 Yn y gweithio, rydyn ni'n amdano'n gwaith y cael ei gael y cyflog gwaith iawn o'r byn ymdod yn hyn. Yn y cyflog gwaith iawn, yn eu cyflog gwaith cymryd y cefnod yn cael ei gael y byn maen nhw, mae'n gweithio'n gwybod o'r prynsibol i chi'n gael ei wneud oherwydd yng nghylch ar first principles. Yn y bydd ymdod y gwaith, rydyn ni'n gweithio'n gweithio'n gwybod yw mwych. Y flow net yw'r diagram yw'r flow lines, yw lines of water flow, against equipotential lines. Equipotential lines are lines that depict areas in the soil with the same pressure. I'll use red for flow lines in my diagram, and I'll use blue for equipotential lines. A flow net is constructed of both flow lines and equipotential lines. For flow nets to be effective, they need to observe certain rules. The first is that flow lines and equipotential lines must cross at right angles. You can't cross these at any other angle. The second is that flow lines cannot cross other flow lines. That would imply that the water molecules are resistant within the same space. That can't happen. Similarly, equipotential lines can't cross other equipotential lines. If an equipotential line denotes an area of the same pressure, then they can't cross by definition. Impermeable boundaries are always flow lines, so you always get flow around an impermeable boundary. That's another rule. Similarly, water bodies within your system are equipotential lines. Finally, for the maths and flow nets to work, you need to draw curved linear squares. What are curved linear squares? If I have a flow line or two flow lines that I've drawn, and let's say the water is flowing like this, to form a curved linear square, I need to draw my equipotential lines to form a shape that looks like this. My equipotential lines should look something like this, where I can draw a circle within this space. That's a curved linear square. This is probably one of the hardest things to do within a flow net, at least drawing it by hand. It's often where some of the mistakes crop in when you're doing a flow net. The trick to getting this diagram right, or getting a flow net right, is to draw it as big as possible. Use a pencil first, because you never get it right first time. Do multiple iterations to make sure you get as curved linear squares as possible. Those are the rules for a flow net. Let's look at an example of drawing a flow net. To draw a flow net, we need to know some things about the geometry of the system we're looking at. Let's say we have an example that looks like this, where we have an impermeable material, and sitting on top of that material is some sort of permeable material. We know water can flow through this permeable material. Let's say we drive a sheet pile through that material like this, and on one side of the sheet pile we have a high water table, and on the other side we have a low water table. To draw a flow net we need to know what the geometry is here. In this example we have two metres on one side of water and one metre on the other side of water. We have five metres depth of this pile into a ten metre body of permeable material. We know the geometry. From that we can start to construct our flow net. The best place to start with a flow net is to start with the realisation of point two and three, in that impermeable boundaries are flow lines, bodies of water are equipotential lines. We can draw a flow line on the bottom of this profile, because this is an impermeable boundary. That's our first flow line. This sheet pile wall is also an impermeable boundary. We can draw a flow line around here. That means in this situation we have particles of water moving along this boundary and it's part of the water flow. We can draw our first equipotential lines on, so we know that at the base of this water body, well at the top of the water body we have constant water pressure at zero, and at the bottom we also have constant water pressure, so we can draw our first equipotential line here, first two equipotential lines. Now what we want to do now is divide up the rest of this space with flow lines and equipotential lines to be able to draw curvilinear squares. The first step I suggest doing is draw your flow lines in, and the best way of doing that is cutting up this space here between the bottom of the sheet pile wall and the impermeable boundary. There must be some flow lines that exist within here. If you pick too few flow lines, your diagram doesn't really quite work, but if you put too many in you end up getting too small squares and it starts to become a little bit confusing. You need a bit of experience in drawing these to get it right, so do practice and make sure you can do this in a sensible way. I would start maybe at least dividing it up into two. Those flow lines would then depict the water movement through this material, so you could imagine them being drawn in this sort of shape, and they'll have to cross these equipotential lines up here at right angles. We can draw our first or second, so we can draw our next flow lines like this. Those must cross this equipotential line at right angles. You can't have them crossing in this angle because that's wrong, so they must cross at right angles. What you've got to do now is try and cut up this diagram into circumlinear squares. This is when it starts to become a bit iterative, and you'll need to rub things out and put new flow lines in and new equipotential lines in. Let's start up here, so we draw our first circumlinear square, and remember we have to cross at right angles between equipotential line and flow line, so it might look something like this. You can see that there's maybe something wrong with this shape, so what I might want to do is redraw this flow line to bring it in a bit. Let's do that in a second. Let's try and draw a few more of these equipotential lines on, so we can draw another one here. Again, careful to cross at right angles, and we can see that there's maybe something, a problem here with the circumlinear square. That's certainly not right, and then we'll draw another one here. You can see that maybe these look okay, so these look like I've got circumlinear squares in. I can draw circles that fit reasonably into these, but you can see that maybe there's a problem here, so what I might want to do is bring this flow line up into the diagram a bit more. That looks a little bit better. I draw circumlinear, and we draw circles and they look reasonably okay. Let's keep going. You can see that this flow line could possibly be a little bit lower, so I could draw that to a situation like that. With a bit of care and a bit of attention, you can probably do a bit better than what I've done here, but it generally demonstrates the principles where we're trying to form curvilinear squares on a sheet of paper graph. Paper would help a lot in this case. What's the next step? The next step is we count up all of the spaces between the flow lines and the spaces between the equipotential lines. The spaces between the flow lines where we have one here, we have two and we have three. We have three spaces between the flow lines, so nf equals three. We also count up the spaces between the equipotential lines and we have one, two, three, four, five, six, seven. We have an n h of equal to seven. The nf represents the number of flow tubes, that's sometimes how it's referred to, and the nh represents the number of equipotential drops, so this represents a drop in pressure. If we take nf and nh, we can relate it to the flow through this equation, where the flow equals the permeability, multiplied by the h, multiplied by the nf over nh. The permeability we can find through testing this material, so let's say we tested it either in the lab or through a pump test, and it had some sort of permeability, and let's say we knew that to be 10 to the minus six metres per second. We knew the permeability of this material. Our h is the total head drop over the system, so the total pressure difference, which is just the difference between these two heights here. So this is h. So if we know k, the permeability, we know h, the head drop, and we know through the flow net we've got an nf value and an nh value, we can work out what the flow is. So in this situation it would be q equals 10 to the minus six, multiplied by one metre, multiplied by three over seven, which equals roughly around four times 10 to the minus seven metres cubed per second, which equals roughly around 35 litres per year. And that's for every metre of retaining wall, so for every metre in the, I suppose the z direction, in and out of the board here, we have 35 litres of flow per year.