ELF ==_
If the orifice is small in __~ r   dimensions compared with h, the filaments will all have nearly the same velocity, and if h is measured to the centre of the orifice, the equation above gives the mean velocity of the jet.
Case of a Submerged Orifice.—Let the orifice discharge below the level of the tail water. Then
using the notation shown in fig. 41, we have at M, vi=o,pi=Gh;+p. at m, p=Gha+pa. Inserting these values in (3), § 29,
o+hi+pa/G—hi =v2/2g+ha—h2+pa/G ; v2/2g =h2ha = h,
n~ 
DD'
But
r s. iron i ssZee/wasirter,vr, t
o+pa/G+hi—hi =v2/2g+pa/G—h ; v2/2g=h; v=J (2gh) =8.o2511 h.
(2) (2a)
(3)
where it is the difference of level of the head and tail water, and may be termed the effective head producing flow.
Case where the Pressures are different on the Free Surface and at the Orifice.—Let the fluid flow from a vessel in which the pressure is po into a vessel in which the pressure is p, fig. 42. The pressure po will produce the same effect as a layer of fluid of thickness po/G added to the head water; and the pressure p , will produce the same effect as a layer of thickness p/G added to the tail water. Hence the effective difference of level, or effective head producing flow, will be
and the velocity of discharge will be
v = V [2g{ho+(pop)/G}]. (4) We may express this result by saying that differences of pressure at the free surface and at the orifice are to be reckoned as part of the effective head.
Hence in all cases thus far treated the velocity of the jet is the velocity due to the effective head, and the discharge, allowing for contraction of the jet, is
Q =cwv =cwJ (2gh), (5) where w is the area of the orifice, cat the area of the contracted section of the jet, and h the effective head measured to the centre of the orifice. If h and w are taken in feet, Q is in cubic feet per second.
It is obvious, however, that this formula assumes that all the filaments have sensibly the same velocity. That will be true for horizontal orifices, and very approximately true in other cases, if the dimensions of the orifice are not large compared with the head h. In large orifices in say a vertical surface, the value of h is different for different filaments, and then the velocity of different filaments is not sensibly the same.
End of Article: ELF 

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