§ 45. _Cases in which the Velocity of Approach needs to be taken into
Account. Rectangular Orifices and Notches._--In finding the velocity
at the orifice in the preceding investigations, it has been assumed
that the head h has been measured from the free surface of still water
above the orifice. In many cases which occur in practice the channel
of approach to an orifice or notch is not so large, relatively to the
stream through the orifice or notch, that the velocity in it can be
disregarded.
[Illustration: FIG. 48.]
Let h1, h2 (fig. 48) be the heads measured from the free surface to
the top and bottom edges of a rectangular orifice, at a point in the
channel of approach where the velocity is u. It is obvious that a fall
of the free surface,
[h] = u²/2g
has been somewhere expended in producing the velocity u, and hence the
true heads measured in still water would have been h1 + [h] and h2 +
[h]. Consequently the discharge, allowing for the velocity of
approach, is