254 



that case was a plank trough. The interpreta- 

 tion of these results will be considered in 

 another connection. 



TRANSPORTATION OF DEBRIS BY RUNNING WATER. 



Substituting in (118), we have 



iff- fl.- 82.28 fcF*. 



TABLE 81. Ratio of the suction at one opening of the Pitot- 

 Darcy gage to the pressure at the other. 



Let A. represent the vertical space through 

 which the column of water is raised by pressure 

 from velocity V on the upstream opening of the 

 receiver, and A t the simultaneous depression of 

 the column connected with the downstream 

 opening. Then, each being assumed to equal 

 the velocity head, 



V 2 



-(116) 

 -(117) 



In practice the full velocity head is not realized 

 in instruments of the Pitot-Darcy type, and the 



r) 



coefficient determined by rating is less than . 



y 



It is a common experience also in practical 

 application of hydraulic formulas to find that 

 qualification is advisable in other respects. I 

 therefore substituted tentatively for (117) the 

 formula 



^JcV* 



(118) 



and sought empiric values of u and &. The 

 readings of the comparator corresponding to A, 

 and A! may bo called H and 11^. The zero of 

 the comparator scale being at its lower end, 

 the difference between the readings corres- 

 ponds to the sum of the spaces A. and \. The 

 readings are in inches, while the unit used for A, 

 A 1; and g is the foot. Moreover, from the incli- 

 nation of the comparator, the space between 

 the two columns, as read on the scale, is 2.09 

 times the vertical space Ji + Ji^ Therefore, the 

 product of 12 by 2.69 being 32.28, 



//-//, =32.28 (A + &,)_. ..(119) 



or, making A'= 32.38 Jc, 



11-11,= KV U (121) 



The observed quantities being //, 7/ 1; and V, 

 it was possible to plot on logarithmic section 

 paper any series of values of H H t in relation 

 to the associated values of V, and thus compute 

 graphically the corresponding values of u and 

 K. The values were computed for all series of 

 observations represented in Table 81, and they 

 are given in Table 82. The mean of the seven 

 values of u is 2.00, but their range is notable. 

 The deviations from the normal may be ascribed ' 

 in part to accidental errors. In the case of the 

 third value, 1.90, and of the seventh, 1.94, the 

 plotted positions are so scattered as to admit 

 of considerable latitude in the drawing of the 

 equation lines, but the control is much stronger 

 for the values 2.09 and 2.12, and these could 

 not be greatly reduced without violence to the 

 facts of observation. It seems clear that the 

 exponent is not whouy free from the influence 

 of special conditions. 



TABLE 82. Values of K and u in //-// I =A'T'. 



For the practical purpose of rating the in- 

 strument, however, there is no advantage in 

 departing from the normal exponent, and that 

 was employed in the preparation of rating 

 tables. The formula used for inferring veloci- 

 ties from readings is 



.(122) 



in which 



The values of A } graphically computed, are 

 given in Table 83, and these values were used 

 in the computations of velocities. 



