Pipe Spacing Research Articles

The stream function of potential theory for a dual‐pipe subirrigation‐drainage system

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.

Soil pipe contribution to steady subsurface stormflow

AbstractFlow through a saturated idealized hillslope with a single soil pipe was simulated using a finite difference solution to the equation for three‐dimensional Darcian flow in saturated heterogeneous media. The proportions of hillslope discharge originating from flow through the soil matrix and from flow through a soil pipe were determined, considering such factors as the radius, depth and length of the pipe, pipe spacing, and the length and slope of the hillslope. Results demonstrate that soil pipes can contribute a significant amount, and in many instances, the majority of total subsurface stormflow.

Transport properties of rocks from statistics and percolation

Two simplified microstructural models that account for permeability and conductivity of low-porosity rocks are compared. Both models result from statistics and percolation theory. The first model assumes that transport results from the connection of 1D objects or “pipes”; the second model assumes that transport results from the connection of 2D objects or “cracks.” In both cases, statistical methods permit calculation of permeability k and conductivity σ, which are dependent on three independent microvariables: average pipe (crack) length, average pipe radius (crack aperture), and average pipe (crack) spacing. The degree of connection is one aspect of percolation theory. Results show that use of the mathematical concept of percolation and use of the rock physics concept of tortuosity are equivalent. Percolation is used to discuss k and σ near the threshold where these parameters vanish. Relations between bulk parameters (permeability, conductivity, porosity) are calculated and discussed in terms of microvariables.

Parameter effects on design and performance of flat plate solar collectors

Under steady-state and transient state conditions, efficiency and warming-up time of flat plate water collectors are calculated. The effects of the variation of a great many parameters are presented. Proper consideration of these effects is important when meteorological conditions are unfavorable. Comparison of collector performance in summer and winter shows the importance of collector inclination, and the effect of pipe spacing. A rule of thumb is given for the approximate transformation of diurnal irradiance curves into effective constant irradiance values. For the conditions considered here an effective irradiance of about 400 W/m 2 in June yields an efficiency of 57 per cent and an effective irradiance of 300 W/m 2 in December gives 46.5 per cent.

Modelling the cost-effectiveness of sanitary landfill leachate control systems

Abstract Leachate leakage is a major risk associated with sanitary and hazardous waste landfills. This paper describes how two simple performance models, time to breakthrough and leachate leakage flux, can be used in conjunction with a cost model to develop cost-effectiveness relationships which can be used to assist the leachate control system design and planning decision-making process, and, thereby, reduce this risk. Sensitivity and marginal analyses indicate that time to breakthrough (tb) is most sensitive to liner hydraulic conductivity and thickness and that increasing liner thickness yields increasing marginal returns to fb. Leachate leakage flux (qL) is sensitive to liner hydraulic conductivity and the leachate collection pipe spacing-liner thickness ratio. For a given pipe spacing, increasing liner thickness yields decreasing marginal returns to qL. Hypothetical cost-effectiveness relationships for tb and qL are developed analytically and numerically. As a means of introducing the concept of risk...

Design procedures for subsurface soil-warming pipe systems

Soil warming has the potential to be an alternative to conventional heating methods in agriculture. It has been proven that crop yield is enhanced and growing periods are shortened with relatively little energy input. A subsurface soil-warming system consists of a network of parallel horizontal hot-water pipes buried at an appropriate depth in the soil to maintain a favourable temperature field throughout the root zone. Theoretical steady-state, constant property soil-warming models for four pipe configurations are presented in dimensionless form. Experimental verification of one of the configurations is presented. A procedure for establishing optimal pipe depth and spacing according to root-zone heating requirements is described and an example is illustrated. Effects of diurnal temperature fluctuations are also considered. Applications for these models include greenhouse crops and small unprotected crops of several hectares.

Greenhouse floor heating system optimization using long-term thermal performance design curves

Steady-state design curves suitable for the determination of long-term thermal performance of the floor heating system are presented in the paper. The dominant design variables considered in the system synthesis are: pipe diameter and spacing, floor depth, greenhouse main air mass temperature, hot water temperature, water flow rate and plant canopy density. The design curves are generated for a wide range of these parameter values. The nomograms are presented in terms of the greenhouse heat gain per unit floor area as a function of the floor depth, with other variables as parameters. The set of design curves also includes the values of the rate of change of heat flux with the floor depth. This facilitates in design optimization by reducing the three dimensional search in geometric parameter, namely, pipe diameter and spacing, and floor depth, to a two dimensional search. The utility of nomograms is illustrated through a design example for a floor heated greenhouse located in the midwest region of the United States. The optimum parameter values for the floor heating system are estimated using the classical calculus technique.

Design of tunnel support systems using ground freezing

One of the more promising techniques in soft ground tunneling through urbanized areas is the use of artificially frozen ground for temporary tunnel support. This paper describes the general design considerations involved in the ground freezing method. Various factors are discussed which influence the selection of the freezing temperature, the thickness of the frozen zones and the spacing of the freeze pipes. The time required to achieve freezing is discussed in addition to the amount and rate of frost heave caused by the freezing. To illustrate the applicability of the freezing method, various considerations in the design of an 8-ft. diameter tunnel in upstate New York, a 75-ft. diameter tunnel in Georgia, and a 12 1/2-ft. diameter tunnel in Washington, D.C. are discussed. All three of the tunnels were to pass immediately beneath mainline railroad tracks. A laboratory testing program was implemented to determine the effects of the repetitive train loads on the zone of frozen soil around the tunnel perimeter. Stress-controlled repeated load triaxial tests were performed on both undisturbed and remolded samples frozen from temperatures of −7°C for the New York tunnel to −10°C for the Atlanta and Washington tunnels. Static testing consisted of both quick triaxial tests and creep tests on frozen samples of the various soil types. It was found that there was little difference between the cumulative strain response from repeated load tests and static tests for the low frequencies investigated (one-quarter to one-half cycles per minute). Hyperbolic stress—strain functions were developed to simulate the stress—strain relationship for various cumulative loading times. The stresses and strains in the frozen soil tunnel configuration were computed by the finite element method, using both linear and hyperbolic stress—strain functions. Tangent modulus values were varied to reflect the decreasing modulus with increasing loading time. The analyses indicated that zones of frozen soil of approximately 3 ft. thick were required for both the New York and Washington tunnels. However, high tensile stresses were calculated for the Atlanta tunnel, precluding the use of the freezing method.

Some aspects of artificial thawing of frozen soils

Despite its important practical value the problem of artificial thawing of frozen soils by the vertical, cylindrical defreezer-pipe method has been studied only comparatively recently. To facilitate excavation and/or foundation work in frozen soil in seasonally freezing and/or permafrost regions, the frozen soil can be loosened up, among other methods, by artificial thawing. For this purpose it is necessary to evaluate the amount of thermal energy needed to bring about the desired thawing. Such an evaluation involves consideration of the relationships between the frozen and thawed soil properties; temperature of the defrosting agent; the size and spacing of the defreezer pipes; and the time required to thaw a certain amount of frozen soil. Although in practice several methods are used for artificial thawing, in this paper, discussion on and calculations for defrosting of frozen soil are presented relative only to thawing by means of vertically installed defreezer pipes.

Studies on subirrigating culture by capillary movement from water-storage pipes

Each of four types of“pipe-beds”was established in the open air (Fig. 1, Table 1). After preliminary tests on various structures of beds and fertilizer concentrations, this experiment was made on the effects of structures of beds on the growth of broccoli. Broccoli seedlings were raised in a “ditch-ded”. It was also devised to make water rise by capillarity. Seeds were sown on August 4, 1967. Four seedlings were planted in each bed on August 26. Water was poured into the water-storage pipe continually to fill the capacity of 8 liters as the water level lowered to leave around 2 liters. Liquid fertilizer (20 cc of 10-5-8) was supplied into the pipe once every week.The results are shown in Table 2 and Fig. 2. It is censidered that the C-type bed is satisfactory for most crops. For root crops the soil underneath the medium should be cultivated.The studies are on the exploratory stage. Further studies should be made on the spacing of water-conducting pipes, the depth of plastic mulch placed in the central half of the bed, proper ingredients and amounts of fertilizer, and other things.When these problems are solved, the method of water and fertilizer application is not only effective and efficient for plant growth and for saving labor but also not too expensive for construction and also durable.

An analytical solution of heat flow versus wire temperature for electric cables buried in plaster

Complete electric heating installations are becoming quite general throughout certain areas. A popular type is the resistance cable embedded in plaster to form a radiant panel heater. For long cable life and maximum safety, the cable temperature must not exceed a definite limit. Various investigators have derived equations describing the temperature throughout the panel. However such equations do not relate temperature to heat input or else they are based on conditions not met in electric cable heating. K. Kalous1 developed equations for embedded pipe using hot water based upon the simplified assumption that heat flows laterally through the panel. This assumption is valid for panel thicknesses near pipe diameter and for pipe spacing, which is large when compared to panel thickness. Neither condition is met in electric cable heating. T. Napier Adlam2 publishes curves for pipe buried in plaster. The pipe sizes and spacings however, are quite large as compared to electric cable sizes and cable spacing.