The only condition required for applying of the
simple integration as described above
is that the otherwise arbitrary course of the
axis ,
in it role of the integration path, passes
everywhere through the same fluid
(if there are several different fluids, integration may be divided
into corresponding segments with different
). The possibility of curvature of the axis
is exploited in the case shown in Fig.B-4
where both positions
as well as
are on liquid surfaces. The task to be solved there is a reversal of the
previous tasks: values of pressure at the surfaces are here known
and it is now the height difference
if the liquid columns, which are displaced from their original
equilibrium position by a given acting pressure difference
, which is be calculated.
Using the same integration as in
Fig.B-2 it is, on the other hand,
possible also in the
U-tube
configuration shown in Fig.B-4 to determine
pressure at
,
if there are known column heights and the starting value of pressure in
. This means that providing the arms of the
U-tube with suitable scales will convert
this device into a manometer.
In fact, this is a well known and widely used principle of pressure
measurement. The devices operation of which is based
upon this principle are called
liquid-filled manometers . In spite of being the simplest and
cheapest instruments for
pressure measurement, the may be - in suitable
arrangement -
very reliable and also very precise. For use in aerodynamic laboratories,
special variants
were developed with very good operational properties
(so that they are gradually displaced from use only recently
due to recent requirements of computer data logging,
which requires the manometer outputs
available in the form of electric signals).
Basic forms of such manometers are shown schematically in
Fig.B-5. The necessity
to read the position of liquid surface usually requires the arms
being made of glass. This makes them easily damageable and this -
together with
relatively large dimensions and necessary maintenance
(liquid evaporates and must be replaced)
means that they are typical laboratory instruments,
not suitable for industrial use.
With water as the liquid in the U-tube
it is possible to measure in the basic arrangement
A in
Fig.B-5
pressure within the range from 10 Pa to 20 kPa
(which corresponds to
from 1 mm to 2 m).
More than one order of magnitude higher pressure
differences may be measured with mercury
(height 2m, which is about the maximum dimension
Fig.
B-4 Connection between heights of liquid columns
and acting pressure difference
in a
U-tube.
of a practical instrument, then corresponds
to = 270 kPa). On the other hand,
for more precise measurement
od small pressure differences the suitable liquid
has to be larger specific volume than water. In this direction, however,
the possibilities are limited: practically
it is only
alcohol, which us used. It makes possible to
obtain at the same acting pressure difference
displaced column height 1,25-times larger
than with water. Accuracy
of liquid-filled manometers is limited on one hand by the precise knowledge
of specific volume (which
varies with impurities in the liquid,
evaporation of a component in case od mixture; in the case of alcohol,
which is hygroscopic,
also by absorption of water from atmosphere), on the other hand also
by capillary elevation. Its influence should be cancelled
in the arrangement A
by its acting in the both arms,
in practice this is not so since capillary elevation
is sensitive to even very small differences in pipe diameters
(this is why precise, callibrated glass pipes are used)
and contamination of walls, which is never
exactly the same in both arms.
Numerous variants were developed, e.g. the Prandtl manometer
(arrangement
B in Fig.B-5)
removes the necessity to read on two scales
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This is page Nr. B02 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS" Any comments and suggestions concerning this text may be mailed to the author
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