DISCHARGE FROM LARGE ORIFICES 171 



And on integrating we have, if t = t 2 h, the time necessary to lower 

 the surface through the distance HI II> 2 , 



where C = coefficient of contraction for the orifice. 



With an orifice in the vertical side of a vessel the effect of the variation 

 of velocity at different depths in the orifice must be considered. 



Thus with a large rectangular orifice of depth tZ, the rate of discharge 

 at the instant when the head of water above the upper edge is H feet, is 

 given by 



o r" s s~n 



Q = - C b *J^Tg [(H + df - H* J cubic feet per second 



= 5-76 C b [(H + df - H*"] cubic feet per second, 

 and the velocity of fall of the surface ( - ^ ) is therefore equal to 



Thus equation (1) above becomes 



and on integrating this between the required limits, the time occupied in 

 lowering the surface through any required distance may be found. 



Time of lowering the Level in a Reservoir through a Rectangular Notch. 

 With the usual notation, the volume discharged per second with a head 

 H behind the notch is given by 



Q = K b H* cubic feet. 



/.At this instant we have the velocity of the free surface in the reservoir 

 given by 



d H KbH* 



d t " A 



Integrating this, the time (2 seconds, to lower oaa lave 1 th rough a 

 distance HI Hz feet, is given by 



** - fi = ' = ~ secomls - 



