[Continued from SUPPLEMENT No. 274, page 4368.]
THE VARIOUS MODES OF TRANSMITTING POWER TO A DISTANCE.
[Footnote: A paper lately read before the Institution of Mechanical Engineers.]
By ARTHUR ACHARD, of Geneva.
But allowing that the figure of 22 H. P., assumed for this power (the result in calculating the work with compressed air being 19 H. P.) may be somewhat incorrect, it is unlikely that this error can be so large that its correction could reduce the efficiency below 80 per cent. Messrs. Sautter and Lemonnier, who construct a number of compressors, on being consulted by the author, have written to say that they always confined themselves in estimating the power stored in the compressed air, and had never measured the gross power expended. Compressed air in passing along the pipe, assumed to be horizontal, which conveys it from the place of production to the place where it is to be used, experiences by friction a diminution of pressure, which represents a reduction in the mechanical power stored up, and consequently a loss of efficiency.
The loss of pressure in question can only be calculated conveniently on the hypothesis that it is very small, and the general formula,
, is employed for the purpose, where D is the diameter of the pipe, assumed to be uniform, L the length of the pipe, p1 the pressure at the entrance, p the pressure at the farther end, u the velocity at which the compressed air travels, Δ its specific weight, and f(u) the friction per unit of length. In proportion as the air loses pressure its speed increases, while its specific weight diminishes; but the variations in pressure are assumed to be so small that u and Δ may be considered constant. As regards the quantity f(u), or the friction per unit of length, the natural law which regulates it is not known, audit can only be expressed by some empirical formula, which, while according sufficiently nearly with the facts, is suited for calculation. For this purpose the binomial formula, au + bu², or the simple formula, b1 u², is generally adopted; a b and b1 being coefficients deduced from experiment. The values, however, which are to be given to these coefficients are not constant, for they vary with the diameter of the pipe, and in particular, contrary to formerly received ideas, they vary according to its internal surface. The uncertainty in this respect is so great that it is not worth while, with a view to accuracy, to relinquish the great convenience which the simple formula, b1 u², offers. It would be better from this point of view to endeavor, as has been suggested, to render this formula more exact by the substitution of a fractional power in the place of the square, rather than to go through the long calculations necessitated by the use of the binomial au + bu². Accordingly, making use of the formula b1 u², the above equation becomes,