301 
1908-9.] Discharge of Water from Circular Weirs. 
2. Circular Orifice, completely drowned. 
It seemed profitable to continue the investigations and experiments with 
the orifice completely drowned. An approximation to the theoretical dis- 
charge of a circular orifice is obtained easily, if the area of the hole is 
multiplied by the velocity corresponding with a head measured from the 
water surface to the centre of the aperture ; or the discharge 
Q = Jig h 7 ,7tD 2 / 4 cubic feet per second 
= 4'731 D 2 H' 1/2 gallons per minute, 
if D and £T are measured in inches for the last expression, H'|being the 
Fig. 4. 
distance from the water surface to the centre of the orifice. This result is 
very nearly accurate when the head is large compared with D, but for 
relatively low values of H' it becomes less so. The true theoretical dis- 
charge was therefore investigated up to a head equal to 3D/2 above the 
centre of the orifice — that is, to a height above the top of the hole equal to 
the diameter. 
The expression for the discharge found on page 2 applies here also, and 
the method of solution adopted was the same. Fig. 4 shows curves similar 
to those of fig. 2, except that now the value of H begins at D, and is in- 
creased by steps of OTD up to 2D. The outermost curve of fig. 2 and the 
