is subject to pressure around
.
It is therefore possible to neglect compressibility with acceptably
small error, if we work with pressure changes smaller than about
30 kPa
- this pressure difference in a vessel will generate
flow into atmosphere with velocity about
130 m/s
. It is common to use as the criterion of the
influence of compressibility the nondimensional quantity called
Mach number
... the ratio of flow speed
(which is connected with the pressure difference) to the speed of sound
(which decreases with increasing compressibility: in water there is
,
while in air, fluid with larger compressibility, there is
... both values are valid for
,
in a gas the speed of sound varies with temperature according to the formula
).
As shown in Fig.A-10, it is possible to delineate
by the values of
individual specialised branches of fluid mechanics.
At values above
compressibility causes a substantial change
in the character of flow, which is then to be solved by
different solution methods.
The methods of hydromechanics, the subject of the present textbook,
are applicable as long as
remains lower than about 0,3
to 0,5
(depending on the acceptable error).
Usual course of problem solution in
fluid mechanics consistes of expressing force balance (Newton's approach)
or energetic balance (Leibniz's approach) for an elementary fluid particle.
This leads to formulation of the diferential equation of the problem.
This is then integrated for the set of given boundary conditions
(in unsteady problems also initial conditions).
In one-dimensional cases, which are in the focus of attention here,
the particle on which the balance is sought degenerates into an elementary length segment
and instead of partial differential equations the balance yields (in steady flow cases)
ordinary differential equations, the solution of which is, of course, much easier.
In principle, the derivation of the differential equation
may be performed either by evaluating conditions in an elementary control volume
(= fluid particle) fixed in space, by investigating how fluid flows through the particle
(the Euler approach), or by following elementary amount of fluid during its spatial motion
(this leads to Legrange form of equations). Here we shall follow the combinantion
of Euler and Leibniz approaches: we shal investigate changes of fluid energy in a
fixed volume.
Magnitude of any sort of energy is determined
by a product of two factors. One of them determines
the difference of the levels between which the investigated change takes place.
It is described
as the intensity factor (
in literature is is also sometimes called "generalised potential"
). The second factor, on the other hand, determined the extent of the
energetic change and is therefore described as
extensity factor
(from lat. "extensio"). In comparison to electric energy
it is also sometimes called "generalised charge".
It is a typical property of quantities in the role of the intensity
factor that in equilibrium state
of the investigated object (fluid volume)
they have identical magnitude in the
whole extent of the object. A typical
quantity of this sort are temperature
or pressure: if the temperature of fluid in
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Obr.A-11
Approximation of the surface of
equilibrium states from Fig.A-9
commonly used in calculations
of usual gas state changes in
technical applications. In the
case of air - probably most often
encountered gas in practical calcu-
lations - the fact should be taken
into account that it usually
contains non-negligible humidity:
in processing experimental data
it is a common practice to insert
somewhat higher value of the gas
constant
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Vaclav TESAR : "BASIC FLUID MECHANICS"
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