Page 31 - Aerodynamics for Engineering Students

14 Aerodynamics for Engineering Students

It should be remembered that this result is obtained from the equation of state for
a perfect gas and the equation of conservation of energy of the flow of a non-heat-
conducting inviscid fluid. Such a flow behaves isentropically and, notwithstanding
the apparently restrictive nature of the assumptions made above, it can be used as a
model for a great many aerodynamic applications.

Entropy
Entropy is a function of state that follows from, and indicates the working of, the
second law of thermodynamics, that is concerned with the direction of any process
involving heat and energy. Entropy is a function the positive increase of which
during an adiabatic process indicates the consequences of the second law, i.e. a
reduction in entropy under these circumstances contravenes the second law. Zero
entropy change indicates an ideal or completely reversible process.
By definition, specific entropy (S)* (Joules per kilogram per Kelvin) is given by the
integral

(1.25)

for any reversible process, the integration extending from some datum condition;
but, as seen above, it is the change in entropy that is important, i.e.

dQ
dS=- (1.26)
T
In this and the previous equation dQ is a heat transfer to a unit mass of gas from an
external source. This addition will go to changing the internal energy and will do work.
Thus, for a reversible process,

but PIT = Rp, therefore

(1.28)

Integrating Eqn (1.28) from datum conditions to conditions given by suffix 1,
Tl
PD
SI = cvln-4- Rln-
TD P1
Likewise,

T2
PD
S2 = cvln-4- Rln-
TD P2
*Note that in this passage the unconventional symbol S is used for specific entropy to avoid confusion
with the length symbols.