Thiem's Equation
This is the Austrian tennis player Dominic Thiem, who reached a number 2 ranking in 2011 under the International Tennis Federation, but it's most unlikely that he's ever even heard of Thiem's Equation with which he shares a name.
Thiem's Equation is simply the application of Darcy's Law to flow to boreholes.
In order to understand Thiem's Equation, I've first got to run through the various parts that it entails.
So up until now my posts regarding Darcy & Transmissivity have only accounted for linear flow, but for flow of water into a well, the flow is RADIAL!! (See figure below).
Applying Darcy's Law to radial flow to a well
Qw = KAi
K = Hydraulic Conductivity
A = Cross Sectional Area = 2πr(h), (where h = height)
i = (dh/dr), (i is the ratio of heigh to radius init)
Rearranging and integrating this equation (which is something I struggle to do without having to worry figure out all the relevant alt key symbols I'd have to find to be able to type it all out - so sod it!) gets you Thiem's Equations:
h2 - h1 = (Qw/2πT) ln (r2/r1)
Where T is the Transmissivity from my earlier post! So Thiem's Equation is the combination of Darcy's Law + Transmissivity, in order to estimate the flow to boreholes - I think.