THE DISCHARGE-MEASURING GATE AND ITS RATING. 



259 



marked. The index was so arranged that by 

 pressure it could be made to indent the pre- 

 pared surface, thereby producing a mark of 

 graduation. Starting with just enough water 

 in the sump to permit the use of the hook, a 

 hue of graduation was marked. Then a cubic 

 foot of water was added, the hook was read- 

 justed, and a second line was marked. By 

 repeating this process a scale was given to the 

 gage, the unit of the scale being 1 cubic foot. 

 The added units of water were measured in a 

 wooden bottle made in the form of a cube 

 with the opening at one corner ; and the volume 

 of the bottle was so adjusted that it contained 

 62.3 pounds of water. The capacity of the 

 reservoir was about 38 cubic feet. 



In the use of the scale thus provided, frac- 

 tions of a cubic foot we/e read by means of a 

 small free scale of equal parts applied obliquely 

 to the space between two lines of graduation. 



THE OBSERVATIONS. 



The record of an observation included (1) 

 the width of gate aperture, (2) the time inter- 

 val, by stop watch, during which the water 

 was delivered to sump No. 2, (3) two readings 

 of the hook-gage scale, and their difference, 

 giving the volume of water received by the 

 sump, and (4) two gage readings of water 

 level in the upper tank, one just before and one 

 just after the period of volume measurement. 



The quotient of the volume of water by the 

 time in seconds gave the discharge for the 

 indicated width of gate opening. The readings 

 of the high-tank water level gave data for a 

 correction to the head, resulting in a small 

 correction to the computed discharges. 



It was found that repeated observations 

 with the narrower gate openings gave results 

 nearly identical, while the results for wider 

 openings showed more variation. The obser- 

 vations with wide openings were accordingly 

 multiplied to increase the precision of the 

 averages. The variation was ascribed to pulsa- 

 tions of the flowing water originating in the 

 stilling tank. The general precision of the 



accepted values of discharge, listed in Table 2 

 (p. 23), is indicated by an average probable 

 error of 0.2 per cent. The largest computed 

 probable error is 0.4 per cent, being that of 

 the discharge for a gate opening of 6 inches. 



The general formula for discharge through a 

 rectangular orifice when, as in the present case, 

 the vertical dimension of the orifice is small in 

 relation to the head, is 



in which h is the head, measured from the 

 middle of the orifice, Id the area of the orifice, 

 and c the constant of discharge. The observa- 

 tions give the following values of c for different 

 settings of the gate: 



For a "standard" orifice 2 inches square and 

 a head of 6 feet Hamilton Smith's tables 1 give 

 0.604 as the value of c. The inner surface 

 about the standard orifice is vertical and plane, 

 whereas the surfaces about the orifice of our 

 gate were oblique. The oblique guiding sur- 

 faces served to increase the velocity at the 

 orifice and thus enlarge the constant of dis- 

 charge. The variation of the constant with 

 width of opening is probably connected with 

 the fact that the beveled surfaces were not 

 symmetrically arranged about the opening. 

 On three sides they made an angle of 45 with 

 the vertical plane of the orifice, but the edge 

 of the slide, constituting the fourth side, was 

 beveled at a smaller angle. The constants of 

 the gate were thus affected by the conditions 

 of its setting and a new rating would be neces- 

 sary with a different setting. 



i Hydraulics, p. 58. 



