Since we have 



J] h < w > 2 dv ■ j"j"J< w > (' f ) dV 



by Green's theorem and 



- (V*) + gz = — - - (p-p o ) 



from the pressure equation, one can write 



dE 

 3t 



...if 



8n 3t 



/3$ p\ 

 l"E" pj V n 



dS 



n 8n 



on S and E n by the boundary condition, while v = on Z and p = on Z n< 

 Then the rate of change of energy becomes 



dE 

 dt 



-JJ.".-pJJfi 



St 



dS 



(251) 



If the time average is taken, the first term on the right-hand side gives 

 the work done by the ship. The ship is floating freely on the free sur- 

 face and no external force exists except the constant towing force and the 

 gravitational force which keep the average position of the ship fixed in 

 space. Therefore, no work is done nor is there any dissipation of energy, 

 because the viscosity is neglected. Therefore, 



SL 



p v dS = 



(252) 



90 



