NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 29 



its viscosity, and upon nothing else for ordinary transportation 

 speeds. 



The most general expression ^ for this statement which satisfies the 

 theory of dimensions is 



in which 



L denotes the length of any linear dimensions of the solid, 

 V, the relative velocity of solid and fluid, 

 p, the density of the fluid, 

 fx, the coefficient of viscosity of the fluid, 



and / is a function of the single variable ^ . 



It will be noted that the compressibility of the fluid has been neg- 

 lected. 



The value of / ( ^j is very nearly constant for bodies of a 



given shape in a given orientation when the motion of the fluid is 

 sufficiently turbulent. Experimentally it is found that R cc V~, nearly, 



and hence not only is / / '') nearly constant, but the influence 



of viscosity is small. The changes in / / ^j with change of scale, 



density, and viscosity are hence in the nature of a correction. 



For objects moving through the air at very low speed, especially 

 objects of easy form, turbulence is not marked and viscosity is of 

 importance. Consequently for such tests the assumption of / con- 

 stant is not justified. 



However, for aeroplane wings, parts, etc., moved through the air 

 at high speeds the resistance to motion is largely due to turbulence, 



/? varies nearly as pF^ and / ( ^) is constant nearly. Therefore, 



we may assume that for the ordinary work of an experimental wind 

 tunnel, forces to be measured will vary as the density of the air. 

 Likewise, the manometer reading obtained from a Pitot tube will 

 vary as the density of the air. 



It has been decided to adopt a standard density for air to be used 

 throughout. Velocity computed from a manometer reading is then 

 referred to this standard air, and forces measured on the balance are 



^ Helmholtz, Wissenschaftliche Abhandlungen, Vol. I, p. 158; O. Reynolds, 

 Phil. Trans. Roy. Soc. 1883, p. 935 ; Lord Rayleigh, Phil. Mag., 1899, p. 321. 



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