In many cases, however, it is convenient to be able to express resist- 

 ance to flow in the forms 



h _flv* 



and to enable this to be done without sacrificing accuracy, the values of 

 / and of C have been calculated from the mean results of the exponential 

 formulae of Unwin, Tutton, and Thrupp, showing, within the range of 

 velocities common in practice, their variation with v and with the pipe 

 diameter, in pipes of different types. 



These values, given in the following tables, may be relied upon to give 

 reasonably accurate results with pipes well laid and jointed. The internal 

 fouling of a pipe due to corrosion and tuberculation, by increasing the 

 roughness of its walls and by reducing its effective area, will generally 

 reduce the effective value of / considerably after a few years' use, and 

 allowance should be made for this in computing the diameter necessary 

 to maintain a given discharge. 



With a small iron pipe under unfavourable circumstances, tuberculation 

 may cause / to attain ten times its original value within as many years' 

 use. In wooden pipes, on the other hand, no corrosion takes place, and 

 /is usually slightly less for an old than for a new pipe. 



Experiments carried out by Herschell, on riveted pipes consisting 

 of alternate large and small rings, with projecting rivet heads, and 

 which were coated with asphaltum, gave values of / in the formula 



f I v^ 

 h = ^ , for a 3J feet diameter pipe, ranging from '00675 with a 



A g m 



velocity of 1 foot per second, to '0055 with a velocity of 6 feet per second. 

 With a similar 4-feet pipe, / varied from '00675 to '0056 with the same 

 range of velocities. 



After four years' use, the latter pipe gave values of /ranging from '0085 

 to -0065 with the same range of velocities. 



Experiments 1 on a bare riveted pipe with butt joints and 6 feet in 

 diameter, when new gave/ = '0052 for all velocities from 1 to 4 feet per 

 second. After two years' use the values of /were found to range from 

 0139 at -5 feet per second to -00975 at 1 foot per second, and -00618 at 

 4 feet per second. 



J. Duane, as a result of experiments on a new 48-inch riveted main of 

 length 5,992 feet, obtained a value of/= '00358 in the same formula 

 with a velocity of 2'28 feet per second. After seven years, considerable 



1 " Transactions American Society Civil Engineers," 1898 and 1900, 



