700 kPa. Determine
the Mach number of the flow in the exit plane, the crosssectional
area at the plane where a normal shock may be
expected in the nozzle, and the Mach number immediately
upstream of the shock. What ambient pressure at exit would
be necessary to produce isentropic supersonic flow without
shocks? What exit pressure would give the same mass flow
rate but with subsonic conditions throughout? Assume that
frictional effects are negligible, that γ for superheated steam =
1.3, and that the steam remains superheated and with constant
specific heat capacities throughout. (Hint: From eqn 11.59
substitute for m in eqn 11.60 to obtain p0 downstream of the
shock.)
11.15 Air flows adiabatically at the rate of 2.7 kg · s −1 through a
horizontal 100 mm diameter pipe for which a mean value f =
0.006 may be assumed. If the inlet pressure and temperature
are 180 kPa and 50 ◦ C. What is the maximum length of the
pipe for which choking will not occur? What are then the
temperature and pressure at the exit end and half way along
the pipe?
11.16 Air enters a 150 mm diameter pipe (mean f = 0.006) at
730 kPa and 30 ◦ C. For a flow rate of 2.3 kg · s −1 . What is the
pressure 2 km from the inlet when the flow is (a) adiabatic,
(b) isothermal?
11.17 Calculate the diameter of a pipe 140 m long required to
transmit air at 0.32 kg · s −1 under isothermal conditions if the
inlet pressure and temperature are respectively 800 kPa and
15 ◦ C and the pressure drop is not to exceed 200 kPa. Take
f = 0.006.