Lecture 14

Lecture 14

Equations of Ground-water Flow

Fetter 5.6

Let us put Darcy’s law in terms of Force and Potential

Express Darcy’s Law in terms of potential

One dimensional form of Darcy’s Law

If flow though an open pipe Channel

		Apply to Darcy’s Law

			Specific Discharge (Darcy Flux)

		This is an Apparent velocity.

		What is not accounted for in a geologic unit?

Area is actually the porosity



	Where n = Effective porosity
		v = Average linear flow velocity

This is the seepage velocity or Average linear flow velocity.

average rate at which water moves between two points in a geologic unit.

For instance

	100	90	80
				K = 0.2ft/d
				n = 0.2



1000 feet between 100 and 80 feet contours

Laplace Equation

governing equation of ground water flow

Assume

(1) Isotropic

(2) Homogeneous

(3) Fluid moving in one direction

Remember

Law of Mass Conservation

-No net change in mass in a small volume of aquifer.

Physics

Law of conservation of energy -

	First Law of Thermodynamics
		Energy can be neither lost nor gained, it can only change forms.

	Second Law
		"there is no such thing as a free lunch"

All used to derive main equations ground-water flow

Control Volume

	q - flow per unit cross sectional area

	P_wq_x - flow perpendicular to x axis

	Therefore, mass flux into control volume = q_xr wdydz along x axis

Total Mass Accumulation

Terms Along 3 axes

Volume water in control = ndxdydz

change in mass of water

Changes in Aquifer and water compress change in head.

Know from Darcy’s Law

Substitute for q in

Get

General equation for flow in three dimensions for isotropic homogeneous, confined aquifer.

	Simplify ® two dimensional, no vertical flow
	know

		T = Kb

		then

Steady-state

	no head change with time
	i.e. water table position does not change with respect to time.

Laplace equation

ENV 302 - Lectures