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FIG. 83.

In 1886, Professor W. C. Unwin plotted logarithmically all the most trustworthy experiments on flow in pipes then available? Fig. 83 gives one such plotting. The results of measuring the slopes of the lines drawn through the plotted points are given in the table.

It will be seen that the values of the index n range from I-72 for the smoothest and cleanest surface, to 2-00 for the roughest. The numbers after the brackets are rounded off numbers. The value of n having been thus determined, values of m/df were next found and averaged for each pipe. These were again plotted logarithmically in order to find a value for x. The lines were not very regular, but in all cases the slope was greater than I to I, so that the value of x must be greater than unity. The following table gives the results and a comparison of the value of x and Reyn0lds's value 3~:1..

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Kind of Pipe. n 3-71 x

Tin plate, ... x~72 1-28 1-ioo

Wrought iron (Smith). 1-75 1-25 1-210 Asphaltcd pipes 1-85 I-15 I-127 lWrought iron (Darcy) 1-87 I-13 1-680 1 Riveted wrought iron 1-87 I°I3 1-390 1New cast iron I-95 I'O5 I-168 Cleaned cast iron 2~00 1-00 I-168 1lncrustecl cast iron 2-00 I-00 I~I6O With the exception of the anomalous values for Darcy's wrought iron pipes, there is no great discrepancy between the values of x and 3-n, but there is no appearance of relation in the two quantities. Ftor the present it appears preferable to assume that x is independent 0 n.

It is now possible to obtain lL s f tl h' d 1 IC 0 ie t ir constant m, using the values found for 71 and The following table gives the results, the values of m being for metric measures. Tffformulae for the Flow of 'ate1TmTPipes, ” Industries i(Manchester, 1886).

1

I

Here, considering the great range of diameters and velocities in the experiments, the constancy of m is very satisfactorily close. The asphalted pipes give iather variable values. But, as some of these were new and some old, the variation is, perhaps, not surprising. The incrusted pipes give a value of m quite double that for new pipes but that is perfectly consistent with what is known of fluid friction in other cases.

I

Diameter V 1 e f'1T~Mean

Kind of Pipe. Min a:Z O Value Authority. etres. ' 0 m.

Tin plate . gzggi '01686 Bossut Wrought iron gig; 'gigii -01310 Hamilton Smith f0~027 'O174Q1 Hamilton Smith

0-306 02058 W. W. Bonn

Asphalted 0-306 -02107 ' MSM W. W. Bonn pipes 0-419 01650 Lampe

I'2I9 ~0I3I7 Stearns

-219 ~O2107. Gale

1'0-278 ~013701

- 0-322 01440

Rweted - < 0-375 01390 s -01403 Hamilton Smith wrought iron 0432 01368

-0-657 ~O144S:l

0°O82 -01725 1

New cast iron < 1* '01658 Dafcb ><>-500 -017459 1

C1 d 0'08O (31979

fig? Cagt < 0-245 -02091 1' -01994 1 Darcy >O~297 ~OI9I3£ 1

11O'()36 03693 1 1

Ingglxfted cast < 0-080 -03530 > -03643 Darcy 1

1 O-243 ~03Zo6 1 1