124 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[April, 



strictly to the main question— tbe velocity of the water— and we shall 

 endeavour to answer our correspondent's objections seriatim. 



The first objection is founded on the momentum of the issuing fluid. 

 We scarcely know in what manner it is intended to show the fallacy 

 of our arguments, by placing the subject in that light. Our corre- 

 spondent admits that the mean velocity of a column of water falling 

 through a vertical pipe 16 feet long would be 16 feet per second, and 

 surely if, as we contend, the issuing velocity of water from such a pipe 

 kept constantly full be the same, the momentum in both cases must 

 be equal. We do not see how this consideration proves any incon- 

 sistency in our arguments, nor that it gives any countenance to the 

 view taken by our correspondent. 



On the next point— the velocity of the water tillering into the ver- 

 tical pipe— the whole question may be said to depend. Our corre- 

 spondent alleges that our "mistake " arises from not considering that 

 the water must enter the pipe as quickly as it issues from it. We 

 maintain, on the other hand, that his error consists in not considering 

 by what force this velocity is imparted to the entering fluid. The 

 water in the reservoir is, by the hypothesis, supposed only just to 

 cover the upper end of the pipe ; therefore the action of gravitation 

 on the water between the surface and the top of the pipe can have no 

 perceptible effect. The pipe is also supposed to be constantly full, 

 and the fall of the water down it to be uniform. By what force, 

 then, is the same velocity given to the water in the upper part of the 

 pipe, as to that which has fallen 16 feet ? Our correspondent asserts 

 that the velocity of the water at the top of the tube is 32 feet in a 

 second ; but we are left completely in the dark as to the nature of the 

 force by which this velocity, which is due only to a fall of 16 feet, can 

 be communicated to the water Honing into the top of the pipe. Ac- 

 cording to our view of the case, the force which communicates the 

 velocity to the entering water is derived from the action of gravita- 

 tion on the water falling down the pipe. Part of the force acquired 

 by the water in its fall towards the lower portion of the pipe is com- 

 municated to the more slowly moving water above. The tendency to 

 accelerated motion is thus continually checked during the flow of the 

 water by the loss of the motion communicated to the fluid in the 

 upper portion of the pipe, and the accelerated is converted into uni- 

 form motion. The laws of dynamics teach, that when accelerated 

 motion is rendered uniform, the resulting velocity is the mean of the 

 initial and final velocities, or one half of the latter ; therefore, in a 

 fall of 16 feet, the accelerated motion being rendered uniform, the 

 mean velocity will be 16 feet, which is half the final velocity acquired 

 by a body falling from that height. 



In the illustration of the glass tube, when our correspondent says 

 that if the water be not poured in with a velocity of 32 feet in a 

 second, the tube will not be maintained full, he appears to forget that 

 water in pouring only obeys the laws of gravity, and that to pour it 

 into a tube with a velocity of 32 feet in a second, it must fall from a 

 height of 16 feet. In the illustration of the rope of shillings, it is 

 plainly admitted, indeed, that in order to obtain a uniform velocity of 

 32 feet in a second, the shillings must be dropped from a height of 

 16 feet before entering the tube ; therefore, even according to our cor- 

 respondent's own illustration of his case, a fall of 32 feet instead of 

 16, is requisite to communicate a uniform velocity of 32 feet in a 

 second. We may observe, in passing, that the illustration of the 

 continuous fall of shillings could never be practically exemplified, for 

 we cannot admit that a row of shillings, or of any other non-cohering 

 bodies, would fall in a uniform stream unless they were all allowed to 

 fall at the same instant of time, like a solid bar. 



Towards the conclusion of his letter, our correspondent calls Be- 

 lidor to his aid; and he appears to imagine that thus supported, his 

 position is impregnable. For our own parts we do not see the utility 

 in any course of original inquiry of relying on authorities, however 

 celebrated, as guides where we are professing to take a new road 

 which they have never trodden. If old authorities were permitted 

 to decide new questions, all scientific researches would be limited to 

 the compilation of different and various opinions, and to the decision 

 of their relative values; and we should never advance beyond the 



present limits of knowledge. The argument of authorities has this 

 further disadvantage, that the opinions quoted very frequently refer 

 to circumstances different from those to which they are applied, and 

 errors thus originating become the more dangerous by the apparent 

 sanction of authorities, which are, if properly understood, opposed, 

 to them. The apparent contradictions in the quotations from Belidor, 

 cited by our correspondent, are sufficient to show, either that they 

 refer to different circumstances, or that Belidor bad not paid special 

 attention to the velocity of water in vertical pipes, but had, like most 

 other writers, assumed without consideration that the efflux of water 

 from vertical pipes is the same as through orifices. To show the 

 contradictory nature of the opinions to be gathered from Belidor, on 

 the supposition that his words apply throughout to vertical pipes 

 and not to pipes and to orifices alternately, we will quote a passage 

 preceding those referred to by our correspondent. In paragraph 424, 

 he says, when speaking of the cause of the velocity of water flowing 

 through orifices, and contrasting such discharge with the flow of 

 water down vertical pipes, " as tbe force on the top of the water is 

 absolutely nothing as compared with that at the bottom of an ideal 

 column, corresponding in size with the orifice, it cannot be said that 

 it is this column constantly renewed from the surface which flows out, 

 but that, generally, all the water in the reservoir assists in the dis- 

 charge through the orifice." He then proceeds to show that if a pipe 

 were inserted in the orifice, and reached to the surface of the water» 

 the exterior of the pipe would bear the pressure of the water in the 

 reservoir, and that the water within tbe pipe would descend by its 

 own gravity alone, unassisted by the pressure of the other fluid. The 

 circumstances of the discharge in the two cases having been thus dis- 

 tinctly shown by Belidor himself to be so different, he could never 

 mean to assert that the quantities discharged in each case are the 

 same. It must be confessed that he has expressed himself in this 

 part of his work rather vaguely; but M. Navier, who was deputed by 

 the French Academy of Sciences, to superintend the publication of a 

 new edition of Belidor's Architecture Hydraulique, in 1S17, adds a 

 note to these passages, from which it clearly appears that lie consi- 

 dered Belidor to refer only to the discharge through an orifice, when 

 stating the velocity to be equal to that of a body falling from the 

 height of the fluid. 



The authority of Belidor, therefore, would avail our correspondent 

 nothing, even were we disposed to admit that it has any weight in 

 the discussion of a question to be decided by reasoning from facts 

 rather than by opinions. As the flow of water down a vertical pipe 

 is assumed to be uniform, it is evident that there must be some other 

 force than its own gravity which communicates to the water entering 

 at the top of the pipe the same velocity as that which has fallen to 

 the bottom and is flowing out. No attempt is made by our corre- 

 spondent to show whence this force is derived, though according to 

 his estimate of the uniform velocity, it must be equal to the pressure 

 of another column of water of the same height as the pipe whence 

 it flows. In our view of the. case, the velocity of the entering water 

 is derived from the gravitating force of the water descending the 

 pipe ; and as the accelerated motion of the falling fluid is thus con- 

 verted into uniform motion, the velocity can be only the mean of the 

 initial and final velocities of a body falling from the same height. 



Iron Dwelling-house. — A large iron mansion has been built by Mr. W. 

 Lavcock, of this town, in separate plates. It is to be sent to Africa, where 

 it will be used as a palace by one of the native kings. This singular building 

 has three floors, exclusive of an attic. The basement story is 7 feet high ; 

 the second, 10 feet ; and the third, in which is the grand suite of state apart- 

 ments, is 12 feet high. In these his sable majesty will give his state au- 

 diences. The principal reception room, the presence chamber, is 50 feet by 

 30, and ornamented throughout in a style of most gorgeous magnificence. 

 To counteract any annoyance from heat, the inventor has contrived the 

 means of admitting a current of air, which can be regulated at pleasure, to 

 pass through an aperture left between the outer plate and the inner panel. — 

 Liverpool million. 



