CHAMBERS'S INFORMATION FOR THE PEOPLE. 



ot a river to descend at a certain speed is 

 checked by friction, by bends in the course of the 

 stream, and by projections on the banks and 

 bottom. It also flows at a slower rate of speed 

 at and near the bottom than at the surface, and 

 also slower at the sides than in the middle. The 

 place at which the velocity is greatest is called the 

 line of current ; it is generally at the deepest part 

 of the channel. The surface of a river is not quite 

 level ; it is slightly convex, the highest part of the 

 convexity being at the line of current. This arises 

 from the fact, that flowing water does not press 

 so much laterally as if it were at rest ; the more 

 slowly flowing side particles thus press in upon 

 the central portions that are flowing fast, and 

 heap them up until there is equilibrium of lateral 

 pressure. 



To get the mean velocity of a river or other 

 stream, find first the surface velocity in the line of 

 current by observing the rate in feet per minute 

 at which a floating body is carried down. As an 

 approximation to the truth, the mean velocity may 

 be taken at four-fifths of the greatest surface 

 velocity ; and if this is multiplied by the area in 

 feet of the cross-section of the stream, the pro- 

 duct is the discharge in cubic feet per minute. 



Resistance of Water to Bodies moving through 

 it, This is greatly affected by the shape of the 

 body, which ought to have all its surfaces oblique 

 to the direction of the motion. When a cylinder 

 terminates in front in a hemisphere, the resistance 

 is only one-half what it is when the cylinder 

 terminates in a plane surface at right angles 

 to the axis ; and if, instead of a hemisphere, 

 the termination is an equilateral cone, the resist- 

 ance is only one-fourth. If a globe is cut 

 in halves, and a cylinder, whose length and the 

 diameter of whose base are each equal to the 

 diameter of the globe, is fixed between them, this 

 cylinder with hemispherical ends experiences less 

 resistance than the globe alone, the diminution 

 being about one-fifth of the resistance of the 

 globe. Ship-builders have become, in recent 

 times, more alive than formerly to the importance 

 of length and of sharp angles both at bows and 

 stern, in order that vessels may sail well. The 

 best form in all respects for ships is still a dis- 

 puted point, though it seems to be agreed that 

 swift-swimming fish present the nearest approach 

 to the true model 



The resistance offered to a body moving in 

 water increases in a higher ratio than the simple 

 one of the velocity. One part of the resistance 

 arises from the momentum that the body has to 

 give to the water it displaces. Moving at a certain 

 rate, it displaces a certain quantity ; moving at 

 twice that rate, it displaces twice the quantity in 

 the same time. But not only does it displace twice 

 the number of particles of water; it also has to 

 displace them with twice the velocity ; the pres- 

 sure of the resistance is thus not merely doubled, 

 but quadrupled or squared. Similarly, when the 

 velocity is tripled, the resistance arising from the 

 simple displacement of water becomes nine times 

 as great. 



Another part of the resistance of liquids to 

 bodies moving in them is owing to the cohesion 

 of the particles, which have not to be thrown 

 aside merely as separate grains, but to be torn 

 asunder. In addition to this, when the velocity is 

 considerable, the water becomes heaped up in 



front, and depressed at the other end, from nor 

 having time to close in behind, thus causing an 

 excess of hydrostatic pressure against the direc- 

 tion of the motion. Owing to the combination of 

 these causes, the real law of the increase of resist- 

 ance is difficult to investigate, and the results of 

 experiments are not a little discordant. 



The law, however, established with regard to 

 that part of the resistance arising from the dis- 

 placement of the water, has an important practical 

 application. We have seen that when the speed 

 of a vessel is doubled, the pressure against her 

 bows must be at least four times as great as 

 before. Now, this fourfold pressure has to be 

 overcome over twice the space in the same time ;. 

 and this amounts to doing eight times the amount 

 of work in one hour or in one minute that was 

 done before, implying, of course, an eightfold 

 working or impelling power. We thus arrive at 

 the important conclusion, that the impelling power \ 

 required for a vessel increases as the cube of the 

 velocity. If an engine of twenty horse-power is- 

 sufficient to impel a steamer six miles an hour,, 

 then, to impel the same vessel twelve miles, or 

 at twice the velocity, would require 2 s X 20, or 

 8 X 20 = 1 60 horse-power. It thus appears that 

 to do twelve miles in one hour requires eight 

 times as much expenditure of coal as to do six 

 miles in one hour ; or it may be put thus : to do- 

 six miles in half an hour costs four times as much 

 coal as to do the same distance in a whole hour. 



WATER-POWER. 



Water is used as a moving power, either by 

 taking advantage of the impulse of its velocity 

 acquired in falling or descending, or by applying 

 its mere weight to bear down one side of a wheel. 

 The impulse of water is used when the fall of the 

 water is low, and is applied to an undershot wheel, 

 that is, to a wheel with float-boards dipping into 

 the stream, which sweeps under the wheel. It is 

 evident that an undershot wheel can never receive 

 but a fraction of the effect due to the head of 

 water, for the water leaves the float-boards retain- 

 ing at least half its velocity. 



The more economical mode is to make the 



Fig- 23. 

 water act by its gravity, and this is done wherever 



