2-D Flow-Seepage And Flow Nets Report Samples

Introduction

Darcy’s Law is utilized to calculate the flow of water through soil. A flow net is an important tool to examine the flow of water. It is used to calculate seepage, uplift pressure, and graphically represent Laplace’s equation of continuity, which holds true to steady state flow condition. In this case, the soil being worked with is isotropic with respect to the hydraulic conductivity (k) meaning kx = kz. This is because flow nets can only describe steady state energy loss of a 2-D flow through a resistive medium. Equation 1 can be used only after assuming saturated flow (S=100%) and no volume change (constant e). This will help fulfill the first objective of studying two dimensional flow of water through a porous media.
(1) h= total head
(2) hp= pressure head, he= elevation head.
Equation 2 is Bernoulli’s equation. Equation 1 can be used to solve simple flow problems on flow through isotropic mediums. A graphical representation can be made consisting of two types of curves that form right angles at points of intersection: (a) flow lines, and (b) equipotential lines. Flow lines represent the path of moving water particles that travel from the upstream to the downstream side of the permeable soil. On the other hand, equipotential lines have constant total head (h). A collection of these two types of curves make up a flow net but only when equipotential and flow lines create right angles at intersection and form approximate squares. This helps simplify the graphical representation because the ratio of length to width of each flow element is 1. Two additional values obtained from the flow net are Nf, the number of flow channels, and Nd, the number of potential drops which are the spaces between equipotential lines. By having a “square” flow net, the total head loss between all adjacent equipotential lines is equal and each flow channel has an equal flux. Equation 3 represents the total flow/flux (Q) through a flow net if the number of flow channels equals Nf.
(3) H= total head loss
When physically constructing the flow net, a lot of trial and error must be conducted. In this experiment a “confined” flow is being dealt with so boundaries must be established. The first boundary is the two surfaces of the soil on either side of the impermeable pile which will be the first and last equipotential lines. The second boundary is the impervious layer and pile which are flow lines. Once boundaries are established three to four flow lines can be drawn starting from the upstream pervious boundary. Then when drawing your equipotential lines perpendicular to the flow lines make it so that approximate “squares” make up the flow net for the previous equations to be valid. Through this the final two objectives of practicing graphical techniques of flow net development and examining the flow net using a hydraulic model will be accomplished.

Conclusion

A critical tool to help determine the flow of water through soil is the flow net. The flow net provides a graphical solution to steady state flow through isotropic soil. From the hydraulic seepage model, this flow could be observed and measured. After applying Laplace’s equation and the total flux equation, the coefficient of permeability of the soil is determined to be 0.17 cm/s. A flow net drawn based on the data allowed for thirteen drops and five channels. This value is comparatively higher compared to k values determined in previous laboratory experiments. The other k values are slightly inconsistent. This could be due to the number of channels and drops used, or calculation error.