Mathematically, the process of constructing a flownet consists of contouring the two harmonic or analytic functions of potential and stream function. These functions both satisfy the Laplace equation and the contour lines represent lines of a constant head (equipotentials) and lines tangent to flow paths (streamlines). Together, the potential function and the stream function form the complex potential, where the potential is the real part, and the stream function is the imaginary part.
The construction of a flownet provides an approximate solution to the flow problem, but it can be quite good even for problems with complex geometries by following a few simple rules (initially developed by Philipp Forchheimer around 1900, and later formalized by Arthur Casagrande in 1937) and a little practice:
-Streamlines and equipotentials meet at right angles (including the boundaries),
-Diagonals drawn between the corner points of a flownet will meet each other at right angles (useful when near singularities)
-Stream tubes and drops in equipotential can be halved and should still make squares (useful when squares get very large at the ends),
-Flownets often have areas which consist of nearly parallel lines, which produce true squares; start in these areas — working towards areas with complex geometry,
-Many problems have some symmetry (e.g., radial flow to a well); only a section of the flownet needs to be constructed,
-The sizes of the squares should change gradually; transitions are smooth and the curved paths should be roughly elliptical or parabolic in shape.