RESISTANCE OF FLUIDS. In hydrodynamics, the force with which a solid body moving through a fluid is re sisted or retarded. Of all the different kinds of resistance which manifest them selves among bodies, there is none of greater importance than this, on account of its application to the theory of naval architecture.
Sir Isaac Newton was the first wbc gave a general theory of the motions and actions of fluids. The Newtonian theory of the resistance of fluids, which is given in the second book of the Principta, is founded on the assumption of the per feet intermobility of the particles of the fluid, and the equal of pres sure n all directions. These are, indeed, the characteristic properties of fluidity ; nevertheless, the results of the mathe matical theory differ so widely in many cases from actual experiment, that some philosophers have called in question the accuracy of the principles from which they are derived. The theory, however, notwithstanding its defects, furnishes some propositions of great practical use, and, indeed, forms the groundwork of all our knowledge on the subject.
It is evident that a solid body, in mov ing through a fluid, must communicate a motion to the fluid particles with which it successively comes in contact. Now, the quantity of motion communicated to the fluid is necessarily equal to that which is lost by the solid, and may there fore be taken as the measure of the re , sistance. To determine this quantity of motion, let us conceive a cylindrical or prismatic body, terminated by a plane perpendicular to its axis, to be propelled through a nonelastic fluid in the direc tion of its axis, so that the particles of the fluid strike against the plane perpen dicularly.
Numerous experiments have been made for the purpose of ascertaining how far the theory of the resistance of fluids agrees with the actual facts, or for form ing an empirical theory for the guidance of the engineer. Of the details of these experiments our limits will not permit us to give an account. The general results of the experiments may be stated as fol lows : I. The force of resistance on bodies moving in fluids is proportional to the square of the velocity, at least within the limits of 2 to 10 feet per second. This is in accordance with the theory.
II. The direct resistance on bodies moving with the same velocities is nearly in the ratio of the surfaces.
III. The resistances on surfaces mov ing obliquely do not by any means vary in the ratio of the squares of the sines of the angles of incidence, especially when the incidence is very oblique ; and for such motions the theory must be entirely abandoned.
The above results are, however, con siderably modified by various circum stances, of which the principal are the following:— 1. The form of the body. The New tonian theory takes account only of the anterior surface of the body ; but it was clearly established by the experiments of Du Beat that the form of the hinder part is not less efficacious in modifying the resistance. A prismatic body, having its prow and poop equal and parallel sur faces, being plunged horizontally into a stream, will require, in order to keep it immovable, a force in the direction of its axis equal to the difference of the real pressure exerted on its prow and poop. If the fluid is at rest, this difference will be nothing, because the opposite dead pressures are equal ; but in a stream there is superadded to the dead pressure on the prow the active pressure arising from the deflection of the filaments of the fluid, which being turned aside and ren dered divergent by the obstruction of the anterior surface, a part of the pressure of the circumambient fluid is employed in turning them into the trough behind the body, and consequently there is less pressure on the posterior surface than if the body were at rest in stagnant water, so that the body is impelled backwards. This force is called by Du Buat the nets pressure ; by Beaufoy the minus pressure. Now, the whole impulse to be withstood if the body is in a stream, or the resist ance to be overcome if it moves in stag nant water, is the sum of the active pres sure on the fore part and the non-pres sure on the hinder part ; and this does not depend solely on the form of the prow and poop, but also, and perhaps chiefly, on the length of the body. The non-pressure on a cube was found by experiment to be reduced to a fourth part, by making the length of the body triple of the breadth. The mere length ening of a ship, without changing the form of the prow or poop, increases the speed.