12:166, Zhang

Spring, 2002

Lecture on

Flownets

· Definition

Flowline or Streamline is an imaginary line. It is tangent to the direction of flow at every point on the line.

Flowtube or Streamtube is the area between two flowlines or streamlines.

Equipotential line is the trace of the equipotential surface in a cross section

Flownet is a set of equipotential lines and flowlines

· Assumptions (under that a flownet is drawn)

· The aquifer is homogeneous and isotropic;

(see p.174 of Freeze & Cherry for flownet in an anisortropic aquifer.)

· The aquifer is saturated;

· Flow is in steady-state;

· All boundary conditions are known.

· Rules (you may follow when you draw a flownet)

1. All flowlines are perpendicular to equipotential lines;

2. The “squares” should be “curvilinear” squares;

3. Flow (or equipotential) lines are parallel (or perpendicular) to the no-flow boundary;

4. Flow (or equipotential) lines are perpendicular (or parallel) to the constant head boundary;

5. Flow (or equipotential) lines are parallel (or perpendicular ) to a water table when there is no recharge to the water table; otherwise they will be at an oblique angle to the water table.

· Procedure

Step 1 Define the flow field or domain;

Step 2 Identify the boundary conditions;

Step 3 Identify the positions of known flow and equipotential lines;

Step 4 Decide the total number of flowlines;

Step 5 Draw a trial set of flow lines, starting from the middle of the flow field;

Step 6 Draw a trial set of equipotential lines, starting at one end of the flow field;

Step 7 If necessary, erase and repeat the step 5 and 6.

· Calculation

The discharge through a flowtube (note: w=DL):

The discharge for a system with m flowtubes:

· Tangent law of flowline refraction

Reading: Section 4.11 and 4.12 (p. 132 – 138)

Homework: See the handout. Due on Monday, Feb. 25.