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Oleh : Arwan Apriyono Sec Introduction Flownet is A network of selected streamlines and equipotential lines to evaluate seepage in water construction. Sec Introduction Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. Sec Introduction Equipotential line is simply a contour of constant total head. Sec Theory 1. 2. 3. 4. Streamlines Y and Equip. lines are . Streamlines Y are parallel to no flow boundaries. Grids are curvilinear squares, where diagonals cross at right angles. Each stream tube carries the same flow. Flow Net Theory 6 Flow Net in Isotropic Soil Portion of a flow net is shown below Y F Flow Net in Isotropic Soil The equation for flow nets originates from Darcy’s Law. Flow Net solution is equivalent to solving the governing equations of flow for a uniform isotropic aquifer with well-defined boundary conditions. 8 Flow Net in Isotropic Soil Flow through a channel between equipotential lines 1 and 2 per unit width is: ∆q = K(dm x 1)(∆h1/dl) m F1 Dq Dq D h1 dm dl n F2 D h2 F3 Flow Net in Isotropic Soil Flow through equipotential lines 2 and 3 is: ∆q = K(dm x 1)(∆h2/dl) The flow net has square grids, so the head drop is the same in each potential drop:∆h1 = ∆h2 If there are nd such drops, then: ∆h = (H/n) where H is the total head loss between the first and last equipotential lines. 10 Flow Net in Isotropic Soil Substitution yields: ∆q = K(dm x dl)(H/n) This equation is for one flow channel. If there are m such channels in the net, then total flow per unit width is: q = (m/n)K(dm/dl)H 11 Flow Net in Isotropic Soil Since the flow net is drawn with squares, then dm dl, and: q = (m/n)KH [L2T-1] where: q = rate of flow or seepage per unit width m= number of flow channels n= number of equipotential drops h = total head loss in flow system K = coefficient of permeability 12 Drawing Method: 1. Draw to a convenient scale the cross sections of the structure, water elevations, and aquifer profiles. 2. Establish boundary conditions and draw one or two flow lines Y and equipotential lines F near the boundaries. 13 Method: 3. Sketch intermediate flow lines and equipotential lines by smooth curves adhering to right-angle intersections and square grids. Where flow direction is a straight line, flow lines are an equal distance apart and parallel. 4. Continue sketching until a problem develops. Each problem will indicate changes to be made in the entire net. Successive trials will result in a reasonably consistent flow net. 14 Method: 5. In most cases, 5 to 10 flow lines are usually sufficient. Depending on the no. of flow lines selected, the number of equipotential lines will automatically be fixed by geometry and grid layout. 6. Equivalent to solving the governing equations of GW flow in 2-dimensions. 15