the kinetic energy and intrinsic energy of the dilatational 

 oscillations, both expressed as energy density (energy per 

 unit volume). The intrinsic energy is really a measure of 

 the departure of the internal energy from that at equilibrium 

 due to compression or dilatation of the fluid. 



The term pv represents the energy flux or transmission 

 of energy per unit time through a unit area. For a trans- 

 ducer which radiates acoustic energy outwards in a fluid 

 medium, the acoustic power of the transducer is given by 

 the integral 



pv 



d 6 



S 



which is evaluated over the exterior surface of the transducer, 

 the surface element d a being associated (in direction) with 

 the outward normal to the surface of the transducer. 



The viscous term on the right side of (19) can be re- 

 written in several different forms depending upon the nature 

 of the flow. Under the approximation of irrotational flow as 

 employed in (14) and in view of (18), it can be shown that the 

 viscous term of the energy equation can be expressed as 



(2|-i +\ ) 



K 



V • 



v^ ] 



+ J- 



' S£ 



2 





. at . 



^0 



9t. 





Substituting the latter expression in (19) yields the 

 following energy equation appropriate to conditions of 

 irrotational acoustic disturbances in a viscous fluid: 



Po U P 



2 IT 



+ V 



9£ 

 St 





(20) 



34 



