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Thread: Circle geometry help

  1. #1
    Aug 2008

    Circle geometry help

    I am working with the diagram and description attached

    The pollen depostion on the lake surface from point source A is approximated as

    $\displaystyle w_i, lake(z,R)=(R/4z)w_i,_c(z,R) $

    where $\displaystyle w_i,_c(z,R) $ is a deposition function.

    My question is a simple one, why R/4z ? What does that represent? It is not the area / circumference etc. of a circle that I recognise.

    Later on it says that the total pollen deposition coming from a circular source of radius z is
    $\displaystyle y_i,_l(z,R) = 2\pi z w_i,_c(z,R)$

    where l= lake

    which I assume is the circumference of the circle z, multiplied by the above function for the deposition over a lake for a single point, so you get the total pollen deposition from a ring around the deposition point. But then it also states that this is equal to $\displaystyle (\pi R/2) $ multiplied by the integral from z-R to z+R of the deposition function. I understand the deposition funtion (the integral part), but don't understand what the piR/2 represents.

    (it seems I also don't understand how to do an integral which has subscripts and superscripts with LaTeX!)

    would anyone be able to clarify just the geometry part in relation to whether it's talking about circumference, radius, area etc.?

    Thank you very much for any help.
    Attached Thumbnails Attached Thumbnails Circle geometry help-pollen_diagram2.bmp  
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