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

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

3. FLOW NETS Total Head Loss, h in water seeping from A to B: hhAhhA A B  datum zzAzzA hhBhhB zzBzzB h h y d r a u l i c g r a d e l i n e L Hydraulic Gradient (Slope), i:In terms of Bernouli:

4. Say we constructed a tank in the lab like this one.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. h

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

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

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

8. Construction of Flow Nets 1. Draw Flow Channel Boundaries2. Draw Equipotential Boundaries Upstream Equipotential Boundary Downstream Equipotential Boundary To construct a flow net, you must start with a scale drawing of the hydraulic structure:

9. The first trial: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.

10. And the final version is: To determine the total head at any point, P2. Show the total head, h driving seepage. h = 4.5-0.5 = 4.0m 1. Downstream free water surface is datum. 3. Number equipotentials as shown: 4. At point P, the total head is 10/12ths of the head driving the seepage 5. Using the given scale, the elevation head, zP is -5.2 m 6. The pore water pressure, uP = (hp – zp)w =(3.33+5.2)x9.8 = 83.3 kPa

11. FLOW NETS Here’s some useful relationships: 2. Each drop in head is equal to: where Nd is the number of partitions or drops in potential 1. Each channel carries an equal flow: ∆q = k∆h 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)