4ζ = α + β/√v = 0.003598 + 0.004289/√v.
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§ 76. Darcy’s Experiments on Friction in Pipes.—All previous experiments on the resistance of pipes were superseded by the remarkable researches carried out by H. P. G. Darcy (1803-1858), the Inspector-General of the Paris water works. His experiments were carried out on a scale, under a variation of conditions, and with a degree of accuracy which leaves little to be desired, and the results obtained are of very great practical importance. These results may be stated thus:—
1. For new and clean pipes the friction varies considerably with the nature and polish of the surface of the pipe. For clean cast iron it is about 11⁄2 times as great as for cast iron covered with pitch.
2. The nature of the surface has less influence when the pipes are old and incrusted with deposits, due to the action of the water. Thus old and incrusted pipes give twice as great a frictional resistance as new and clean pipes. Darcy’s coefficients were chiefly determined from experiments on new pipes. He doubles these coefficients for old and incrusted pipes, in accordance with the results of a very limited number of experiments on pipes containing incrustations and deposits.
3. The coefficient of friction may be expressed in the form ζ = α + β/v; but in pipes which have been some time in use it is sufficiently accurate to take ζ = α1 simply, where α1 depends on the diameter of the pipe alone, but α and β on the other hand depend both on the diameter of the pipe and the nature of its surface. The following are the values of the constants.
For pipes which have been some time in use, neglecting the term depending on the velocity;
ζ = α (1 + β/d).
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