Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls
Homework VII
Due
Friday March 6, 2020, in class (or before).
Problems (MYO is the textbook; 8th edition)
MYO 11.28
MYO 11.37
MYO 11.39
MYO 11.41
MYO 11.48
MYO 11.52
Write 2-3 paragraphs about the Concorde supersonic passenger
aircraft, including design, technology, political climate and
fate.
Comments
I will lecture Section 11.5 after Section 11.9.
Section 11.1 reviews the ideal gas law. This should be familiar, but
is a good time to review enthalpy, the ratio of specific heats and
entropy.
Section 11.2 concerns stagnation properties, that is the properties
a fluid would have if brought to rest without any addition or loss
of energy. The resulting formulas link temperature to stagnation
temperature, pressure to stagnation pressure and so on.
Section 11.3 discusses the speed of sound. Sound is the basic linear
response of a compressible fluid: fluid particles expand and
contract, leading to a propagating signal. Since this is the
result of the interplay of density and pressure, the speed of
sound comes out as the square root of the derivative of pressure
with respect to density. Hence incompressible fluid corresponds to
infinite sound speed: the fluid adjusts instantaneously everywhere.
This is not possible in reality, but is a good approximation if the
speed of sound is much larger than the characteristic velocity of
fluid in the system, i.e. if the Mach number, V/c, is small.
Section 11.4 explores different flow regimes at different Mach
numbers. One can distinguish incompressible flow, compressible
subsonic flow, transonic flow, (compressible) supersonic flow, and
hypersonic flow. In supersonic flow, the disturbance induced by a
body is localized inside a Mach cone
Section 11.5 presents shock waves (normal shocks in fact). A shock
wave is an infinitesimally thin discontinuity in fluid properties.
The underlying conservation laws of mass, momentum and energy can be
used to obtain a relation between the upstream and downstream Mach
numbers. The stagnation temperature does not change across a shock.
The second law leads to the result that the upstream flow must be
supersonic.
Section 11.6 discusses isentropic flow along a duct. We consider the
case with no shaft work; then the condition of constant entropy
leads to the result that all stagnation properties are constant. The
critical state corresponds to exactly sonic flow.
Section 11.7 uses these results to examine flow in a variable-area
duct. The most important application is to rocket engines.
Section 11.8 and 11.9 discuss Fanno and Rayleigh flow, namely
compressible flow in ducts with friction and heat addition
respectively.