### Abstract

An explicit closed-form analytical solution giving the water-table depression is obtained for the steady-state problem of seepage to a water-bearing substratum from two reservoirs separated by a strip of land over which water loss by evaporation occurs at a constant rate. Two hydrodynamic situations can occur. In the first, there is only drainage into the substratum and all evaporating water originates from the reservoirs. In the second, the substratum, while accepting water draining from the reservoirs, also supplies some water to the evaporating surface. The method of boundary-value problems is used through the conformal mapping of a strip in the Zhukovskii plane to an auxiliary half-plane and reconstruction of the complex physical coordinate by the Signorini formula. The two hydrodynamic regimes are demarcated in the solution with the shape of the water table obtained in a closed form. The results of calculations show the effect of the evaporation rate, the hydraulic conductivity of the soil, the pressure in the water-bearing substratum, the distance between reservoirs, and the depth to the substratum. The method of boundary-value problems is also used to obtain an analytical solution for the water-table depression caused by evaporation from a strip in an infinite extent of land above a water-bearing substratum under pressure. Journal of Hydrologic Engineering

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

Pages (from-to) | 295-301 |

Number of pages | 7 |

Journal | Journal of Hydrologic Engineering |

Volume | 10 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jul 2005 |

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### Keywords

- Boundary values
- Conformal mapping
- Evaporation
- Seepage
- Water table

### ASJC Scopus subject areas

- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology
- Civil and Structural Engineering

### Cite this

**Steady-state water-table depressions caused by evaporation in lands overlying a water-bearing substratum.** / Kacimov, A. R.; Youngs, E. G.

Research output: Contribution to journal › Article

*Journal of Hydrologic Engineering*, vol. 10, no. 4, pp. 295-301. https://doi.org/10.1061/(ASCE)1084-0699(2005)10:4(295)

}

TY - JOUR

T1 - Steady-state water-table depressions caused by evaporation in lands overlying a water-bearing substratum

AU - Kacimov, A. R.

AU - Youngs, E. G.

PY - 2005/7

Y1 - 2005/7

N2 - An explicit closed-form analytical solution giving the water-table depression is obtained for the steady-state problem of seepage to a water-bearing substratum from two reservoirs separated by a strip of land over which water loss by evaporation occurs at a constant rate. Two hydrodynamic situations can occur. In the first, there is only drainage into the substratum and all evaporating water originates from the reservoirs. In the second, the substratum, while accepting water draining from the reservoirs, also supplies some water to the evaporating surface. The method of boundary-value problems is used through the conformal mapping of a strip in the Zhukovskii plane to an auxiliary half-plane and reconstruction of the complex physical coordinate by the Signorini formula. The two hydrodynamic regimes are demarcated in the solution with the shape of the water table obtained in a closed form. The results of calculations show the effect of the evaporation rate, the hydraulic conductivity of the soil, the pressure in the water-bearing substratum, the distance between reservoirs, and the depth to the substratum. The method of boundary-value problems is also used to obtain an analytical solution for the water-table depression caused by evaporation from a strip in an infinite extent of land above a water-bearing substratum under pressure. Journal of Hydrologic Engineering

AB - An explicit closed-form analytical solution giving the water-table depression is obtained for the steady-state problem of seepage to a water-bearing substratum from two reservoirs separated by a strip of land over which water loss by evaporation occurs at a constant rate. Two hydrodynamic situations can occur. In the first, there is only drainage into the substratum and all evaporating water originates from the reservoirs. In the second, the substratum, while accepting water draining from the reservoirs, also supplies some water to the evaporating surface. The method of boundary-value problems is used through the conformal mapping of a strip in the Zhukovskii plane to an auxiliary half-plane and reconstruction of the complex physical coordinate by the Signorini formula. The two hydrodynamic regimes are demarcated in the solution with the shape of the water table obtained in a closed form. The results of calculations show the effect of the evaporation rate, the hydraulic conductivity of the soil, the pressure in the water-bearing substratum, the distance between reservoirs, and the depth to the substratum. The method of boundary-value problems is also used to obtain an analytical solution for the water-table depression caused by evaporation from a strip in an infinite extent of land above a water-bearing substratum under pressure. Journal of Hydrologic Engineering

KW - Boundary values

KW - Conformal mapping

KW - Evaporation

KW - Seepage

KW - Water table

UR - http://www.scopus.com/inward/record.url?scp=23044432270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044432270&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)1084-0699(2005)10:4(295)

DO - 10.1061/(ASCE)1084-0699(2005)10:4(295)

M3 - Article

VL - 10

SP - 295

EP - 301

JO - Journal of Hydrologic Engineering - ASCE

JF - Journal of Hydrologic Engineering - ASCE

SN - 1084-0699

IS - 4

ER -