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.




Going to another page: click
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 address tesar@fsid.cvut.cz

WWW server administrators: Jiri Kvarda, Zdenek Maruna ...... Contact: webmaster@vc.cvut.cz
Last change : 25.02.1997