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 =h2-ha = 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+(po-p)/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 .