APPENDIX A 



THE FORCE GENERATED ON A BODY IN POTENTIAL FLOW BY AN 

 ISOLATED SINGULARITY 



Consider a body immersed in a uniform stream, V , with an isolated 

 point singularity located external to the body at r = ^q- The flow is 

 assumed to be steady, irrotational, and incompressible. If the body is 

 represented by a surface distribution of source singularities a(r ), then 

 the force exerted on the body is given by (Equation (13) in the text) 



F = - P / a(f^) VQ(f^) dS(rg) 

 ^B 



where V (r ) is the velocity induced by the singularity at the body surface. 



Q B 

 This relation may be derived by considering the control volume illustrated 



in Figure A-1. 



Figure A-1 - Control Volume for Analysis of Force on Body 



69 



