Skip to main content
The stream function of potential theory for a dual-pipe subirrigation-drainage system
Water Resources Research
  • Don Kirkham, Iowa State University
  • Robert Horton, Jr., Iowa State University
Document Type
Publication Version
Published Version
Publication Date

An exact mathematical solution to Laplace's equation is presented for appropriate boundary conditions associated with the problem of dual-pipe subirrigation and drainage. The solution can be used to determine a flow net within the groundwater flow region and the associated water table shape. The solution is general. The effects of several hydraulic and geometrical parameters on the groundwater system, such as thickness of saturated zone, position of subirrigation and drainage pipes, heads in the subirrigation and drainage pipes, crop evapotranspiration, fraction of inflowing subirrigation water that exits through the drains, and the aquifer hydraulic conductivity system are evaluated. Calculations are presented showing how pipe spacing affects the shape of the water table. For example, with hydraulic conductivity of 10 m/d, evapotranspiration of 0.01 m/d, drainpipe radius of 0.05 m, and subirrigation pipe radius of 0.0375 m, calculations show that the maximum water table elevation for a pipe spacing of 40 m is 0.64 m greater than for a pipe spacing of 16 m when 40% of the input subirrigation water volume is being removed from the system by drainage. Finally, the general mathematical solution can be used to predict chemical movement as well as water flow through the system.


This article is published as Kirkham, Don, and Robert Horton. "The stream function of potential theory for a dual‐pipe subirrigation‐drainage system." Water resources research 28, no. 2 (1992): 373-387.Doi:10.1029/91WR02484 .Posted with permission.

Accepted for publication in Water Resources Research. Copyright 1992 American Geophysical Union. Further reproduction or electronic distribution is not permitted.”
Copyright Owner
American Geophysical Union
File Format
Citation Information
Don Kirkham and Robert Horton. "The stream function of potential theory for a dual-pipe subirrigation-drainage system" Water Resources Research Vol. 28 Iss. 2 (1992) p. 373 - 387
Available at: