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Fluid mechanics (currie)

  1. Mar 29, 2013 #1
    1. The problem statement, all variables and given/known data

    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^2-a^2)


    So i have already solved the problems 4.1 through 4.3 and i tried the same trick of aproximating ln(1/1-x) 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
     
  2. jcsd
  3. Dec 8, 2014 #2

    Hello Benjamin,

    Could you please share how you arrived at the result .

    I tried this by adding the source potentials and subtracting the sink potential and then differented it to get the complex velocity.But I could not arrive at the answer it represents the complex potential for a circle of radius a.

    Pls Help.

    Thanks!
    Abi
     
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