Page 50 - 48Fundamentals of Compressible Fluid Mechanics
P. 50
12 CHAPTER 1. INTRODUCTION
Mumenthaler from UTH University, no copy of the thesis can be found in the orig-
40
inal University and perhaps only in the personal custody of the Fanno family .
Fanno attributes the main pressure reduction to friction. Thus, flow that is domi-
nantly adiabatic could be simplified and analyzed. The friction factor is the main
component in the analysis as Darcy 41 was already proposed in 1845. The arrival
of the Moody diagram, which built on Hunter Rouse’s (194x) work made Darcy–
Weisbach’s equation universally useful. Without the existence of the friction factor
data, the Fanno model wasn’t able to produce a prediction useful for the indus-
try. Additionally an understating of the supersonic branch of the flow was unknown
(The idea of shock in tube was not raised at that time.). Shapiro organized all the
material in a coherent way and made this model useful.
Meta
id Fanno realize that the flow is choked? It appears at least in Stodola’s
book that choking was understood in 1927 and even earlier. The choking
was assumed only to be in the subsonic flow. But because the actual Fanno’s
thesis is not available, the question cannot be answered yet. When was
Gas Dynamics (compressible flow) as a separate class started? Did the
explanation for the combination of diverging-converging nuzzle with tube for
Fanno flow first appeared in Shapiro’s book?
Meta End
expanding model by others
1.3.3.5 Isothermal Flow
The earliest reference to isothermal flow was found in Shapiro’s Book. The model
If it turned out that no one had
done it before Shapiro, this
and it appears that Shapiro was the first
Shapiro’s flow. Call for others
to help in this information. one to realize this difference compared to the other models. In reality, the flow is
to one for cases that are between Fanno (adi-
flow model should be called suggests that the choking occurs at
abatic) and isothermal flow. This fact was evident in industrial applications where
the expectation of the choking is at Mach one, but can be explained by choking at
choked somewhere between
a lower Mach number. No experimental evidence, known by the undersigned, was
ever produced to verify this finding.
1.3.4 External flow
When the flow over an external body is about .8 Mach or more the flow must
be considered to be compressible flow. However at a Mach number above 0.8
(relative of velocity of the body to upstream velocity) a local Mach number (local
velocity) can reach
. At that stage, a shock wave occurs which increases
the resistance. The Navier-Stokes equations which describe the flow (or even
40 This material is very important and someone should find it and make it available to researchers.
41 Fanning based radius is only one quarter of the Darcy which is based on diameter