### Abstract

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 language | English |
---|---|

Pages (from-to) | 1866-1880 |

Number of pages | 15 |

Journal | Water Resources Research |

Volume | 52 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 1 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Water Science and Technology

### Cite this

**Tension-saturated and unsaturated flows from line sources in subsurface irrigation : Riesenkampf's and Philip's solutions revisited.** / Kacimov, A. R.; Obnosov, Yu V.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 52, no. 3, pp. 1866-1880. https://doi.org/10.1002/2015WR018221

}

TY - JOUR

T1 - Tension-saturated and unsaturated flows from line sources in subsurface irrigation

T2 - Riesenkampf's and Philip's solutions revisited

AU - Kacimov, A. R.

AU - Obnosov, Yu V.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - ADE for Kirchhoff's potential

KW - complex potential

KW - flow net-isobars-isotachs-isochrones

KW - pipe discharge

KW - sorptive number versus air-entrance pressure

KW - Zhukovsky function

UR - http://www.scopus.com/inward/record.url?scp=84960539730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960539730&partnerID=8YFLogxK

U2 - 10.1002/2015WR018221

DO - 10.1002/2015WR018221

M3 - Article

AN - SCOPUS:84960539730

VL - 52

SP - 1866

EP - 1880

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 3

ER -