Page 47 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

32 BASICS OF FLUID MECHANICS AND INTRODUCTION TO CFD

constant pressure, and the other C,, for dv = 0 ( v = constant), called

the specific heat at constant volume. Thus

Cp = (at) 40> hy, (55), +7 - (ar),
(sr),
11
and

gz
= (B), (gyn (i),

0 (g),” er)

Obviously, for the reversible processes (ideal media) we also have CZ =
(at), =T (Sp and Co = (5h), =T (FB )o-

Concerning thedifference C, — Cy, this is equal to T (Fh) ($F), a

result which can be found, for instance, in [33].
Now, let us introduce a new state variable H called enthalpy or total
heat. The enthalpy A per unit mass or the specific enthalpy is defined
by h=e+ pu.
Differentiating this relation with respect to 7, while keeping p con-
stant, we obtain

($8), ~ (2), t(f),-¢ Dp:
—_
=
—
=
———
OT
p
p
>
OT
OT
In terms of h, the above Gibbs’ equation could also be written as
Tds = dh — vdp,
a form which will be important in the sequel.

3.2 Constitutive (Behaviour,
*‘Stresses-Deformations’’ Relations) Laws

The system of equations for a deformable continuum medium — the
translation of the Newtonian mechanics principles into the appropiate
language of these media — should be closed by some equations of spe-
cific structure characterizing the considered continuum and which in-

fluence its motion. Such equations of specific structure, consequences

'' We have used here some results of the type Ry = (34)
Vv etc. which come from the
Q
Bu) p Pp
classical calculus.