6) Flow Nets

6) Flow Nets

1. Laminar flow through earth dams

   • δ^2h/δ^2x + δ^2h/δ^2z = 0
   • Graphical representation
     • Equipotentials - line of constant head
       • h(x,z)=constant
         • [dh/dx]EP = -δh/δx*δz/δh
           • Slope of the equipotentials
       • Orthogonal to one another
     • Flow lines - paths followed by water particles
       • [dx/dz]FL=vx/xz
         • [dx/dz]FL = δh/δx*δz/δh
         • vx=-kδh/δx vz=-kδh/δdz
           • Darcys law

2. Characteristics of flow nets

   • Flow lines represent flow paths
   • Flow lines are orthogonal to equipotential lines
   • Δq is constant
   • Flow occurs only in flow tubes
   • Δh is constant between adjacent equipotential lines
   • Common boundary conditions
     • Submerged soil boundary - equipotential
     • Impermeable soil boundary - flow line
     • Line of constant pressure - Δh=Δz

3. Estimating quantity of seepage

   • Q=khNf/Nd
     • Nf - number of flow tubes
     • Nd - number of equipotentials
     • h - net hydrolic head
     • k - coefficient of permeability

4. Value of head equipotentials

   • Δh=H/No of drops

5. Calculation of pore pressure

   • uw=(h-z)γw

6. Hydrolic uplift force under a dam

   • U=γw(Area of pressure head diagram)