Exponential formulas have been developed as the result of experiments which have demonstrated that V does not vary as the one-half power of R and S but that the relation should be expressed as,
V = CRpSq,
in which p and q are constants and C is a factor dependent on the character of the material. The various formulas coming under this classification have been given the names of the experimenters proposing them. Examples of these formulas are: Flamant’s, in English units, for new cast-iron pipe, which is,
V = 232R.715S.572,
and Lampé’s for the same material which is,
V = 203.3R.694S.555.
These formulas are useful only for the material to which they apply, but they can be used for conduits of any shape. A. V. Saph and E. W. Schoder have shown[[31]] that the general formula for all materials lies between the limits,
V = (93 to 142)S.50 to .55R.63 to .69.
Hazen and Williams’ formula is in the form,
V = 1.31CR.63S.54,