Part-IV-Flow

Part-IV-Flow - PART IV A GROUNDWATER FLOW(1D FUNDAMENTALS...

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1 Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 1 PART IV - A GROUNDWATER FLOW (1D) ± FUNDAMENTALS ² CONSERVATION OF MASS ² BERNOULLI’S EQUATION ² TOTAL AND PIEZOMETRIC HEAD ² HYDRAULIC GRADIENT ± DARCY’S LAW ± HYDRAULIC CONDUCTIVITY ± SEEPAGE VELOCITY ± CALCULATION OF HEADS ± LABORATORY MEASUREMENT OF k ² CONSTANT HEAD TEST ² FALLING HEAD TEST ± STRATIFIED SOILS ² EXAMPLE Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 2 ± FUNDAMENTALS ² Flow in soil: STEADY, INCOMPRESSIBLE and for today 1D All fluid parameters (p, T, v, etc.) are constant in any cross section perpendicular to the direction of flow * . Density changes are negligible ( ρ w , γ w = constant) At any point conditions do not vary with time. GROUNDWATER FLOW THROUGH SOILS
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2 Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 3 ± CONSERVATION OF MASS v = discharge velocity A= cross sectional area q = flow rate FUNDAMENTALS A 1 A 2 v 1 v 2 q 1 = v 1 A 1 q 2 = v 2 A 2 q = v 1 A 1 = v 2 A 2 = constant (continuity equation) For INCOMPRESSIBLE FLOW Conservation of MASS: [L/T] [L 2 ] [L 3 /T] Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 4 ENERGY = KINETIC + POTENTIAL Relates pressure, velocity and elevation between any two points in the flow field. Expresses principle of CONSERVATION OF ENERGY FUNDAMENTALS ± BERNOULLI’ EQUATION Elevation Velocity Pressure v 2 /2g + p/ γ w + z = TOTAL ENERGY PER UNIT WEIGHT (or HEAD) Datum z p/ γ w v 2 /2g In the case of a perfect, incompressible fluid in steady flow, TOTAL HEAD IS CONSTANT v 1 2 /2g + p 1 / γ w + z 1 = v 2 2 /2g + p 2 / γ w + z 2 h
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3 Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 5 TOTAL HEAD LOSS between 1 and 2 • In porous media there are ENERGY (or HEAD) losses associated with the fluid flow. FUNDAMENTALS v 1 2 /2g + p 1 / γ w + z 1 = v 2 2 /2g + p 2 / γ w + z 2 + h Expresses work spent to win resistance to flow • In flow through soils velocities are in general very small and thus yield a small contribution to the total head e.g. a high velocity such as 2 ft/min gives a velocity head of 0.00002 ft …. . far less than the accuracy with which we can measure pressure or elevation head 1 2 ± TOTAL HEAD AND FLOW THROUGH SOILS h = p 1 / γ w + z = h p + h e Prof. M. Santagata CE 383 GROUNDWATER FLOW SLIDE 6 FUNDAMENTALS h = h 1 –h 2 HAS TO BE >0 h 1 = p 1 / γ w + z 1 1 2 h 2 = p 2 / γ w + z 2 1 2 Datum z 1 z 2 p 1 / γ w p 2 / γ w h 1 = h 2 p/ γ w z h • TOTAL HEAD DETERMINES THE MOVEMENT OF FLUID THROUGH SOILS
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This note was uploaded on 02/27/2011 for the course CE 383 taught by Professor Marika during the Spring '07 term at Purdue.

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Part-IV-Flow - PART IV A GROUNDWATER FLOW(1D FUNDAMENTALS...

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