THE FLOW OF WATER IN WOOD-STAVE PIPE. 87 
The causes of the large deviations in the constants of any formula so far proposed 
have been the subject of frequent discussion. The varying amount of curvature is 
undoubtedly one of these causes, and its separate effect upon resistance may well 
engage the attention of experimenters. Age appears generally to have little effect 
on carrying capacity of wood pipe. Errors in the experiments themselves are becom- 
ing smaller with greater refinement and the use of coloring matter in determining 
the velocity directly may be considered as a distinct advance. The main reason for 
the apparently arbitrary variations probably lies in the difference in smoothness, of 
the interior surface, which may be due to vegetable growth, effect of wear, variability 
of the wood, and in some measure to workmanship. So long as it is not practicable 
to specify and insure a known degree of smoothness, so long will the application of 
judgment be necessary in the use of any formula. 
Entry head is due to eddy currents above and below the point of entry. The loss 
due to eddy currents in the intake basin is very variable, depending upon the lines 
of approach which at times favor the formation of whirls and vortexes. This item of 
loss is, however, relatively small and may generally be neglected. The loss below 
the point of entry is due to an uneven distribution of velocity throughout the section 
immediately below the point of entrance. 
The area so far as it is occupied by rapidly forward-moving water is contracted as in 
the case of open-air discharge, although under conditions of counterpressure probably 
to a smaller extent. The area between the contracted section and the pipe shell 
is a cavitation space which may be filled with eddying water or may become under 
high-velocity discharge a complete vacuum. The energy of the moving water in the 
contracted area is greater, due to higher average velocity, than in the moving water 
farther down the pipe, the difference being destroyed by internal friction and con- 
stituting the principal part of entry head. 
Where the assumption is made by the author that h e =i h v , it is equivalent to assign- 
ing a constant value of 0.82 to the coefficient of contraction. While this assumption 
is not unusual it must be evident that this coefficient must be largely affected by con- 
ditions of velocity, depth of pipe entrance below water surface, shape of intake basin 
and elevation of floor with reference to pipe invert. 
Table 6, presented by the author on this subject, yields no positive information. 
The influence of velocity of approach is neglected, which may be permissible in 
cases such as tests 7 and 8 where the outlet is at right angles to the direction of approach, 
but is not correct in tests 5 and 6 where the flow is straight toward the entrance. The 
table gives results which are erratic, as might be expected. For tests 7 and 8 it indi- 
cates that the entry head equaled 0.89 h v and 0.63 h v , respectively, instead of 0.50 h Vj 
equivalent to coefficients of contraction 0.73 and 0.78, respectively, instead of 0.82, 
The usual assumption of 0.82 as the coefficient of contraction, or £ h v as the entry 
head, may be justified in some cases, but will at times lead to serious error. (See 
also, Merriman's Hydraulics, 9th ed., p. 214.) 
Mr. Moritz: It will generally be conceded on the basis of the showing made in 
this paper that the new formulas proposed fit all observations so far made on wood- 
stave pipe better than any other formula heretofore offered. The problem is, how- 
ever, not susceptible of cold-blooded scientific analysis and the personal equation of 
the analyst must necessarily affect the ultimate result. The present paper can not 
be considered as the final answer to the problem of flow of water in wood-stave pipes 
and in view of the close agreement between the author's formula and others that have 
been used, the writer is not satisfied that there is sufficient justification for a radical 
departure from formula constants that have been well established and accepted. The 
writer has in mind especially the exponent of d which for upward of 10 years or more 
has stood unchallenged at 1.25 and this figure has been accepted by such well-known 
hydraulicians and experimenters as Dr. E. W. Schoder, of Cornell University, and 
