Tension-saturated and unsaturated flows from line sources in subsurface irrigation: Riesenkampf's and Philip's solutions revisited

A. R. Kacimov*, Yu V. Obnosov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Riesenkampf's (1938), R-38 (referred to here as R-38), analytical solution for steady 2-D flow from a buried line source in a homogeneous Green-Ampt soil, with a wetting plume bounded by a free surface (capillary fringe), is compared with Philip's (1969), (P-69), one for genuinely unsaturated wetting of Gardner's infinite-extension soil. Conformal mappings are used in R-38, from which we derived the flow net, pore-water isobars, isochrones, fields of Darcian velocity and resultant force acting on saturated porous skeleton, fine geometry (shape and size) of the constant-head contour encompassing a mole-emitter or leaky-pipe, as well as the dependence of the total discharge per unit pipe length on uniform pressure in the pipe, capillarity of the soil, radius of the pipe, and saturated hydraulic conductivity. An ovalic "water table" isobar, encompassing P-69 source, is compared with one of R-38 for a fixed discharge and saturated conductivity but adjusted sorptive numbers. The Whisler and Bouwer (1970) relation between the static height of capillary rise and sorptive number is shown to give a good match between R-38 and P-69 isobars. This allows to use R-38 in the source vicinity and P-69 in the far-field zone. Computer algebra (Mathematica) routines are used for visualization of the known and extended R-38 and P-69 solutions.

Original languageEnglish
Pages (from-to)1866-1880
Number of pages15
JournalWater Resources Research
Issue number3
Publication statusPublished - Mar 1 2016


  • ADE for Kirchhoff's potential
  • Zhukovsky function
  • complex potential
  • flow net-isobars-isotachs-isochrones
  • pipe discharge
  • sorptive number versus air-entrance pressure

ASJC Scopus subject areas

  • Water Science and Technology


Dive into the research topics of 'Tension-saturated and unsaturated flows from line sources in subsurface irrigation: Riesenkampf's and Philip's solutions revisited'. Together they form a unique fingerprint.

Cite this