sma06 - Flow Nets Flow through a Dam Drainage blanket...

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Unformatted text preview: Flow Nets Flow through a Dam Drainage blanket Phreatic line Unsaturated Soil Flow of water ∂ ∂ ∂ ∂ 2 2 2 2 h x h z + = z x Graphical representation of solution 1. Equipotentials Lines of constant head, h(x,z) Equipotential (EP) 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) h(x,z) = constant (1a) ∂ ∂ ∂ ∂ h x dx h z dz + = Thus: (1b) Properties of Equipotentials Flow line (FL) Equipotential (EP) h(x,z) = constant (1a) ∂ ∂ ∂ ∂ h x dx h z dz + = Thus: (1b) Equipotenial slope dz dx h x h z EP = - ∂ ∂ ∂ ∂ / / (1c) Properties of Equipotentials Flow line (FL) Equipotential (EP) ∆ 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) ∆ 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) 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 ∆ 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 ∆...
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This note was uploaded on 08/30/2011 for the course CIVL 2410 taught by Professor Dairey during the Three '11 term at University of Sydney.

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sma06 - Flow Nets Flow through a Dam Drainage blanket...

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