(5)

and from 255 experiments obtained for the constants the values

α = 0.007409; β = 0.1920.

This gives the following values at different velocities:—

v =0.30.50.7111⁄223571015
ζ =0.012150.010250.009440.008830.008360.008120.907880.007690.007610.007550.00750

In using this value of ζ when v is not known, it is best to proceed by approximation.

§ 98. Darcy and Bazin’s Expression for the Coefficient of Friction.—Darcy and Bazin’s researches have shown that ζ varies very greatly for different degrees of roughness of the channel bed, and that it also varies with the dimensions of the channel. They give for ζ an empirical expression (similar to that for pipes) of the form

ζ = α (1 + β / m);

(6)

where m is the hydraulic mean depth. For different kinds of channels they give the following values of the coefficient of friction:—