αβ
For drawn wrought-iron or smooth cast-iron pipes.004973.084
For pipes altered by light incrustations.00996.084

These coefficients may be put in the following very simple form, without sensibly altering their value:—

For clean pipesζ = .005 (1 + 1/12d)
For slightly incrusted pipesζ = .01 (1 + 1/12d)

(9a)

Darcy’s Value of the Coefficient of Friction ζ for Velocities not less than 4 in. per second.

Diameter
of Pipe
in Inches.		 ζ Diameter
of Pipe
in Inches.		 ζ
New
Pipes.		 Incrusted
Pipes.		 New
Pipes.		 Incrusted
Pipes.
2 0.00750 0.01500 18 .00528 .01056
3 .00667 .01333 21 .00524 .01048
4 .00625 .01250 24 .00521 .01042
5 .00600 .01200 27 .00519 .01037
6 .00583 .01167 30 .00517 .01033
7 .00571 .01143 36 .00514 .01028
8 .00563 .01125 42 .00512 .01024
9 .00556 .01111 54 .00509 .01019
15 .00533 .01067

These values of ζ are, however, not exact for widely differing velocities. To embrace all cases Darcy proposed the expression

ζ = (α + α1/d) + (β + β1/d2) / v;

(10)

which is a modification of Coulomb’s, including terms expressing the influence of the diameter and of the velocity. For clean pipes Darcy found these values