26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



evidently be regarded as a quantity w^hich is proportional to the 

 impact or velocity pressure p. Hence equation (6), as applied to the 

 Pitot tube at rest in a current of fluid, may be written 



p = pS^c^l^^^-,^,r',r",...>i, (15) 



and it is interesting to compare this with the known behavior of Pitot 

 tubes and with the Pitot equation as ordinarily given. 



In the first place, we know by experience that if the impact opening 

 is the mouth of a long tube pointed up stream, the precise form of 

 the tube and the shape and diameter of its mouth have no appreciable 

 influence on the impact pressure recorded. This means not only that 

 the shape variables r', r ",■ . . . . , etc., are of no importance and may be 

 omitted from among the arguments of </>, but also that D is likewise 



DS • 

 of no importance, so that the argument in which it appears may 



be omitted. Equation (15) thus reduces to the form 



/) = p5^^(|). (16) 



When the fluid is nearly incompressible, like water, the compres- 

 sion caused by the impact pressure p will be so slight that it cannot 

 afifect the general behavior of the fluid. Hence compressibility may 

 be left out of account and if/ treated as a constant, so that we have 



^l]• ('7) 



6" = const X 



\ P 



If p is measured as a head h of the liquid, we have p = gph, and equa- 

 tion (17) reduces to 



vS" = const X Vgh. 

 The value of the constant, which cannot be found by dimensional 

 reasoning, is, in practice, V2 for a properly constructed tube. 



If the fluid is a gas, equation (17) is still applicable when the speed 

 is low. But when the speed is so high that the pressure p causes 



appreciable compression, -^ cannot be neglected and we must return 



to equation (16). A form of «// ( ^ ) for high gas speeds may readily 



be found from thermodynamics, but so many approximations and 

 unproven assumptions have to be made in the course of the argument 

 that the results are not at all convincing. 



