An engineer encounters quite often the task to evaluate the force (or forces) by which fluid acts on an element of a hydraulic or pneumatic system (- a device or pipeline segment) through which it flows. The solution of the problem enables him make proper dimensioning of suspensions or anchorings which hold the device in its position. An example is given in Fig.H-5, where there is a vessel with an inlet and an outlet and the task is to evaluate the two forces transmitted by the vessel legs into the foundation. To simplify the problem, the forces transmitted by the flange connections into the inlet and outlet pipes (which, of course, usually represent the substantial proportion of transmitted forces - so that many elements are held in position only by these connections) are here neglected. Solution is a direct application of the relations derived on the previous two pages.
This is actually a one-dimensional problem, all forces of interest act in vertical direction.
They are:


 |
 |
Fig.H-5
|
To the fluid gravity force
is then added the weight of the element (vessel) itself. In case of evaluating horizontal forces (
= 90 deg), the gravity force does not come into the account. It is also usually negligible if the fluid is a gas.
The dynamic force 
becomes zero if fluid is stationary and also if there is
= 1 . The last case is, of course, quite common in usual two-terminal devices and pipe segments: the mass flow rate at the inlet is the same, changes in specific volume are rarely large and if there is no requirement of a
diffuser or confuser effect, there is no reason for changing cross sectional area.
This most common situation is shown in Fig.H-6. The problem which is to be solved there is evaluation of the resultant horizontal force
. Note
 |
Fig.H-6
|
that because of
= 1 there is

= 0 , the only force is caused by the pressure drop across the element. This drop, of course, is the consequence of dissipation "loss", given by the Bernoullis' theorem in which there are only the terms:


If the pressure difference
evaluated this way is inserted into the the equation for
, the resultant equation, as written in Fig.H-6, is formally equivalent to the expression for the
drag of bodies exposed to fluid flow, as discussed in chapter [J]. The basically equal meaning of the loss coefficient and drag coefficient
has led to denoting them by the same symbol.
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This is page Nr. H03 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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tesar@fsid.cvut.cz
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Last change : 25.02.1998