Analytical solution for tension‐saturated and unsaturated flow from wicking porous pipes in subsurface irrigation: The Kornev‐Philip legacies revisited

Abstract

The Russian engineer Kornev in his 1935 book raised perspectives of subsurface “negative pressure” irrigation, which have been overlooked in modern soil science. Kornev's autoirrigation utilizes wicking of a vacuumed water from a porous pipe into a dry adjacent soil. We link Kornev's technology with a slightly modified Philip (1984)'s analytical solutions for unsaturated flow from a 2‐D cylindrical pipe in an infinite domain. Two Darcian flows are considered and connected through continuity of pressure along the pipe‐soil contact. The first fragment is a thin porous pipe wall in which water seeps at tension saturation; the hydraulic head is a harmonic function varying purely radially across the wall. The Thiem solution in this fragment gives the boundary condition for azimuthally varying suction pressure in the second fragment, ambient soil, making the exterior of the pipe. The constant head, rather than Philip's isobaricity boundary condition, along the external wall slightly modifies Philip's formulae for the Kirchhoff potential and pressure head in the soil fragment. Flow characteristics (magnitudes of the Darcian velocity, total flow rate, and flow net) are explicitly expressed through series of Macdonald's functions. For a given pipe's external diameter, wall thickness, position of the pipe above a free water datum in the supply tank, saturated conductivities of the wall and soil, and soil's sorptive number, a nonlinear equation with respect to the total discharge from the pipe is obtained and solved by a computer algebra routine. Efficiency of irrigation is evaluated by computation of the moisture content within selected zones surrounding the porous pipe.

Creating Clay emitters for Low-Head Subsurface Irrigation

“…The preferred operating pressure head for ceramic emitters is usually less than 100 cm and greater than or equal to 20 cm. As a result, the emitter discharge is minimal, the variance is low, and the distribution is uniform, ensuring that the root zone is kept at a suitable water level (Cai et al, 2021;Kacimov & Obnosov, 2017). It is a non-pressure compensated emitter since the ceramic emitter discharge exponent is 1 (ASABE EP405.1 2003).…”

Steady Darcian Flow in Subsurface Irrigation of Topsoil Impeded by a Substratum: Kornev–Riesenkampf–Philip Legacies Revisited

“…In this regime, Kornev () used ceramic pipes (isolated from air), which exude water (maintained under negative pressure in the lateral of Figure b) to the ambient soil, which is even at a higher suction than the pipe water. In this case, there is no positive pressure zone in the porous wall or adjacent soil (Kacimov and Obnosov, ).…”

“…We expand Philip's () solution to examine the flow topology from a single emitter. Kacimov and Obnosov (, ) compared the two models and bridged the Riesenkampf () and Philip's solutions for the case when a → ∞in Figure (a), i.e. no low‐permeable substratum.…”

Steady Flow from an Array of Subsurface Emitters: Kornev’s Irrigation Technology and Kidder’s Free Boundary Problems Revisited

“…If the "deep drainage" conditions at infinity (point D 1 -D 2 ) in Fig. 1 are known by specification of the pore pressure for saturated flows (as for example, in Kidder 1956;Kacimov and Obnosov 2016) or moisture content for unsaturated flows (as for example, in Kacimov and Obnosov 2017), then Q for a "circular" (or any other shape) emitter is determined by the above-mentioned triad. Vedernikov (1939) analyzed the shape of real equipotential lines around mathematical sinks-sources and found when they deviate from prescribed circles, although this affects flow in the very vicinity of the mathematical singularities.…”