of the mass flow rate resulting from the
one-dimensional formula with experimental data. Fig.C-22 below gives an example.
The same corrective effect is achievable by using the drag coefficient
as will be introduced in Chap.[D]. This is, in fact,
a more modern and preferable approach, use of discharge coefficient being
substantiated only on the grounds of historical reasons. From comparison of the corresponding
expressions,

there is the following formula for conversion of available dicharge
coefficient data into the more modern expression: 
The task to evaluate the efflux (discharge) velocity during
the
discharge is so simple that it is possible to generalise our approach and to
do some elementary computations involving consideration of other dimensions. The
actual integration will be here still one-dimensional, but the integration will
be performed along a path perpendicular to the flow direction.
This approach is useful in evaluating discharge through an orifice in cases where
the velocity in individual points of the orifice are will be not the same. This
variation of velocity is due to the fact that velocity depends upon
depth
and if the orifice is large,
the depth variations cannot be
 |
Fig.C-24 |
neglected (Fig.C-23). The basic idea is to evaluate flow through an area
element 
which is so small that
within its extent the variations are negligible, and then to find the overall
discharge flow by evaluating the integral across the whole area. Since velocity does
not vary in horizontal direction, the area element is here taken as a flat rectangle
(Fig.C-24). The result of the integration, of course,
depends upon the variations of orifice width
with depth
. It should be kept in mind that the actual velocity profile will be
more complex than the simple part of quadratic parabola shown in Fig.C-24, which results
from the Torricelli equation,
because of effects neglected in the present one-dimensional lossless approach.
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This is page Nr. C09 from textbook
Vaclav TESAR : "BASIC FLUID MECHANICS"
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