556 



XXI. " On the Thermal Effects of Fluids in Motion : Tempe- 

 rature of a Body moving slowly through Air." By Prof. 

 W. THOMSON, F.R.S., and J. P. JOULE, Esq., F.R.S. 

 Received June 18, 1857. 



The motion of air in the neighbourhood of a body moving very 

 slowly through it, may be approximately determined by treating the 

 problem as if air were an incompressible fluid. The ordinary hydro- 

 dynamical equations, so applied, give the velocity and the pressure 

 of the fluid at any point ; and the variations of density and tempe- 

 rature actually experienced by the air are approximately determined 

 by using the approximate evaluation of the pressure thus obtained. 

 Now, if a solid of any shape be carried uniformly through a perfect 

 liquid *, it experiences fluid-pressure at different parts of its surface, 

 expressed by the following formula, 



where n denotes the fluid-pressure at considerable distances from the 

 solid, p the mass of unity of volume of the fluid, V the velocity of 

 translation of the solid, and q the velocity of the fluid relatively to 

 the solid, at the point of its surface in question. The effect of this 

 pressure on the whole is, no resultant force, and only a resultant 

 couple which vanishes in certain cases, including all in which the 

 solid is symmetrical with reference to the direction of motion. If 

 the surface of the body be everywhere convex, there will be an aug- 

 mentation of pressure in the fore and after parts of it, and a dimi- 

 nution of pressure round a medium zone. There are clearly in every 

 such case just two points of the surface of the solid, one in the fore 

 part, and the other in the after part, at which the velocity of the fluid 

 relatively to it is zero, and which we may call the fore and after pole 

 respectively. The middle region round the body in which the relative 

 velocity exceeds V, and where consequently the fluid pressure is dimi- 

 nished by the motion, may be called the equatorial zone ; and where 

 there is a definite middle line, or line of maximum relative velocity, 

 this line will be called the equator. 



* That is, as we shall call it for brevity, an ideal fluid, perfectly incompressible 

 and perfectly free from mutual friction among its parts. 



