THE PITOT-DARCY GAGE. 



255 



TABLE 83. -Values of A in V=A*^h JJ t and values of gage efficiency. 



An inspection of the values of A with due 

 attention to their probable errors serves to 

 show that their differences are not to be re- 

 garded as wholly accidental, but must be as- 

 cribed in part to the variation of the instru- 

 mental constant with conditions. That the 

 nature of the variations may be appreciated, 

 the conditions will be more fully described. 

 As already stated, gages 3a and 3b are the same 

 symmetric instrument, but with opposite faces 

 turned toward the current, while the instru- 

 ment was modified to some minute extent by 

 an injury and repair occurring between the Los 

 Angeles and Berkeley ratings. Practically 

 there were four gages, but so far as the mech- 

 anician could make them the four gages were 

 identical in form. The reservoir at the Los 

 Angeles rating station was broad and deep. 

 The course followed by the receiver of the gage 

 was several feet from the bank, at least 6 inches 

 below the surface, and at least 1 foot above the 

 bottom. The plank reservoir used in Berkeley 

 was 1.96 feet wide, and the depth of water was 

 0.44 foot. In the ratings tabulated as at " mid- 

 depth" the opening of the receiver was central 

 in the cross section of the water. In the " near 

 bottom" rating the center of the opening (its 

 diameter being 0.01 foot) was 0.02 foot from 

 the bottom; in the "near surface" rating the 

 center was 0.03 foot below the surface of the 

 water; and in the "near side" rating the cen- 

 ter was 0.25 foot above the bottom and varied 

 from 0.01 to 0.11 foot in its distance from the 

 side, the course and the trough side not being 

 quite parallel. The several relations of the 

 opening to the water section are shown in fig- 

 ure 86. 



There is nothing novel in the variation of the 

 instrumental constant with minute differences 

 in the shape of the receiver. This has been 

 observed by all critical users of such instru- 

 ments, and the custom is well established of 



giving a separate rating to each receiver. So 

 far as I am aware the variation of the constant 

 with the relation of the receiver to the walls of 

 the conduit and to the water surface has not 

 previously been recorded, and this is a matter 

 of considerable moment, for various elaborate 



FIGURE 8ti. Cross section of prism of water in trough, showing positions 

 given to gage opening in various ratings. 



discussions of the distribution of velocities 

 within a cross section have assumed the con- 

 stancy of the instrumental constant for all posi- 

 tions. As clearly indicated by the tabulated 

 results, the constant A increases when the free 

 surface of the water is approached and dimin- 

 ishes when a rigid wall of the conduit is 

 approached. 



In the application of these results (and of 

 cognate results with which it was thought best 

 not to burden these pages) to our velocity de- 

 terminations a graphic table was constructed 

 to show the relation of the instrumental con- 

 stant to the position of receiver in the conduit; 

 and this table (fig. 87) supplied the constant 

 to be used with each individual observation. 

 This procedure had an important influence on 

 the interpretation of the running-water rating, 

 making the apparent correction for that rating 

 less than it would be if the mid-depth constant 

 were used exclusively. Its influence on the 

 vertical velocity curves (figs. 74 to 82) was to 

 give them less curvature near the water surface, 

 greater curvature in approaching the channel 

 bed, and (sometimes) a somewhat lower level of 

 maximum velocity. 



2o 



In equation (117) -^ V 2 equals twice the theo- 

 retic velocity head. If in equation (118) the 

 exponent u be replaced by its mean value 2, 



