Flow Nets and Two-Dimensional Flow

In two-dimensional flow scenarios, the uplift pressure beneath a hydraulic structure remains unaffected by alterations in the anisotropic properties of the subsurface soil.

The graphical solution of Laplace's equation for two-dimensional flow is uniquely represented by a velocity hodograph, irrespective of the boundary conditions.

In a flownet, the intersection of flow lines and equipotential lines at acute angles signifies a mathematically valid solution for isotropic soil conditions, indicative of non-Darcian flow.

For anisotropic soils where $k_h$ significantly exceeds $k_v$, the accurate representation of a flownet necessitates shortening the vertical distance of the problem by a factor of $\sqrt{k_h/k_v}$ to account for directional permeability differences.

In a confined aquifer subjected to two-dimensional flow, the hydraulic gradient is solely a function of the total head loss and the thickness of the aquifer, remaining invariant to the flow path's tortuosity.

In the context of seepage analysis beneath hydraulic structures, the exit gradient is invariably minimized at the downstream toe, ensuring structural stability against piping and soil erosion, regardless of soil heterogeneity.

The Laplace equation, when applied to two-dimensional flow through porous media, directly quantifies the advective transport of contaminants, thereby precluding the necessity for separate solute transport modeling.

In a flownet construction, equipotential lines always converge towards regions of higher hydraulic conductivity, irrespective of the geometric constraints imposed by impermeable boundaries.

A flow line represents the locus of points where the total mechanical energy of a fluid particle is constant, thus remaining invariant to changes in the fluid's velocity or elevation within the flow field.

The critical hydraulic gradient for the onset of piping in a soil is exclusively dictated by the soil's void ratio and specific gravity, rendering it independent of the effective stress conditions within the soil matrix.

In a typical flownet diagram, the total number of flow channels ($N_f$) and equipotential drops ($N_d$) are inversely proportional such that their product always equals a constant value determined by the hydraulic conductivity of the medium.

The presence of a low-permeability clay layer at the base of an excavation invariably mitigates the risk of heaving, irrespective of the pore water pressure distribution and the geometry of the excavation.

In a fully confined aquifer beneath a dam, the uplift pressure at any point is calculated assuming a linear equipotential drawdown between the upstream and downstream boundaries, irrespective of the flownet configuration.

The average path of a water particle flowing from upstream to downstream in a porous medium, also known as a flow line, is influenced by the largest gradient.

The solution of Laplace's equation gives two sets of lines, namely flow lines and equipotential lines, which intersect each other at right angles.

The space between two adjacent flow lines is called the flow channel.

In isotropic soil, the flow follows the path of largest gradient; therefore, the flow lines intersect the equipotential lines at a right angle.

A flow net is a numerical solution of Laplace's equation in 3-dimensional flow for a given set of boundary conditions.

In seepage analysis, flow nets are constructed to determine seepage losses, water pressure under a dam or structure, and the amount of exit gradients.

An imperious boundary is a flow line.