22 



HYDRODYNAMIC MOMENT 



Up to a certain point, the development for the hydrodynamic moment is exactly parallel 

 to the development for the force. The net moment acting on a given mass of fluid is 



M = ^^ 



dt 



where'Tft is the total moment of momentum of the fluid about the center of moments (in our 

 case, the origin). Then 



M +-M^.= p{T xn)da=-j-\ p(rxq)c?: 



5+5' Vr 



■ p(r X n)c?a+4-l p(rxq)(fT 

 Jc. ' dt J,/ 



M 



s .5. 



which can be written 



M^ = ( J-p(q • q)(r X n)(^<7- o^r xnda +4-\ P^rxq)^ 



[49] 



s' dt 



T he second term of Equation [49] can be rewritten as before 



r pl$rxn^a-f p^(r xn)cfa+r p (q • « x r) (r xrx)da 

 J ' d t J ' dt J g ' 



= A-\ p$(r x n)c?CT - fa» X n$(rxn)c^CT-t p (q • w x f)(r x n)c?(7 



The last term of Equation ft9] can be transformed to 



^=^1 p{txq)dT-\ p(r xq)(q . n)c?a + p (w x r • n) (r x q)c?a [51] 



dt dt Jy ' J„ ' Jo ' 



[50] 



