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Hydrogeology : Chapter 5

Hydrogeology : Chapter 5. *This presentation was prepared using different sources and web sites. Chapter 5: Principles of groundwater flow. Introduction. Groundwater possesses energy in mechanical, thermal, and chemical forms.

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Hydrogeology : Chapter 5

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  1. Hydrogeology: Chapter 5 *This presentation was prepared using different sources and web sites.

  2. Chapter 5: Principles of groundwater flow

  3. Introduction • Groundwater possesses energy in mechanical, thermal, and chemical forms. • The amount of energy vary spatially, groundwater is forced to move from one region to another region in order to eliminate these energy differentials. • The flow of groundwater is controlled by laws of physics and thermodynamics. • Three forces act on groundwater: gravity, external pressure, molecular attraction. • Forces resisting the fluid movement: shear stresses, normal stresses. (viscosity).

  4. Bernoulli Equation Kinetic Energy Work Pressure

  5. Hydraulic Head • Piezometer is used to measure the total energy of the fluid flowing through a pipe packed with sand. • Total energy per unit mass: • The hydraulic head (ignore velocity): • Pressure equal: Piezometer measuring fluid pressure and the elevation of water Total head, h, elevation head, z, and pressure head, hp.

  6. Head in Water of Variable Density Definition of point-water head and fresh-water head.

  7. Head in Water of Variable Density Point-water heads for a system of three aquifers, each containing water with a different density.

  8. Force Potential and Hydraulic Head kinetic Potential • The total potential energy (Force potentialF) equal to: = h • The force potential is the driving force for groundwater flow. • The total head h controls the groundwater flow.

  9. Force Potential and Hydraulic Head • The fluid is moving from a region of low pressure to one of higher pressure. • Neither elevation head nor pressure head alone controls groundwater motion. • The total hydraulic is the controlling force in groundwater flow. • Smaller the opening, the greater friction and the lower hydraulic head. • With movement of water, the mechanical energy is transformed to thermal energy.

  10. Darcy’s Law • Flow is proportional to the decrease in hydraulic head divided by the length of the pipe. The ratio is called hydraulic gradient. • Fluid potential F is equal to gh. Hydraulic gradient

  11. The Applicability of Darcy’s Law • Laminar Flow: molecules of water follow smooth lines called streamlines. The velocity of water is small and dominated by viscous forces. • Turbulent Flow: Increase of velocity of water, increase of kinetic energy, the molecules of water move in erratic fashion. • Reynolds number: determine whether the flow will be laminar or turbulent (if R >600): • R is the Reynolds number, q is the discharge velocity, d is the diameter of the passageway through which the fluid moves,mis the viscosity. ris fluid the density. Figure: (A) Flow paths of molecules of water in laminar flow. (B) Flow paths of molecules of water in turbulent flow.

  12. Specific Discharge and Average Linear Velocity • The discharge of water is equal to the product of the velocity v, and the cross-sectional area of flow, A. v is specific discharge (or Darcy flux) and smaller than velocity v in open pipe. vx: Average linear velocity (average water flow velocity) ne is effective porosity

  13. Specific Discharge and Average Linear Velocity • All presented equations don’t take into account dispersion in flowing groundwater. Dispersion is the phenomenon that results because groundwater flows through different pores, at different rates, and various flow paths differ in length. • Also these equation don’t take into account the diffusion, where water moves from a greater concentration to lesser concentration.

  14. Equations of Groundwater Flow • The law of fluids through porous media is governed by the laws of physics. • The law is described by differential equations. • The spatial coordinates, x, y, z and time t are the independent variables. • During derivation of the equation of groundwater flow, the law of mass conservation (or first law of thermodynamics) is used.

  15. Gradient of Hydraulic Head • s is the distance measured parallel to grad h. • grad h has a direction perpendicular to the equipotential surfaces (from lower values of head toward the higher values of head) 2D flow 3D flow

  16. End of chapter 5

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