On the Thermal Effects of Fluids in Motion. 477 



" On the Thermal Effects of Fluids in Motion -.—Temperature of a 

 Body moving slowly through Air." By Prof. W. Thomson, F.R.S., 

 and J. P. Joule, Esq., F.R.S. 



The motion of air in the neighbourhood of a body movmg 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 bv the following formula, — 



where II 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 sohd, at the point of its surface in question. The effect of this 

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

 couj)le 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 eveiywhere 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 j<ist 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 volocity, 

 this line will be called tlie equator. 



If the fluid be air instead of the ideal "perfect hquid," and if the 

 motion be slow enough to admit of the approximation referred to 

 above, there will be a heating effect on the fore and after parts of 

 the body, and a cooling effect on the equatorial zone. If the di- 

 mensions and the thermal conductivity of tlie body be such that 

 there is no sensible loss on these heating and cooling effects by 

 conduction, the temperature maintained at any point of the surface 

 by the air flowing against it, will be given by the equation 



'=<0"- 



where G denotes the temperature of the air as uninfluenced by the 

 motion, and^> and 11 denote the same as beforef- Hence, using for 



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

 and ])erfectly free from mutual friction among its parts. 



t The temperatures are reckoned according to the ahsolute thermodynamic 

 scale whicii \vc liave proposed, and may, to a degree of accuracy correspondent 

 with that of the ordinary " gabcous laws," be taken as temperature Centigrade by 



