Resistance of Fluids. 339 



501. The resistance which a body suffers from the fluid 

 medium through which it is impelled depends on the velocity, 

 form, and magnitude of the body, and on the inertia and tenacity 

 of the fluid. For fluids resist the motion of bodies through them T 

 (1 .) by the inertia of their particles ; (2.) by their tenacity, that is, 

 the adhesion of those particles ; (3.) by the friction of the body 

 against the particles of the fluid. In perfect fluids the two last 

 causes of resistance are very inconsiderable, and therefore are 

 not taken into the account ; but the first is always very con- 

 siderable, and obtains equally in the most perfect as in the most 

 imperfect fluids. And that the resistance varies with the velo- 

 city, shape, and magnitude of the moving body is sufficiently 

 obvious. 



We must carefully distinguish between resistance and retard- 

 ation ; resistance is the quantity of motion, retardation the quan- 

 tity of velocity, which is lost ; therefore, the retardations are as 

 the resistances applied to the quantities of matter ; and in the 

 same body the resistance and retardation are proportional. ' 



502. To determine the force of fluids in motion, or the resist- 

 ance of fluids against bodies moving in them. 



(I.) In fluids uniformly tenacious, the resistance is as the 

 velocity with which the body moves. For, since the cohesion of 

 the particles of the fluid is always the same for the same space, 

 whatever be the velocity, the resistance from this cohesion will 

 be as the space described in a given time ; that is, as the 

 velocity. 



(2.) In a fluid whose particles move freely without disturb- 

 ing each other's motions, and which flows in behind as fast as a 

 plane body moves forward, so that the pressure on every part 

 of the body is the same as if the body were at rest, the resist- 

 ance will be as the density of the fluid. 



(3.) On the same hypothesis the resistance will be as the 

 square of the velocity. For the resistance must vary as the 

 number of particles which strike the plane in a given time, mul- 

 tiplied into the force of each against the plane ; but both the 

 number and the force is as the velocity, and consequently the 

 resistance is as the square of the velocity. 



