same whether the computation is made, as by Froude, on the basis of experiments at different velocities, or as done here on the basis of change of linear dimension; and secondly, the quantitative discrepancy between columns 1, 2 and 3 is in the direction anticipated from the nature of the provisional assumption.
§ 48. Fronde's Experiments (continued)—Roughened Surfaces.—When we examine the cases of roughened surface which form part of the series of experiments quoted, we find results that are not capable of such ready interpretation. In the case, for instance, of a surface coated with coarse sand, the index determined by Froude from experiments at different velocities was found not to differ sensibly from the maximum possible; that is, the index value is given as = 2. The constant velocity data in this case are:—
| Surface. | 2 feet. | 8 feet. | 20 feet. |
| Coarse sand . . . | 1.10 | .714 | .588 |
Calculating as before, we obtain the index values 1.69 and 1.728 respectively, which have no apparent resemblance to Froude's value. It is not possible to attribute this failure to the dissimilarity of geometrical proportion, for the previous calculations give an indication of the maximum value of the error introduced on this account; it is evident, therefore, that the cause must be sought elsewhere.
In the first three examples the nature of the surface is physically speaking smooth, that is to say, the roughness, such as it is, may be considered as molecular. Now we know in such a case that the drag produced on the fluid arises from the viscous connection between the film of the fluid actually contiguous to the surface and the strata more remote, and this connection—viscosity—is one fully taken account of in the equation; and even if the molecular roughness of one substance differs from that of another, the application of the theory will not be affected.
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