2>4 



i-^ + y 



(33) 



boiling occurs. For many applications in naval hydrodynamics, we may 

 imagine that the term -(a + c )/t ~ 1 so that Brennen's \ function can 

 be made dimensionless with the result that if the term 



z 



c T 



c T 



/ U L 



k 



(34) 



boiling is said to occur. In this group of terms, E is the Eckert number, 



and P is the usual Peclet number, both familiar in heat transfer. An 

 e 



example, here, may illustrate the point. We consider water with reference 

 speed of 10 m/sec and reference length of 3 cm to form Table 3. 



TABLE 3 - COMPARISON OF THERMAL PARAMETERS FOR WATER 

 U = 10 m/s, L = 3 cm 



T = 20° C 



260° C 



360° C 



E T = 1.4 x lo -9 



-4 

 7 x 10 H 



5 x io -3 



E, Iff = 1.5 x l(f 6 

 k e 



1.5 x io -6 



1.5 x io -6 



— *- Cavitation 



Boiling 



Boiling 



We see then, that these thermal effects are not important for hydro- 

 dynamics, but may be for power machinery. Brennen (1973) includes 

 comparisons with many other fluids, and concludes, interestingly, that 

 liquid hydrogen almost always boils rather than cavitates. 



66 



