
#1
Jan1413, 10:15 AM

P: 2

the probem is from the book:
Fundamental mechanics of fluids by I.G. Currie is from the chapter 4 ( 2 dimentianal potential flows ) is the problem 4.4: . Consider a source of strength m located at z = −b , a source of strength m located at z= a^2 / b , a sink of strength m located at z =a^2 /L, and a sink of strength m located at z = L. Write down the complex potential for this system, and add a constant − m/(2π) logb. Let b → ∞ , and show that the result represents the complex potential for a circular cylinder of radius a with a sink of strength m located a distance I to the right of the axis of the cylinder. This may be done by showing that the circle of radius a is a streamline. Use the Blasius integral theorem for a contour of integration which includes the cylinder but excludes the sink, and hence show that the force acting on the cylinder is X=(ρm^2 a^2 )/( 2πL)(L^2a^2) So i have already solved the problems 4.1 through 4.3 and i tried the same trick of aproximating ln(1/1x) and ln(1+x), that i applyied in the first problems but i cant get to a result that makes the stream line zero ( the imaginary part of the complex potential ), and i think thats why i always get that the residues of the complex integral force sum up to zero . i someone has some advice about this problem i would appreciate it a lot . thanks benjamin 


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