Page 48 - 48Fundamentals of Compressible Fluid Mechanics

10 CHAPTER 1. INTRODUCTION

It was commonly believed 34 that the choking occurs only at
.
for isothermal flow was
Shapiro (195x). It is so strange the giant like Shapiro did not realize his model on
isothermal contradict his conclusion from his own famous paper. Later Romer at el
The first one to analyzed that choking occurs at
extended it to isothermal variable area flow (1955). In this book, this author adapts
E.R.G. Ecert’s idea of dimensionless parameters control which determines where
the reality lay between the two extremes. Recently this concept was proposed (not
35
explicitly) by Dutton and Converdill (1997) . Namely, in many cases the reality is
somewhere between the adiabatic and the isothermal flow. The actual results will
be determined by the modified Eckert number to which model they are closer.

1.3.3.1 Nozzle flow

The first “wind tunnel” was not
a tunnel but a rotating arm at-
tached at the center. At the
end of the arm was the ob-
ject that was under observation
and study. The arm’s circular
motion could reach a velocity
above the speed of sound at its
end. Yet, in 1904 the Wright
brothers demonstrated that re-
sults from the wind tunnel and
spinning arm are different, due
to the circular motion. As a
result, the spinning arm was
no longer used in testing. Be- Fig. 1.3: The measured pressure in a nozzle taken
tween the turn of the century from Stodola 1927 Steam and Gas Turbines
and 1947-48, when the first supersonic wind tunnel was built, models that ex-
plained choking at the throat have been built.
A different reason to study the converging-diverging nozzle was the Ven-
turi meter which was used in measuring the flow rate of gases. Bendemann 36 car-
ried experiments to study the accuracy of these flow meters and he measured and
refound that the flow reaches a critical value (pressure ratio of 0.545) that creates
the maximum flow rate.
There are two main models or extremes that describe the flow in the
nozzle: isothermal and adiabatic.

34 The personal experience of this undersigned shows that even instructors of Gas Dynamics are not
aware that the chocking occurs at different Mach number and depends on the model.
35 These researchers demonstrate results between two extremes and actually proposed this idea.
However, that the presentation here suggests that topic should be presented case between two ex-
tremes.
36 Bendemann Mitteil ¨uber Forschungsarbeiten, Berlin, 1907, No. 37.