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FLOW NETS

FLOW NETS. Bernoulli's Equation. water travels very slowly through soil as opposed to channel flow. 0. Total Head, m. Elevation Head, m. Velocity Head, m. Fluid Pressure Head, m. FLOW NETS. For Seepage through soil:. Pore Water Pressure, kPa. Bernoulli's Equation. FLOW NETS.

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FLOW NETS

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  1. FLOW NETS Bernoulli's Equation water travels very slowly through soil as opposed to channel flow 0 Total Head, m Elevation Head, m Velocity Head, m Fluid Pressure Head, m

  2. FLOW NETS For Seepage through soil: Pore Water Pressure, kPa Bernoulli's Equation

  3. FLOW NETS Hydraulic Gradient (Slope), i: In terms of Bernouli: L hydraulic grade line h hA Total Head Loss, h in water seeping from A to B: A hB B zA zB datum 

  4. The water would seep from the left chamber, through the soil and into the right chamber. The energy driving the seepage, h? The path of the flow would be curved as shown. FLOW NETS h Say we constructed a tank in the lab like this one.

  5. Lines ab and cefd are the boundaries of this flow channel Line ca is the upstream equipotential boundary where the total head is h FLOW NETS Line bd is the downstream equipotential boundary where the total head is 0 If we stretch the tank, we have a mainly horizontal channel for the seepage flow from the left chamber to the right h

  6. FLOW NETS at ca h = h at bd h = 0 The water would rise to the same level on the hydraulic grade line from each of these points. If we divide the seepage journey into equally spaced drops in head then we get a flow net. What would the total head be at the half way mark (at points x, y or z)? Each point has equal potential and therefore the line through them is an “equipotential”. half way mark In order to determine the total head and pore water pressure at any point in the mass of soil we subdivide the flow channel into smaller channels h = 0.5h h = h x h = 0 y z

  7. FLOW NETS If we recompressed the tank the flow net would look something like this:

  8. To construct a flow net, you must start with a scale drawing of the hydraulic structure: Construction of Flow Nets Downstream Equipotential Boundary Upstream Equipotential Boundary 1. Draw Flow Channel Boundaries 2. Draw Equipotential Boundaries

  9. Not all elements are “square” The bottom flow channel intersects the impervious layer It may take several iterations to finally come up with a satisfactory flow net. Construction of Flow Nets The first trial:

  10. 6. The pore water pressure, uP = (hp – zp)w =(3.33+5.2)x9.8 = 83.3 kPa 5. Using the given scale, the elevation head, zP is -5.2 m 4. At point P, the total head is 10/12ths of the head driving the seepage 3. Number equipotentials as shown: 1. Downstream free water surface is datum. To determine the total head at any point, P 2. Show the total head, h driving seepage. Construction of Flow Nets h = 4.5-0.5 = 4.0m And the final version is:

  11. FLOW NETS 1. Each channel carries an equal flow:∆q = k∆h 2. Each drop in head is equal to: where Nd is the number of partitions or drops in potential Here’s some useful relationships: 3. The total flow carried:q = Nf∆q where Nf is the number of flow channel partitions 4. Or, the total flow carried: 5. And, the head at any point P: where nd is equipotential number (0 at downstream FWS)

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