ON THE RESISTANCE OF A FLUID TO A BODY IN MOTION.

Circumstances affecting the resistance which a body meets with in its motion in a fluid.

The resistance which a body meets with in its motion through a fluid will depend upon three principal causes, viz:—

1st. Its velocity, and the form and magnitude of the surface opposed to the fluid.

2nd. Upon the density and tenacity of the fluid or cohesion of its particles, and also upon the friction which will be caused by the roughness of the surface of the body.

3rd. Upon the degree of compression to which this fluid, supposed to be perfectly elastic, is subjected, upon which will depend the rapidity with which it will close in and fill the space behind the body in motion.

The resistance of a fluid to a body as the squares of the velocities.

Firstly, with regard to the velocity of the body. It is evident that a plane moving through a fluid in a direction perpendicular to its surface, must impart to the particles of the fluid with which it comes in contact, a velocity equal to its own; and, consequently, from this cause alone, the resistances would be as the velocities; but the number of particles struck in a certain time being also as the velocities, from these two causes combined, the resistance of a fluid to a body in motion, arising from the inertia of the particles of the fluid, will be as the square of the velocity.

Cohesion of the particles of a fluid, and friction.

Secondly, a body moving in a fluid must overcome the force of cohesion of those parts which are separated, and the friction, both which are independent of the velocity. The total resistance then, from cohesion, friction, and inertia, will be partly constant and partly as the square of the velocity.

Result.

The resistances therefore are as the squares of the velocities in the same fluid, and as the squares of the velocities multiplied by the densities in different fluids.

Hitherto, however, we have imagined a fluid which does not exist in nature; that is to say, a discontinued fluid, or one which has its particles separated and unconnected, and also perfectly non-elastic.

Atmosphere, and its properties bearing on the question of its resistance.

Now, in the atmosphere, no one particle that is contiguous to the body can be moved without moving a great number of others, some of which will be distant from it. If the fluid be much compressed, and the velocity of the moving body much less than that with which the particles of the fluid will rush into vacuum in consequence of the compression, it is clear that the space left by the moving body will be almost instantaneously filled up, ([plate 23], fig. 2); and the resistance of such a medium would be less the greater the compression, provided the density were the same, because the velocity of rushing into a vacuum will be greater the greater the compression. Also, in a greatly compressed fluid, the form of the fore part of the body influences the amount of the retarding force but very slightly, while in a non-compressed fluid this force would be considerably affected by the peculiar shape which might be given to the projectile.

Resistance increased when the body moves so fast that a vacuum is formed behind it.

Thirdly. If the body can be moved so rapidly that the fluid cannot instantaneously press in behind it, as is found to be the case in the atmosphere, the resisting power of the medium must be considerably increased, for the projectile being deprived of the pressure of the fluid on its hind part, must support on its fore part the whole weight of a column of the fluid, over and above the force employed in moving the portion of the fluid in contact with it, which force is the sole source of resistance in the discontinued fluid. Also, the condensation of the air in front of the body will influence considerably the relation between the resistances and the velocities of an oblique surface: and it is highly probable that although the resistances to a globe may for slow motions be nearly proportional to the squares of the velocities, they will for great velocities increase in a much higher ratio.