2.1. Flow Nets

Graphical form of solutions to Laplace equation for two-dimensional seepage can be presented as flow nets. Two orthogonal sets of curves form a flow net:

Flow nets are graphical representations that illustrate how water seeps through soil in two dimensions. They are formed using two sets of curves that are orthogonal, meaning they intersect at right angles. These curves help visualize the behavior of groundwater flow in various engineering problems.

Imagine a map of a river system. The flow nets are like the paths that water would take as it travels through the landscape, represented by lines on the map corresponding to path options alongside rivers and streams.

Equipotential lines connecting points of equal total head h and flow lines indicating the direction of seepage down a hydraulic gradient.

In a flow net, equipotential lines are curves that connect points where the total hydraulic head is the same. These lines indicate where water pressure is equal. On the other hand, flow lines show the path that water takes as it seeps through the soil, indicating the direction of water flow based on the hydraulic gradient, which is the slope of the water table.

Think of a water park slide. The slide's surface has different heights (like the equipotential lines), while the direction the water flows down the slide represents the flow lines. The slide’s gradient determines how quickly the water flows from the top to the bottom.

Two flow lines can never meet and similarly, two equipotential lines can never meet.

This principle is fundamental in hydraulic engineering. Flow lines and equipotential lines are distinct because they represent different aspects of water movement. If they were to cross, it would imply that there are simultaneous contradictory conditions for flow, which is not physically possible.

Imagine two cars racing down a straight track; if they tried to occupy the same space at the same time, it would create a collision. Similarly, flow lines and equipotential lines must maintain their distinct paths without overlapping.

The space between two adjacent flow lines is known as a flow channel, and the figure formed on the flownet between any two adjacent flow lines and two adjacent equipotential lines is referred to as a field.

Flow channels are the regions between two flow lines where the seepage occurs. The area bounded by two flow lines and two equipotential lines is known as a field, which helps in calculating flow characteristics effectively within that bounded area.

Picture a series of streets (flow channels) and blocks (fields) in a neighborhood. The streets direct how cars travel, just like flow lines guide water, while each block represents a specific area of interest for the flow of water.

If standpipe piezometers were inserted into the ground with their tips on a single equipotential line, then the water would rise to the same level in each standpipe.

Standpipe piezometers are instruments used to measure groundwater levels. When they are placed at the same altitude on an equipotential line, the water will rise to the same height in each piezometer, reflecting the equal hydraulic pressure at that level, even if the actual pore pressures differ due to elevation differences.

Think of filling water in multiple connected bottles at the same height. Even though each bottle has its own shape (like varying elevations), water will adjust to the same level due to gravity acting uniformly, similar to the behavior observed in piezometers.

Consider a field of length L within a flow channel. There is a fall of total head ∆h. The average hydraulic gradient is... If N is the no. of flow channels, then the total flow rate is...

To calculate flow rates, we consider the length and the hydraulic gradient in a flow channel. The fall in head (∆h) along these channels helps determine the average hydraulic gradient, which is critical for assessing how quickly water flows. The total flow rate can be summed up if we know the number of channels (N) involved in the seepage process.

Imagine a system of highways with varying gradients leading down to a valley. The steeper the gradient (the higher the hydraulic gradient), the faster cars can travel down those highways. Similarly, in flow nets, the rate of water flow is directly related to the gradient.

There is an advantage in sketching flow nets in the form of curvilinear 'squares' so that a circle can be inscribed.

Sketching flow nets as curvilinear 'squares' allows for mathematics involving circles to be applied. Inscribing a circle ties geometry with fluid flow calculations, providing a simplified way to understand flow characteristics within the bounded area.

Imagine shaping a round pizza into square slices. While the slices are straight-edged, the circular pizza helps conceptualize how it can be divided. In flow nets, inscribing circles within outlined channels simplifies complex calculations and visualizes flow patterns.

For a complete problem, the flow net can be drawn with the overall head drop h divided into N so that ∆h = h / N.

This step involves breaking the total head drop into multiple increments, enabling detailed calculations of flow through each discrete channel. By dividing the total head drop (h) by the number of flow channels (N), you establish a refined approach to calculate the total flow as it occurs.

Consider a long staircase with several steps leading to the ground. Instead of jumping down all at once, breaking your descent into steps (N) helps you manage your progress more safely and with greater control, similar to how dividing head drops aids in flow calculations.

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