470 PHILOSOPHICAL TRANSACTIONS. [aNNO 17Q5. 



fore it varies in the same ratio in the former case ; hence if the length mr of the 

 pipe bear but a very small proportion to ab, the velocity with which the fluid 

 flows out of the pipe will be very nearly equal to the velocity with which it would 

 flow through an orifice at the bottom equal to rs or mn, the pipe being supposed 

 to be cylindrical. To find how far this conclusion agrees with experiment, I 

 made a cylinder 12 inches deep, and at the bottom I made a circular orifice, 

 whose area was about the 130th part of the area of the bottom of the cylin- 

 der : I also put a cylindrical pipe into the bottom, whose internal diameter was 

 exactly equal to that of the hole, and length 1 inch. Hence, according to the 

 theory, the velocity of the fluid out of the pipe ought to be to the velocity 

 out of the orifice as v'13 to v'12, or as 26 to 25 nearly. But by ex 

 periment, the quantity of fluid which ran through the pipe in 12% the 

 vessel being kept full, v/as to the quantity which ran through the orifice 

 in the same time, very nearly in the ratio of 4 to 3, and consequently 

 that ratio expresses the ratio of the velocities; a consequence totally different 

 from that which the theory gives. I then took a vessel of a different base, but 

 the same altitude, and altered the diameter of the orifice and pipe, still keeping 

 them equal, and made the pipe only half an inch long ; in this case the veloci- 

 ties, by the theory, ought to have been in the ratio of v^l2.5 to v/12, or as 4g 

 to 48 nearly ; whereas by experiment the ratio of the velocities came out the 

 same as before, that is, as 4 to 3 nearly. I then reduced the pipe to the length 

 of a quarter of an inch, and in that case the velocity did not sensibly differ from 

 that through the orifice. On examining the stream, in consequence of this 

 great difference in the two cases, when the lengths of the pipes difi^ered by so 

 small a quantity, I found that in the latter case the stream did not fill the pipe, 

 as it did in the former case, but that the fluid was contracted as when it ran 

 through the simple orifice. At what length of pipe the stream will cease to fill 

 it, is a circumstance to which no theory has ever been applied, but the determi- 

 nation of it must be a matter of experiment entirely, 



I next inserted pipes of different lengths, and found that when the length of 

 the pipe was equal to the depth of the vessel, the velocity of the effluent fluid 

 by theory was to that by experiment as about 7 to 6 ; and by increasing the 

 length of the pipe, the ratio approached nearer to that of equality. In long 

 pipes therefore, the difference between theory and experiment is not greater than 

 what might be expected from the friction of the pipes, and other circumstances 

 which may be supposed to retard the velocity. 



If the pipe be conical, increasing downwards, the velocity by theory is still 

 the same, and consequently the quantity run out will be in proportion to the 

 magnitude of rs. As long as the expelling force can keep the tube full, this 

 appears to be the case; but by increasing the orifice r.s, the pipe will, at a cer- 

 tain magnitude, cease to be kept full ; at what time this happens must depend 



