THE FLOW OF WATER IIST WOOD-STAVE PIPE. 55 



COMPARISON OF THE VARIOUS FORMULAS. 



The comparison of the various formulas is shown in columns 19 to 

 23 and 18 to 22, inclusive, Tables 2 and 3, respectively, and graphically 

 in Plate VII, which presents the following information: 



First, a comparison in per cent of observed velocities to velocities 

 computed by the Wilhams-Hazen formula (with 0^ = 120), the 

 Moritz, Tutton, Weisbach, and the new formulas, for all accepted 

 experiments on wood-stave pipes known to the writer where sufficient 

 data are given. 



Second, the mean of the various percentages, awarding each 

 observation the same weight; also the mean of the various percentages, 

 awarding the average percentage for each reach of pipe the same 

 weight. These items correspond with the footings under columns 

 19 to 23, inclusive. Table 2, and columns 18 to 22, Table 3. 



Third, lines underscoring the observations used in deriving their 

 formulas by Moritz and Scobey, and the observations leading WiUiams 

 and Hazen to recommend a value of 120 as the coefficient to be used 

 in their formula in the design of wood-stave pipe. (The Weisbach 

 formula was derived from tests on metal pipes.) 



Tutton apparently assigned the same weight to each series of tests, 

 although he had but one observation on the Moon Island Conduit 

 (No. 49) against five for No. 1, and eight for each of the other two 

 (Nos. 22 to 33). 



For the new formula double lines are used, the upper line denoting 

 the observations used and the weight assigned (1, 2, or 3) in determin- 

 ing the general equation for m', and the lower line denoting the 

 observations used and the weights assigned in determining the 

 exponent of V. (These lines correspond to the figures in columns 

 15 and 14, respectively, Table 3.) 



As an example of the use of this chart, take observation No. 274 

 (nm 9 on pipe No. 51). Near the top of the plate above the figures 

 274 (tlie reference number), Scobey is given for the experimenter and 

 1914 as the year. Under 274 it will be noted (as indicated by the 

 cross) that the observed velocity (column 8, Table 2, 6.19 feet per 

 second), is 0.1 per cent less (column 19, Table 2) than the velocity 

 (6.20 feet per second, column 14, Table 2), as computed by the new 

 formula for the same sized pipe with the same loss of head. Similarly 

 the open circle shows that it is 5.9 per cent more than the velocity 

 (5.83 feet per second) as computed by the Wilhams-Hazen formula 

 (column 20, Table 2); the black dot shows it to be 17.2 per cent less 

 than the velocity (7.48 feet per second) computed by the Moritz 

 formula (column 21, Table 2); the winged circle shows it to be 0.8 

 per cent more than the velocity (6.14 feet per second) computed by 

 the Tutton formula (column 22, Table 2); the fact that there are no 



