THE FLOW OF WATER IN CONCRETE PIPE. 45 
a low velocity in a large pipe is so small that it conflicts with the 
ordinary errors of experimentation. 
For observation No. 1 (not included in Table 3) the water column 
at gauge No. 2 was 0.017 foot higher than the column at gauge No 1 for 
a velocity of 1.76 feet per second, whereas it should have been in the 
neighborhood of 0.070 lower. There was absolutely no error in the 
levels. Agreement between levels of the gauge glasses at the ends of 
the reach as developed by the wye level and as shown by the static 
pressure in the siphon with still water was within 0.001 foot. The 
writer can account for the discrepancy between the actual gauge 
heights (which indicated that there was a gain instead of a loss of 
head) and the heights that might be expected only by explaining that 
piezometer No. 1 is impinged upon by the water soon after pitching 
downhill at the intake of the siphon, while piezometer No. 2 is sub- 
jected to the current after the water has passed through 850 feet of 
10-foot pipe, the last 200 feet of which are straight. 
The observations on this pipe listed in Table 3 were made at 
velocities great enough so that a distinct loss of head was recorded, 
but there is probably some of the same error that showed the gain 
in head for observation No. 1. For this reason the writer does not 
accord any weight to this series, but does not wish to suppress the 
tests and uses them to emphasize the necessity of testing relatively 
long reaches of pipe in order that the actual loss of head may far 
overshadow the unavoidable experimental errors. 
For experience on pipes of larger sizes see Appendix. 
ANALYSIS OF THE EXPERIMENTAL DATA. 
Water flowing under pressure, confined on all sides, probably 
follows a slightly different scheme as regards velocity distribution 
from that of water which but partially fills the conduit, thus having a 
surface exposed to the air. For this reason the results of experiments 
under these two conditions will be discussed separately. 
FLOW IN PIPES UNDER PRESSURE. 
It has come to be generally understood that the relationship of 
friction loss to velocity within a given pipe of any material can be 
represented by the equation 
E = m V z (12) 
in which the values of z are as a rule between 1.70 and 2.00, although 
there are many records of experiments in which the value of the 
exponent z was in excess of 2. 
For a series of pipes of the same general characteristics but of 
varying diameters the values of m follow the general equation 
m=Kd x (13) 
Substituting in formula 12 
H=Kd*V z (14) 
This expressed logarithmically becomes 
log H = log K+ x log d + z log V (15) 
