This equation is encountered mainly when computing discharge of liquid through an orifice in the wall (or bottom) of a vessel Fig.C-17- in this basic form is is the case of liquid
Fig.C-17
discharging into space in which there is the same (ambient) pressure as the pressure above the liquid surface. The pressure-energy term may be neglected - although it should be kept in mind that there are changes of pressure energy along the integration path between and so that liquid leaves the vessel actually under the influence of acting presssure - as shown in the diagram of energetic changes in Fig.C-17. Integration of the equation without pressure term leads to the wll-known Torricelli equation (derived in 1644). It is very similar to what we have seen in Fig.C-3. In the next case discussed here, shown in Fig.C-18 we shall make use of the Castelli Theorem and the results is again similar to what we already know - this time to Fig.C-10. The experimental verification by the procedure shown in Fig.C-20 used to be performed already in 18th century - and inevitably revealed discrepancies, because real discharge is neither one-dimensional nor without
Fig.C-18
losses. Classical approach to a remedy was introduction of the discharge coefficient - Fig.C-21 (it is sometimes also encoundered under other symbols, such as in English literature, though care must be taken in this case not to confuse it with the drag coefficient from Chap. [J]). To find the value of this coefficient is outside the scope of the one-dimensional approach and although present-day computer software may be capable of computing it, the classical way how to evaluate it was comparison
Fig.C-19 Fig.C-20
Evangelista Torricelli
Born: 15 Oct 1608 in Faenza, Romagna (now Italy)
Died: 25 Oct 1647 in Florence, Tuscany (now Italy)
entered the Jesuit College of Faenza
in 1624. He went to the Collegio Romano
in Rome where he showed such talent that
he was taught by Castelli at the University
of Sapienza. Torricelli became his secretary
and held this post from 1626 to 1632.


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This is page Nr. C08 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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