This preview shows pages 1–15. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ∆...
View
Full
Document
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.
 Three '11
 DAirey

Click to edit the document details