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GENERAL PRINCIPLES OF HYDRAULICS . 451 
orifice (Fig. 738) of breadth , the upper and lower edges being at depths 
h, and h, below XX, the free surface of the water. Consider a narrow 
horizontal strip of the orifice of depth dy at a depth = 
y below XX. Neglecting contraction and all losses, “t-.—-+-.-f-_—” 
the discharge through this strip is dQ=tdy J2yy, }) ‘ Y 
and the theoretical discharge through the whole h, — 
orifice 18 | dy”* 
t-bh--4 
x Po he : 
— Q=] bay /27y=8 25 dy = 3b {i -n}) 
coh ay 2g) vdy= 3b a/2A Bs Ih win fen 
4 “If it may be assumed that the coefficient of discharge & is the same 
_ for all values of b, h, and hy, then the actual discharge is 
2kb we a id). 
_ Experiments on the flow through large vertical rectangular orifices 
however show that & depends on the proportions of the orifice, and also on’ 
_ the head of water over it. An approximate average value of & is 0°62. 
890. Rectangular Notches or Weirs.—If the head h, over the 
_ rectangular orifice of the preceding Article is zero, the orifice becomes a 
_rectangulcr notch or weir (Fig. 739); and if the formula of the preceding 
Article still applied, the discharge would be given by the expression 
kb ,/29 -h, where h takes the place of h,. This expression may be used 
_ in determining the discharge through a rectangular notch if the value of 
the coefficient / is known with sufficient certainty for the particular notch 
_ to which it is applied. 
When the vertical edges of the notch project into the stream, as in 
Fig. 739, the notch or weir is said to have end contractions. In Fig. 
Fig. 741. 
_ 739 the weir has two end contractions. In Fig. 740 there is only one 
end contraction, and in Fig. 741 there are no end contractions. 
__ In a weir with no end contractions, called a suppressed weir, the 
width of the outflowing stream is uniform, and the discharge is directly 
proportional to the width, and is given by an ex- 
pression of the form &,),A3. To prevent any lateral 
_ spreading of the stream as it flows over a suppressed 
weir, the sides should be prolonged, as shown in 
‘Fig. 742. 
_ The effect of an end contraction is to reduce Tic tae 
the effective width of the stream through the weir, py 
but the influence of the end contraction only extends over a limited 
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