The subject of hydrostatics (from Greek
"hudor" = water, "statikos" = equilibrium) are fluids at rest
(... a relative rest with respect to surrounding walls of the vessel -
there is no absolute rest on Earth, which moves in space). The basis for the solutions
is the equation derived already in chap.[A]:
- the sum of the position energy
and pressure energy changes in fluid at rest is
zero. It does not mean that both components of energy remain constant along any
investigated path. What is meant is that
any positive value of change in one energy component
along the axis
must be balanced by negative change of the other one.
Fig.B-1
An example of a distributiion
of the pressure energy along
an element of a pipeline in
which fluid does not flow.
Practical conseqence is that if height decreases along a path,
( > 0) - and vice versa. A typical investigated problem
in hydrostatics is calculation of pressure drop along a pipeline element between its
input
and output - such as in Fig.B-1, where there is
, the resultant drop
is negative.
Details of the integration are shown in Fig.B-2 where the solved problem is slightly
different: there is no pipeline segment, the task is to determine the
pressure at a particular position under the liquid surface
in a vessel. The integration may follow any arbitrary path - axis
. Again, the sum of specific energy along
remains constant
and what undergoes a change is only its distribution into the position component
(proportional to height )
and pressure component (proportional to pressure ).
The graphical representation shown in Fig.B-1 may be a useful mental image to follow in
solving all similar problems. In Fig.B-2, there is no inlet an outlet, but just the
starting point of the integration and the final point, in which the conditions are to be
evaluated. At the starting point
it is necessary to know the pressure : in this case it is the barometric pressure,
which is assumed to act in whole atmosphere and therefore also on the liquid surface,
which is here open to
the atmosphere. In problems of this sort it is customary to assume the barometric pressure
to be everywhere the same. It varies with height, of course, but the variations in gas (air)
are by three decimal orders of magnitude smaller than in liquid (cf.
the values in Fig.B-3 and B-5) and may be
neglected.
Fig.B-2 The course followed during the solution of the problem
to find the magnitude of
pressure
at a given
position under the liquid surface in a vessel.
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This is page Nr. B01 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS" Any comments and suggestions concerning this text may be mailed to the author
to his addresstesar@fsid.cvut.cz
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