THE FAEMER's short-box MEASURING FLUME. 5 



height of crest a suiEcient number of tests was made to locate defi- 

 nitely the position of the discharge curves for the free-flow and the 

 submerged-flow conditions. This required a total of 271 tests, or 

 about 17 tests each, for the 16 different settings. In addition, 8 

 special tests were made to determine the effect of various minor 

 changes in the structure upon the discharge. 



DERIVATION OF DISCHARGE FORMULAS. 



The formulas for the free flow and for the submerged flow were 

 deduced from these data. The discharge per unit width (1 foot) of 

 flume was first determined for each head and height of weir. By 

 comparing the discharges for unit widths of the different flumes for 

 the same head and height of weir it was noted that there was no 

 uniform difference in the discharges per unit width; therefore, in 

 order to simplify the work, the average values were used. These 

 values were plotted logarithmically, and from the lines drawn through 

 the corresponding points the individual equations were determined. 

 The free-flow and the submerged-flow equations were determined 

 separately on account of the difficulty in determining a general 

 equation for both conditions. 



The equations for the two conditions are as follows : 



Free flow: 



n 3.^66 J TT1.525 ('T^ 



V- (p_ 0.300) "o^^* ^ ^ ^ 



Where Q = discharge in cubic feet per second. 

 P = height of the weir in feet. 

 L = width of the flume in feet. 



B^=head in feet, measured at the upper gauge point. 

 Submerged flow: 



77 0.41S (P -0.300)0-360= 1.37gd°-°^' „-p. 



^ = 4.12^L LE^ p- (11) 



Where Q = discharge in cubic feet per second. 

 P = height of the weir in feet. 

 Z/ = width of the flume in feet. 



He, = head in feet measured at the upper gauge point. 

 ^d = difference of head in feet between the upper and the 

 lower head. 



Formulas I and II are empirical formulas based on the calibration 

 of 1, 2, 3, and 4 foot flumes, with 4, 8, 12, and 16 inch weirs, for 

 various heads and differences of head. They should not be used for 

 larger or smaller flumes and weirs, nor for heads and differences of 

 head beyond the limits of the experimental data. These limiting 

 heads and differences of head are given in the tables and diagrams 

 computed from the formulas. 



