THE FLOW OF WATER IN WOOD-STAVE PIPE. 5 
The amount of loss at the entry, due to the effect of contraction 
eddies and other retarding influences, is variable and uncertain, but 
most authorities agree that it should be taken as half the velocity head 
unless the inlet structure is especially designed to minimize this loss. 
For further discussion see page 59. 
Friction head, h f , is that lost in overcoming the retarding in- 
fluences within a reasonably straight pipe. In pipes of great length, 
the amount of this loss so far exceeds the two losses first mentioned 
that they may often be neglected, especially in small pipes. This 
is the loss upon which the experiments described in this paper were 
concentrated. Apart from all other losses of head it must be found 
in order to permit solution of the various formulas for the flow of 
water in pipes with the view to securing additional values for the 
factor representing the retarding influences designated as friction. 
In addition to the above losses, there may be others, such as those 
due to bends and valves or other obstructions; but, as a general thing, 
these items do not enter the design of wood-stave pipes, especially 
for irrigation purposes. In this use the pipe is laid on such gentle 
curves, both horizontal and vertical, that such losses need not be 
considered. Valves are seldom set across the line of the pipe, 
although there are often one or more valves of various sizes leading 
from the pipe. The loss in the main line due to these valves is 
also negligible compared with the friction and velocity head losses. 
In 1775, Chezy, a French engineer, offered his now well-known 
formula for the flow of water in both open channels and closed 
conduits : 
v=cvrs: o) 
Here C is a coefficient, originally thought to be constant, but now 
known to vary with functions of the slope, the hydraulic radius, the 
velocity, and with some factor representing the retarding influences 
in the channel. Many of the formulas used in this country for the 
design of pipes have accepted the Chezy formula as a basis and made 
only such modifications as experience dictated, some of them merely 
assigning definite values to the coefficient C for definite conditions of 
velocity, roughness, and size of pipe. 
Since the hydraulic elements secured in the field experiments fur- 
nish the necessary data for the determination of the factor repre- 
senting the retarding influences in all the formulas most used in this 
country, this publication will show this factor as developed by field 
tests for several formulas as follows : 
(a) The Chezy formula, 3 on page — , 
V = CVR^ = CR ' 5 s°- 5 (4) 
