On the Resistance of Fluids.

The weight of a cubic foot of water, is about 62 lbs. To put this quantity in motion equal to 16 feet per second, requires a power equal to that required to raise the same quantity four feet perpendicularly; or about equal to 5-6th of one horse-power. To produce a continuous current of water with the same velocity through a channel one foot square, would require sixteen times as much power, because the quantity thus put in motion, would be sixteen cubic fee per second instead of one foot. If the paddle-wheel of a steamboat be 16 feet in circumference, with paddle-boards or buckets one foot square; and if the paddle-boards are made to pass through a channel, so constructed that the water cannot escape in but one direction, then the power required to put the wheel in motion, of one revolution per second, would be 16 5-8—ten horse-powers. This is on the supposition that the boat remains at rest; but if the boat should be moving with a velocity of eight feet per second, and in a direction contrary to that of the current produced by the wheel, then only 2 1-2 horse-powers would be required to maintain the rotary motion of the wheel; for in this case, the velocity of the water would be only eight feet per second; and by the reduction of the velocity one half, the requisite power is reduced three fourths.---But if the boat moves 16 feet per second, no less than 80 horse-powers will be required to produce and maintain a current of equal velocity, because, in the first instance, as above stated, ten horse-powers are required to give that motion to 16 cubic feet of water per second; and in the second place, in consequence of the forward motion of the boat, the wheel must encounter and put in motion double the quantity of water, or 52 feet per second. In the third place, to produce this effect, the wheel must be driven with double velocity, rotarily; and, in the fourth place, to produce this double velocity of the wheel, four fold power is required, even if the quantity of water and consequent resistance were not increased. To give the wheel and consequently the current a velocity of 32 feet per second, while the boat remains at rest, would require 80 horse-powers; because, first, the quantity of water put in motion, is double to that of the first mentioned, which would increase the requisite power from 10 to 20 horse powers, even if the resistance of each specific quantity of water was not increased; but as the velocity of the water is double, and to produce double the motion, requires quadruple power, the 20 horse powers must be multiplied by 4, which shows a requisite of 80 horse powers. Again, if the boat is of such a size and form that 2 1-2 horse powers will give it a motion of 8 feet per second, at the same time that a current of equal velocity is produced in the water, then to double the speed of the boat, will require 16 times as much, or 40 horse powers; because, first, each specific quantity of water must receive double velocity, which will require four fold, or ten horse powers; and second, the quantity of water thus put in motion is quadrupled—being doubled first by the increased velocity of the water, and again, by the forward motion of the boat. And this 16 fold power is actually required, in order to double the speed of the boat: first, because the resistance of the water against the bows is quadrupled; and second, because the motion of the wheel is quadrupled, first, by the increased motion of the paddles in, and with the current of water, and again by the forward motion of the boat by which the axle of the wheel being moved in a direction contrary to that of the paddles, a more rapid rotary motion becomes necessary. Moreover, if the paddles of the wheel have not an artificial channel or flume, to prevent the escape of the water from before the paddle, but merely dip in the free and unconfined water of the ocean, then an additional increase of power will be required to counterbalance the deficiency of resistance of the water, and the consequent requisite additional motion of the wheel; and this circumstance will increase the requisite to nearly 60 horse powers or 24 times as much as would be required to maintain a speed of 8 feet per second, as before mentioned. To double the speed again, or increase it to 30 feet per second would again require a 24 fold power, or 576 times as much as that required for the velocity of 8 feet per second. These statement will explain the mysterious difficulty of increasing the speed of steam boats, to any great extent, beyond that of ordinary boats.