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FRICTION OF WATER.

It remains to consider the friction of water upon the bottom of the vessel, and this is by much the most important part of the resistance which ships have to encounter. Beaufoy made a number of experiments to ascertain the amount of this resistance by drawing a long and a short plank through the water: and, by taking the difference of their resistances and the difference of their surfaces, he concluded that the friction per square foot of plank was, at one nautical mile per hour, 014 lbs.; at two nautical miles per hour, 0472 lbs.; at three, 0948 lbs.; four, 153 lbs.; five, 2264 lbs.; six, ·3086 lbs.; seven, ·4002 lbs.; and eight, 5008 lbs. At two nautical miles an hour, the force required to overcome the friction was found to vary as the 1.825 power of the velocity, and at eight nautical miles an hour as the 1-713 power. Other experimentalists have deduced the amount of friction from the diminished discharge of water flowing through pipes. If there were no friction in a pipe, the velocity of the issuing water should be equal to the ultimate velocity of a body falling by gravity from the level of the head to the level of the orifice.* But as the velocity is found by the diminished discharge to be only that due to a much smaller height, the difference is set down as the measure of the power consumed by friction. This mode of estimating the friction is not applicable to the determination of the friction of a ship; for, in the first place, the discharge is a measure not of the maximum, but of the mean velocity; and, in the second place, there is every reason to believe that the friction per square foot on the bottom of the ship is quite different near the bow from what it is near the stern. As the water adheres to the bottom there will be a film of water in contact with the ship, which will be gradually put

*There is sometimes misconception on this subject, arising from a neglect of the difference between the ultimate and mean velocities of a falling body. Thus, if water flows from a small hole in the side of a cistern, the water will issue with the ultimate velocity which a heavy body would acquire by falling from the level of the head to the level of the orifice, which, if the height be 16 feet, will be 823 feet per second. The mean velocity of falling, however, is only 16 feet per second, so that the ultimate velocity is twice the mean velccity.

into motion by the friction; and the longer the vessel is the less will be the friction upon a square foot of surface at the sternseeing that such square foot of surface has not to encounter stationary water, but water which is moving with a certain velocity in the direction of the vessel. The film of water moving with the vessel will become thicker and thicker as it passes towards the stern, and it will rise towards the surface by reason of the virtual reduction of weight consequent upon the motion. The whole of the power, therefore, expended in friction is not lost, as the power expended in the front part of the vessel will reduce the friction of the after part; added to which, the rising current which the friction produces may be made to aid the progress of the ship, if we give to the after-body of the ship such a configuration as to be propelled onward by this rising current. Finally, when the screw is the propelling instrument, the slip of the screw will be reduced, and may even in some cases be rendered negative, by the circumstance of the screw working in this current; and whatever brings this current to rest will use up the power in it, and so far recover the power which has been expended in overcoming the friction.

In my investigations respecting the physical phenomena of the river Indus in India, I observed that the water not only ran faster in the middle of the stream, but that it also stood higher in the middle, so that a transverse section of the river would exhibit the surface as a convex line. At the centre of the river the stream is very rapid, but it is slow at the sides, so that boats ascending the river keep as close as possible to either bank; and in some parts at the side there is an ascending current forming an eddy. I further observed, that not merely were there rapid and considerable changes in the velocity, which I imputed partly to the agency of the wind in deflecting the most rapid part of the current to the one side or the other of the river, but there were also diurnal tides; or, in other words, the stream ran more swiftly in the afternoon than in the early morning. This had been long before observed, and was imputed to the heat of the sun melting the snows in the mountains more during the day than during the night. But although such an effect might be

weight of the body answerable to that velocity. In two columns of water, therefore, moving at different velocities, the slower will exert most hydrostatic pressure on the pipe or channel containing it; and where two such columns are connected together sideways, as in a river, the faster must rise to a greater height to be in hydrostatic equilibrium sideways with the slower. The surface of the water consequently becomes convex, as shown at м in fig. 54, where H is the water and A B C D the bed.

It will be seen from these observations that there is a hydraulic as well as a hydrostatic head of water; and the hydraulic

2

Fig. 55.

head is equal to the hydrostatic head, diminished by the height due to the velocity with which the water flows. This law is further illustrated by fig. 55, which represents a bulging vessel in which the water is maintained at a uniform height by water flowing into it at the top, while it runs out at E at the bottom. The velocity with which the water flows downward from A to E, varies with the amount of enlarge Fment or contraction of the vessel; and the height of water which will be supported in the small pipes b, c and d, varies as the velocity of the water at their several points of insertion. Thus, the area at B, being greater than the area at ▲, the velocity will be less, and consequently the water will stand in the small pipe b at a point higher than the surface of a. The area at D being less than the area at A, the velocity will be greater; and the height of the water in the small tube d will not come up to the level of A. At o, the velocity of the water being very great, not only no height of column will be supported in the tube c there inserted, but the water will be sucked up through the inverted tube c, out of the small cistern F; and if there be no cistern air will be drawn through the tube. So also in fig. 56, if a pipe be led out at the bottom of a cistern of water, a