‘on one side of the orifice has been 
450 APPLIED MECHANICS 
An important application of the foregoing formula is to the filling ¢ 
emptying of a canal lock (Fig. 736). The upper and lower reaches 0 
the canal may be assumed to have 
constant levels during the operation — 
of filling or emptying the lock. When 
the gates are shut, communication “Thor 
between the lock and the upper or Reach. 
lower reaches of the canal is either 
through sluices in the gates themselves, . 
or through culverts in the walls of WSS 5s 
the lock. 
In the foregoing cases the head 
S37 Essay 
Fiaq. 736. 
assumed to be constant, but when one vessel of limited capacity dische 5 
into another, the level in the second rises as the level in the first falls. ; 
Assuming that the vessels (1) and (2), ; 
Fig. 737, have vertical sides, let A and 
B denote the areas of the free surfaces re 
of the water in (1) and (2) respectively, 1? 
and let the level in (1) fall from CD ER= 
to EF by discharging into (2) through H- 
the orifice O below the level KL of the : 
water in (2). Be 
When the free surface of the water 
in (1) is at the height y above KL, 
the level in (2) will have risen 
through the height y’ such that 
A(H-y)=By’. In the time dé let y change to y—dy, then 
ERT B)y - AH 
ka J2g(y —y/) dt = Ady, but yy = (A+ Y i 
therefore 
A JB: dy A /B { \e 
A+B)y-AH 
~ ka J2g J(A+B)y—AH ka, J Shi ad dy. 
Hence t= — te {: {( + B)y- AH} 7 
a SBE /BH- J(A+By—Au}. 
When the level has become the same in both vessels, % will become 
= af , and then f= 2AB /H 
A+B (A+ B)ka ,/2g° 
389. Large Rectangular Orifices——When the orifice in the side 
of a vessel is small compared with the head of water over it, the head 
may be assumed as the same for all parts of the orifice; but when the 
orifice is so large that this assumption involves serious error, the formula — 
for the discharge must be determined by taking into account ‘the variation 
of head. 
Large orifices are generally rectangular. Consider a rectangle 
