HYDRODYNAMIC FORCES 



The pressure in the fluid is given by Bernoulli's equation 



P = - P U^+g^+^ |V(J)|^j (78) 



By substituting Equation (3) into Equation (78), the pressure becomes 



p = p(ia)c})2-Vc})^-V(J)2) e ^""^ - pgC (79) 



Then, the forces and moments with respect to the origin of the coordinate system are 

 given by 



'r- if ""i 



dS for j = 3 and 5 (80) 



where S is the submerged portion of the ship hull, and n. is defined in Equations 

 (20) and (21). By substitution of Equation (79) into Equation (80), the hydrodynamic 

 forces can be expressed by 



F. = -p 



11 [±o^(^^-V<^-^'^<t>^] n. dS e ^"^ (81) 



The second term of Equation (81) can be transformed by means of a theorem due to 

 Ogilvie and Tuck (Appendix A of Reference 8) 



11 (Vc})^.V(^2) ""j '^^ = - JJ "j *2 ^^ ^^^^ 



In Equation (82) , the line- integral term along the intersection of the ship hull with 

 the plane z = is ignored as a higher order term. By substitution of Equations 

 (82) and (17) into Equation (80), the hydrodynamic forces are given as 



18 



