Resistance in Fluids, is that opposition to the motion of a body which arises from the inertia, tenacity, and friction of the parts of the fluid in which it moves. If any body move through a fluid with a given velocity, it will evidently displace a certain number of particles with a given velocity; but in thus giving motion to the particles of fluid, it must lose a part of its own, which loss of motion is the effect of resistance. When a body changes its velocity, the resistance is not changed in the same proportion; for if a body move with double .its former speed, it will manifestly set in motion twice as many particles, and each of these particles will be moved with double its former velocity. In the same way, if the velocity be tripled, three times the number of particles must be put into motion with a triple velocity. Thus it appears that a double velocity produces a fourfold resistance, a triple velocity a ninefold resistance; that is, the resistance increases proportionally to the square of the velocity. The resistance is also increased in the same proportion as the area of the plane immersed: it is also increased as the density of the fluid medium.
If the plane does not move with its face perpendicular to the direction of its motion, the resistance will be diminished, both on account of a less surface being exposed, and the oblique action of the particles on the plane. From these two causes the resistance will be diminished as the cube of the sine of the angle that the plane makes with the direction of its motion. The resistance is the same, whether the body move in the fluid, or the fluid move against the body. The absolute resistance to a given plane, by a fluid acting with a certain velocity perpendicularly to its face, is equal to the weight of a column of fluid, whose base is the plane and height equal to that through which a heavy body must fall to acquire the given velocity: a consideration of the law of resistance, a limit to our speed in navigation, which soon becomes insuperable.