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# sma06 - Flow Nets Flow through a Dam Phreatic line...

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Flow Nets

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Flow through a Dam Drainage blanket Phreatic line Unsaturated Soil Flow of water 2 2 2 2 0 h x h z + = z x
Graphical representation of solution 1. Equipotentials Lines of constant head, h(x,z) Equipotential (EP)

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Phreatic line Flow line (FL) 2. Flow lines Paths followed by water particles - tangential to flow Graphical representation of solution Equipotential (EP)
Properties of Equipotentials h(x,z) = constant (1a) Flow line (FL) Equipotential (EP)

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h(x,z) = constant (1a) h x dx h z dz + = 0 Thus: (1b) Properties of Equipotentials Flow line (FL) Equipotential (EP)
h(x,z) = constant (1a) h x dx h z dz + = 0 Thus: (1b) Equipotenial slope dz dx h x h z EP = - / / (1c) Properties of Equipotentials Flow line (FL) Equipotential (EP)

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z x Geometry v z v x Kinematics Properties of Flow Lines From the geometry (2b) dx dz v v FL x z = Flow line (FL) Equipotential (EP)
z x Geometry v z v x Kinematics Properties of Flow Lines From the geometry (2b) Now from Darcy’s law dx dz v v FL x z = v k h x x = - v k h z z = - Flow line (FL) Equipotential (EP)

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z x Geometry v z v x Kinematics Properties of Flow Lines From the geometry (2b) Now from Darcy’s law Hence (2c) dx dz v v FL x z = v k h x x = - dx dz h x h z FL = ∂ ∂ ∂ ∂ v k h z z = - Flow line (FL) Equipotential (EP)
Orthogonality of flow and equipotential lines dz dx h x h z EP = - / / dx dz h x h z FL = ∂ ∂ ∂ ∂ On an equipotential On a flow line Flow line (FL) Equipotential (EP)

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Orthogonality of flow and equipotential lines dz dx h x h z EP = - / / dx dz h x h z FL = ∂ ∂ ∂ ∂ On an equipotential On a flow line Hence dx dz dx dz FL EP × =- 1 (3) Flow line (FL) Equipotential (EP)
Q X y z t T Y Z X FL FL Geometric properties of flow nets Q h h+ h h+2 h EP

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Q X y z t T Y Z X FL FL v Q yx = (4a) From the definition of flow Geometric properties of flow nets Q h h+ h h+2 h EP
Q X y z t T Y Z X FL FL v Q yx = v k h zt =

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