Flow line vs equipotential line

[tzx9633]

Homework Statement

It's stated in the notes that line fg is the flow line . Why is it so ?

Homework Equations

The Attempt at a Solution

I think it's wrong . The flow line is defined as a line along which the water paticle travel from upstream to downstream in the permeable medium .

However , in my textbook , it's stated that the water can move only thru the flow net , not in one direction only . So , how could the line fg be the flow line ? How could water flow thru line fg ( horizontally in one direction only) ? [/B]

 

[NascentOxygen]

This isn't my usual area, but I think I follow it.

The solid curves represent flow lines, and as you look deeper below the wall the roughly-circular curves become of greater radius. In the limit, at the fartherest depth, the radius is going to be one of roughly infinite radius, i.e., a straight line.

If you trace the path of a particle of water starting near f (i.e., just above the impervious layer), it will travel directly across to g, hence tracing out its flow line. It can't go deeper (the layer under it is impervious), and it won't rise higher (that would mean going against the flow of water coming from the upper regions), so it is constrained to traveling horizontally from near f over to near g.

A flow net is the 3-D concept they introduce for cases where a 2-D approximation is inadequate. Imagine a permeable medium containing a huge buried basalt boulder—flow around this obstruction will be directed left/right as well as up/down—in a complicated 3-D pattern. There will still be flowlines, but now they'll be in a complicated 3 dimensional non-intersecting pattern.

 

[NFuller]

The equipotential lines are perpendicular to the impervious boundary at ##\overline{fg}##, so they point straight up. The flow is always the the direction of decreasing potential. In this case, that would mean the flow is in the horizontal direction at the boundary.

 

[tzx9633]

The equipotential lines are perpendicular to the impervious boundary at ##\overline{fg}##, so they point straight up. The flow is always the the direction of decreasing potential. In this case, that would mean the flow is in the horizontal direction at the boundary.

Why ? Why when the flow is horizontal , the potential is decreasing ?

 

[NascentOxygen]

Why ? Why when the flow is horizontal , the potential is decreasing ?

That's why the water moves, it's going from a higher potential to a lower. To the left of the wall the pressure from the dam water overhead is greater, forcing water to migrate to where there's less pressure, from the left to the right.

 

[tzx9633]

it will travel directly across to g, hence tracing out its flow line. It can't go deeper (the layer under it is impervious), and it won't rise higher

thanks for the point