Here, considering the great range of diameters and velocities in the experiments, the constancy of m is very satisfactorily close. The asphalted pipes give rather 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.
| Kind of Pipe. | Diameter in Metres. | Value of m. | Mean Value of m. | Authority. |
| Tin plate | 0.036 | .01697 | .01686 | Bossut |
| 0.054 | .01676 | |||
| Wrought iron | 0.016 | .01302 | .01310 | Hamilton Smith |
| 0.027 | .01319 | |||
| Asphalted pipes | 0.027 | .01749 | .01831 | Hamilton Smith |
| 0.306 | .02058 | W. W. Bonn | ||
| 0.306 | .02107 | W. W. Bonn | ||
| 0.419 | .01650 | Lampe | ||
| 1.219 | .01317 | Stearns | ||
| 1.219 | .02107 | Gale | ||
| Riveted wrought iron | 0.278 | .01370 | .01403 | Hamilton Smith |
| 0.322 | .01440 | |||
| 0.375 | .01390 | |||
| 0.432 | .01368 | |||
| 0.657 | .01448 | |||
| New cast iron | 0.082 | .01725 | .01658 | Darcy |
| 0.137 | .01427 | |||
| 0.188 | .01734 | |||
| 0.500 | .01745 | |||
| Cleaned cast iron | 0.080 | .01979 | .01994 | Darcy |
| 0.245 | .02091 | |||
| 0.297 | .01913 | |||
| Incrusted cast iron | 0.036 | .03693 | .03643 | Darcy |
| 0.080 | .03530 | |||
| 0.243 | .03706 |
General Mean Values of Constants.
The general formula (Hagen’s)—h/l = mvn/dx·2g—can therefore be taken to fit the results with convenient closeness, if the following mean values of the coefficients are taken, the unit being a metre:—
| Kind of Pipe. | m | x | n |
| Tin plate | .0169 | 1.10 | 1.72 |
| Wrought iron | .0131 | 1.21 | 1.75 |
| Asphalted iron | .0183 | 1.127 | 1.85 |
| Riveted wrought iron | .0140 | 1.390 | 1.87 |
| New cast iron | .0166 | 1.168 | 1.95 |
| Cleaned cast iron | .0199 | 1.168 | 2.0 |
| Incrusted cast iron | .0364 | 1.160 | 2.0 |
The variation of each of these coefficients is within a comparatively narrow range, and the selection of the proper coefficient for any given case presents no difficulty, if the character of the surface of the pipe is known.
It only remains to give the values of these coefficients when the quantities are expressed in English feet. For English measures the following are the values of the coefficients:—
| Kind of Pipe. | m | x | n |
| Tin plate | .0265 | 1.10 | 1.72 |
| Wrought iron | .0226 | 1.21 | 1.75 |
| Asphalted iron | .0254 | 1.127 | 1.85 |
| Riveted wrought iron | .0260 | 1.390 | 1.87 |
| New cast iron | .0215 | 1.168 | 1.95 |
| Cleaned cast iron | .0243 | 1.168 | 2.0 |
| Incrusted cast iron | .0440 | 1.160 | 2.0 |
§ 78. Distribution of Velocity in the Cross Section of a Pipe.—Darcy made experiments with a Pitot tube in 1850 on the velocity at different points in the cross section of a pipe. He deduced the relation