Giovanbattista Venturi, according to whom
the device shown in Fig.C-10) is named,
studied at the beginning of the 18th century discharge from vessels through
outlets the cross section of which decreased at first and then increased. He did not
propose to use them for flow measurement - this was invented much later by an American
engineer named Herschell. Integrating the Bernoullis' Theorem between
and
the following expression is obtained
between the two unknown velocities,
and
:

... where there is
-
=
.
A second relation we now need follows from the Theorem of Castelli,
, so that there is
and as a result (considering Fig.C-8) we receive for
mass flow rate (according to Fig.C-8) the expression:

- it should be noted that the diameters
and
should be manufactured with utmost care,
because they enter the above expression in
where the dimensions are in fourth power - and it will be also the fourth power in which
their errors will influence the accuracy of the measured flow rate.
 |
 |
Fig.C-10
|
The disadvantage of the classical Venturi flowmeter is
that it is relatively expensive and unpleasantly long. In practice it
is often replaced by simple orifice meter: there is, between two flanges, a disk with
central hole smaller than inner diameter of the pipe. The small hole also generates a
cross-sectional contraction and a correspinding measurable pressure difference - albeit
wich much larger loss than the Ventruri tube. The effect of the loss is included into the correction factor, marked
as "k" in Fig.C-10.
Diffusers and confusers
- are transformer elements, performing changes between the energetic components. In the contraction
(the term "confuser" is used in middle Europe but it is les common
in English-speaking
world) the kinetic energy increases in the direction of fluid flow,
at the expense of the pressure component. Ot the other hand,
in the diffuser it is the pressure energy which increases and flow velocity becomes smaller.
If we do not take losses into account here,
the achieved change is etermined uniquely by the area ratio
. It is an important fact that while the
cross-sectional change in a contraction may be rather sudden without deleterious effects,
in the diffuser only very slow changes are acceptable (divergence angle larger than
about 15 deg would result in separation of flow from the walls).
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This is page Nr. C06 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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tesar@fsid.cvut.cz
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