3S 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Fkbruary, 



gravity of water expressed in pounds, and h the number by which yon 

 must divide the square of the velocity, in order to find the resistance 

 of the air; it is generally taken as equal tu 5001b. 



"You have then three equations and three unknown quantities. 



1st. s X D = ''i resistance of the air at the moment of equilibrium. 



3rd. D-' = 64 x taking 8 as the multiplier. 



.". J*8 S = 64 x, from which x the height at which the equilibrium 

 between the accelerating and retarding forces exists, would be found. 

 As might be expected this number would be very great. The above 

 equations are a'so useful in finding the velocity due to any given 

 height when the water flows directly into the air, but in the case of 

 the hydraulic railway, where the vertical pipe deflects into one hori- 

 zontal, the velocity of the water issuing from the vertical pipe will 

 be gradually diminished, in consequence of the friction of the hori- 

 zontal pipe, and therefore the velocity of the whole column (as will 

 be seen) will be reduced to that of the water issuing from the extre- 

 mity of the horizontal pipe. 



I shall next proceed to show that cohesion does not account for the 

 uniform flow of the whole column so simply, and consequently not so 

 well, as the pressure of the atmosphere on the surface of the water. 

 For suppose that in some part of the passage of the. water through 

 the pipe, two consecutive portions separated, a vacuum would be 

 formed between them, consequently the atmosphere wo8ld act as an 

 accelerating force on the upper portion, and as a retarding force on 

 the lower portion, and evidently would cause the junction of the two 

 parts — the vacuum then ceasing, the whole column would move toge- 

 ther. A familiar illustration of this explanation is afforded by the 

 well-known experiment of half-a-crown, and a piece of paper of the 

 same form placed at the back, falling together to the ground. It is 

 not the action of gravity alone which makes them fall together, but 

 the pressure of the atmosphere on the half-a-crown. It is, I believe, 

 clear, if these results be correctly deduced from sound principles, 

 that cohesion does not satisfactorily explain the uniform flow of the 

 column of water, and certainly does not reduce the velocity by one 

 half, and consequently demonstrates the errors of the fifth paragraph, 

 alluded to at the commencement of this letter. Some curious results, 

 explaining the uniform flow of the column, even in the case of the 

 atmosphere not acting on the surface of the water, might be deduced 

 from the above equations, by differentiating them. 



" You would oblige me by inserting this letter. 

 " I remain, Sir, 



" Your obedient servant, 



«T. F n." 



Before we reply to the two points to which our correspondent par- 

 ticularly directs attention, we must correct a misapprehension lie ap- 

 pears to have, respecting the statement of the diminution of velocity 

 by increase of aperture. What we stated was, "that if the size of 

 the aperture approximate to that of the pipe, the velocity will be di- 

 minished, and that if the aperture be of the same size as the pipe, so 

 that the whole column must fall as rapidly as the issuing fluid, the 

 velocity will be diminished one half, without making allowance for 

 friction." 



We never intended to assert, as our correspondent appears to 

 imagine, that the velocity of water through a small aperture would 

 be greater than through a large one, unless the aperture he increased 

 so much as to bear a sensible proportion to the size of the containing 

 vessel. 



We shall reverse the order in which our correspondent has con- 

 sidered the subject, and direct attention in the first instance to the 

 cause of the continuously equal flow of water down a vertical pipe, 

 because the main question rests on the admitted uniform flow of the 

 fluid. The initial and the final velocities being the same, there must, 

 as we contend, be a deviation in this case from the usual law that re- 

 gulates the velocities of falling bodies. With respect to the cause 



of this equal fall of water, the difference between us is rather a dif- 

 ference in form than in substance. Our correspondent admits that 

 the flow is uniform, but he attributes it entirely to the pressure of the 

 atmosphere; we attribute its immediate cause to the cohesion of the 

 particles of the fluid, without which, the pressure of the atmosphere 

 could have no effect. Were it not for the coherence of the particles 

 of the water, they would immediately separate in falling, and the 

 particles would fall independently and with different degrees of ve- 

 locity. Their coherence prevents this. Each particle of water in the 

 pipe coheres to the particle immediately above it, with sufficient force 

 to overcome the minutely different degrees of gravitating momentum, 

 due to the difference in their respective times of falling. The effect 

 of this continuity of coherence, transmitted from particle to particle, 

 is to form a running rope of water in the pipe. This rope of water, 

 if we may be allowed the expression, being supposed of equal size 

 throughout, must have an equal velocity in every part of its course; 

 for as water is practically incompressible, a motion communicated to 

 one part of the fluid in the pipe will be communicated to all other 

 parts as effectually as if it were a solid moveable column. It is true 

 that the pressure of the atmosphere tends materially to prevent the. 

 separation of the water flowing down a vertical pipe, in the manner 

 stated by our correspondent; but were it not for the coherence of the 

 fluid particles, the pressure of the atmosphere would have no effect. 

 Small round shot, for example, would not fall down a vertical pipe in 

 a continuous stream, but in separate particles, and with differing velo- 

 cities. The experiment of the half-crown and piece of paper, ad- 

 duced by our correspondent as an illustration of his explanation, is 

 not, we conceive, applicable to the purpose. It is not the pressure of 

 the atmosphere on the paper that causes it to fall in the same time as 

 the half-crown, for it is well known, that in a vacuum, even a feather 

 will fall to the ground as soon as a guinea. The cause of the paper 

 falling through the air in the same time as the half-crown, must be 

 attributed not to the pressure of the atmosphere, but to the avoidance 

 of resistance from the air, in consequence of the paper following 

 closely in the wake of the half-crown, which sustains all the resistance. 



It will be a curious, and we believe a new point, to ascertain to 

 what extent atmospheric pressure influences the flow of water down 

 vertical pipes. Many of our readers may have noticed the farce 

 with which water in a reservoir is drawn into the orifice of a long 

 vertical pipe as the fluid flows down. This force results from the 

 weight of water in the pipe, and from the pressure of the atmosphere 

 on the surface of the water in the reservoir ; the one tending to se- 

 parate the cohering column of fluid, and to produce a vacuum, the 

 other pressing in the water to counteract this effort. If the hand be 

 held on the orifice it is pressed against the aperture with a force cor- 

 responding, within certain limits, to the height of water in the pipe. 

 Were the length of the pipe greater than 33 feet, so that the weight 

 of water surpassed the pressure of the atmosphere, a Torricellian 

 vacuum would be produced, between the surface of the water in the 

 pipe and the hand, and the latter would be [drawn, or forced, against 

 the orifice with a pressure equal to that of the atmosphere. No ad- 

 ditional leugth of pipe would theu increase the pressure. The va- 

 cuous space between the hand and the water in the | ipe would be in- 

 creased, but the pressure would evidently remain the same. The 

 inferences to be drawn from these premises, are — first, that the velo- 

 city of the flow increases with the length of the vertical pipe, until 

 the column of water balances the pressure, of the atmosphere ; se- 

 condly, that when an equilibrium is established between the column 

 of water and the pressure of the atmosphere, [the maximum effect is 

 produced, and no additional length of pipe will add to the velocity of 

 the flow from the reservoir. 



Having thus disposed of the first_objection raised by our correspon- 

 dent, we shall proceed to consider the point on which we more essen- 

 tially differ. Our position is, that the velocity with which water is- 

 sues from a vertical pipe is half the final velocity due to the height of 



