12 BULLETIN 852, IT. S. DEPARTMENT OF AGRICULTURE. 
encountered, still the change is not so marked as that found in the 
study of wood-stave pipes. 
The Williams-Hazen formula appears to more nearly apply if the 
value of C w is chosen as suggested on page 64. 
NECESSARY FIELD DATA FOR DETERMINING THE RETARDATION ELE- 
MENTS OF VARIOUS FORMULAS. 
A glance at pages 5 to 7 shows that for study of the various 
formulas the same hydraulic elements must be determined by field 
tests. These are: 
(1) The mean velocity, V, of water in the pipe. 
(2) The loss of head, lif, clue to retardation in a section of pipe of 
uniform size, within a known distance. 
(3) The internal size of pipe, D or d. 
The above data having been secured, the coefficient of retardation 
may be computed for each of the various formulas. 
MEAN VELOCITY OF WATER. 
The velocity of the water flowing in a reach of pipe may be meas- 
ured in two general ways : 
(1) Directly, by timing a given volume of water through a known 
distance. 
(2) Indirectly, by measuring the discharge of the pipe, thus 
determining the quantity, Q, and solving the equation V=-~ m 
Where the velocity is tested by the direct method the error is 
probably smaller than where the indirect method is used, unless 
exceptional facilities for complete measurements, including interior 
diameters, are at hand. 
LOSS OF HEAD DUE TO RETARDATION. 
Most of the recent experiments on the flow of water in pipes of 
uniform size have been made with piezometer columns. This was 
the method used by the writer. If a piezometer (fig. 1) be properly 
attached to the pipe, the pressure in the latter will support a column 
of water whose surface is at elevation E x , on the hydraulic grade line. 
In the same way the pressure at gauge No. 2 will lift a column to 
elevation E 2 . The difference between these elevations is the head 
lost, Jif, due to the retarding influences. 
INTERNAL SIZE OF PIPE. 
The method used in ascertaining the inside cross-sectional area 
of the pipe is recounted in the description of each test. In some 
cases several joints of pipe, remaining from construction, were 
measured and their mean inside cross-sectional areas accepted as 
the internal sizes of the operated pipes. In other cases the nominal 
diameter of the pipe was accepted. 
