888 
vage 26. In the cases which interest us here 6, /e is very small. 
Assume 6,/@ = 0.10. Then cavitation should not apnear, according 
to (26.1) unless R/L = 20. Hence cevitation should be expected 
only for very thin, wafer shaped pistons, which are never used. 
22. Effects of viscosity and turbulence in the fluid behind 
the recoiling vistons are usually emall, but they may become 
appreciable in long bores of small diameter. In the appendix, 
varagraph 12., a short calculation on these points is given. 
Tarbulence is to be exvected in tubes when the Reynolds number 
(see anpendix) reaches approximately 2000. Behind the recoiling 
pistone R, the Reynolds number, may be of the order of 10° - 10°, 
Hence the flow may certainly become turbulent. At low velocities 
the pressure gradient necesssry to maintain a given flow against 
viscosity is given by Poiseuille's law send is pronortional to the 
velocity. When turbulence appears, resistance increases and the 
required vreasure gradient is provortional nearly to the square of 
the velocity. According to the avvendix, varagraph ]12., however, 
the pressure necesssry to overcome turbulence is not large - about 
1 atmosphere for pistons of the usual diameter. 
28. In references (5) and (11) the possibility of a non-neg- 
ligible "Bernouili pressure" has been pointed out. The reason it 
doea not appear in the treatment given here is that the rundamental 
equation (9.3) 18 based on acoustic theory, which neglecte non- 
linear terms in the hydrodynamical equations. In paragraph 10. it 
was remarked that the acoustic avproximation is in error by not 
Lao) 
