538 



HYDRODYNAMICS. 



Vmion of is not attracted by the glass, flows more rapidly than 

 Water in water . 



These experiments are, however, very far from satis. 

 . -_[_. factory ; and it was reserved to M. Girard to ascertain 

 the precise influence of temperature on the motion of 

 water in capillary tubes. The experiments of this emi- 

 nent engineer were made with tubes of copper accurate- 

 ly calibred, and whose lengths could be varied at 

 pleasure. The first series of tubes had a diameter of 

 2.96 millimetres, and each tube was two decimetres 

 long, having at each of its ends a brass virrel, one of 

 which had a male, and the other a female screw, so that 

 the tubes could be all put together, so as to form diffe- 

 rent lengths, from 20 to 222 centimetres. The second 

 series of tubes was formed in a similar manner, and each 

 tube had a diameter of only 1.83 millimetres. The ex- 

 periments were made in the manner which we have al- 

 ready described in our History of HYDRODYNAMICS. 



In applying to these experiments the general for- 

 mula 



which expresses the condition of a linear and uniform 

 motion, M. Girard has obtained the following results : 



1. That whatever be the head of water, provided the 

 capillary tube is of a sufficient length ; the term /3 U, 

 proportional to the square of the velocity, disappears 



from the general formula, so that it becomes _ & 



4" A U 



which expresses the conditions of the uniformity of 

 the simplest linear motion. 



2. That in every case where the conditions of the mo- 

 tion are expressed by this formula, the variations in 

 the temperature of the water have a very great in- 

 fluence on the velocity with which it flows in the tube, 

 so that if the head of water, and the length and diame- 

 ter of the pipe remain the same, the velocity which is 

 expressed by 10 at of the centigrade thermometer is 

 expressed by 42 at 85 of that thermometer. 



3. That in every case where the formula - = = 



does not satisfy observation, that is, when the length 

 of the tube is below a certain limit, the variations 

 of temperature have but a slight influence on the ve- 

 locity with which the water is discharged ; so that if 

 this velocity by a pipe 55 millimetres long, and at 5 

 of temperature, is represented by 10, it will be repre- 

 sented by 12 at 87 degrees, every other circumstance in 

 the experiments being the same. 



4. That at equal temperatures the expression yr= 



decreases with the diameter of the tube employed. 



5. That the influence of temperature upon the veloci- 

 ties follows the same law in capillary tubes of an unequal 

 diameter, that is, that the successive differences of the 







expression - becomes as much less for equal 



4 1 A \J 



differences of temperature as the temperature is raised. 



6. That this law shews itself with more regularity, Motion of 

 as the observations are made upon tubes of a smaller Water in 

 diameter, or, which is the same thing, that the linearity F JP es * nd 

 of the motion is more perfect. ^__ ", 



7. That the values of the formula^ n= a > calcula- 



4 A U 



ted in the same circumstances for two tubes of unequal 

 diameters, differ more from one another as the temper- 

 ature becomes lower, and that these values appear to 

 have a tendency to become identical in proportion as 

 the temperature increases ; so that if their difference is 

 represented by 6 at 0" of temperature, it is represented 

 only by 1 when the temperature approaches to 80. 



8. And lastly, that the temperature which exercises 

 so great an influence on the phenomena of the uniform 

 discharge of water by capillary tubes, has scarcely any 

 influence in ordinary conduit pipes, whose diameters 

 exceed the limits of capillarity. 



An account of the preceding experiments was laid 

 before the Institute of France on the 28th Nov. 1814, 

 and on the l6'th January and 13th February 1815. 

 The remaining part of the paper was laid before the 

 same learned body on the 13th January 1817, and con- 

 tained various experiments on the discharge of different 

 fluids through capillary tubes. Income future article, 

 we expect to have it in our power to lay before our 

 readers, a fuller view of the very interesting results 

 which M. Girard has obtained. 



SECT. V. Account of Mr Smeaton's Experiments on the 

 Friction of' Water in Pipes. 



Mil SMEATON seems to have made a number of va- 

 luable experiments on the discharge of water through 

 openings, and from conduit pipes ; but no particular 

 account of these has been left among his papers. We 

 have been favoured, however, by Mr Farey, with two 

 Tables containing the results of Mr Smeaton's experi- 

 ments, which were found among his MSS. and have 

 never before been published. Although the last of the 

 Tables relates to the subject of a preceding Section, we 

 shall make no apology for inserting it in this place, as 

 it was not in our possession when that part of the vo- 

 lume was printed. 



The following Table, computed by Mr Smeaton from 

 his own experiments, shews the head of water which 

 is necessary to overcome the friction, &c. in horizontal 

 pipes 100 feet long, and to produce the velocity con- 

 tained in the two first columns of the Table. Hence, 

 if a certain supply of water is required from a given 

 pipe, the Table shews us the different heads or heights 

 of the reservoir, by which the velocity necessary to af- 

 ford this supply will be produced. By comparing this 

 Table with the formula of Du Buat, it will be seen that 

 Mr Smeaton makes the effects of friction considerably 

 greater than that formula, the velocities given by the 

 Table being less than those given by the formula. 



