Darcy and Bazin give, for the relation of the mean velocity vm and bottom velocity vb.

vm = vb + 10.87 √ (mi).

But

√ mi = vm √ (ζ / 2g);

∴ vm = vb / (1 − 10.87 √ (ζ / 2g)).

Taking a mean value for ζ, we get

vm = 1.312 vb,

and from this the following values of the mean velocity are obtained:—

Bottom Velocity
= vb.		Mean Velocity
= vm.
1. Soft earth 0.25 .33
2. Loam 0.50 .65
3. Sand 1.00 1.30
4. Gravel 2.00 2.62
5. Pebbles 3.40 4.46
6. Broken stone, flint 4.00 5.25
7. Chalk, soft shale 5.00 6.56
8. Rock in beds 6.00 7.87
9. Hard rock.10.0013.12

The following table of velocities which should not be exceeded in channels is given in the Ingenieurs Taschenbuch of the Verein “Hütte”:—