Laminar Fountains – What are they?

My first working laminar fountain

My first working laminar fountain

Water water everywhere! There are no two ways about it, water fountains are just plain fun. Show a water fountain to any five year old and just see if they don’t start playing and giggling. Which leads me to this conclusion: I never grew up because I still get a ridiculous grin on my face when I get to play in a water fountain. And the coolest of all the fountains in my opinion is the laminar fountain. I built a laminar fountain a few years back and am now working on designs for a 3D Printed laminar fountain which I will post online once I get a semi-working alpha version. In preparation for all that let me explain a little about what laminar flow and fountains are.

What is laminar flow?
The simplest way to explain laminar is probably to say that it is the opposite of turbulent flow. Turbulent flow is the most common type of flow you will see in nature. A drinking fountain is a good example of turbulent flow with how blobby and wiggly the water is when it comes out. White water rapids in a river would be an extreme case of turbulent flow. So in contrast, laminar flow is super smooth flowing liquid or gas. The full reality of laminar flow is that it means all of the water particles are flowing exactly parallel to each other, in the same direction, and as such are not bumping in to one another.

Laminar flow profile showing the velocity of water as it moves through a pipe. (Taken from wikipedia)

Laminar flow profile showing the velocity of water as it moves through a pipe. (Taken from wikipedia)

Laminar Stream

Real world picture of a laminar water stream after it exits my laminar fountain. Because the water is all flowing in the same direction it stays perfectly together and creates a glass rod effect where light can pass right through.

So why it cool?
Because it’s science! But also because it has some really cool application properties we can make use of:

1) Its moving… buts it doesn’t look like it
Because a laminar stream is perfectly smooth the flow path will stay in exactly the same place at all times. A traditional fountain will wobble and sputter as it pumps water out which makes it very obvious that the water is moving since you can follow the individual water blobs as they pass through the air. A laminar stream is perfectly uniform and does not waver which means there are now individual water droplets to follow with your eyes. The water is flowing quickly but its hard to tell. It literally looks like a perfect glass arch coming from the fountain going all the way to where it hits lands. (See the picture above)

2) No splash
Because the water stream is so smooth it will not break apart when it encounters another body of water or smooth object. If it lands in a pool of water it will disappear without a trace. If you put a smooth ball in its way it will spread out and wrap around the ball without splashing. Its a really cool effect and also has the benefit of making it quiet too!

3) It Jumps
Because the flow stream is so smooth it has a nifty visual effect when you suddenly block the stream. It looks like the stream is “jumping”. The water that is not blocked continues to fly through the air on the original path and stays together. You get little water snakes that that fly through the air. If you string multiple fountains together you can create the illusion that water is jumping from one fountain to the next.

4) It transmits light like a fiber optic cable
A fiber optic cable is a perfectly smooth medium that transmits light from one end to the other. The perfectly smooth sides of the cable reflect the light inside back in to the cable to keep it bouncing down the length until it reaches the other end. A laminar stream also has super smooth sides and therefore will also bounce light back inside of itself. This means that if you shine a bright enough light directly in to the laminar stream it will light up all the way from end to end! Even around the curve!

Here is a cool video that shows the laminar fountain forum user MagicNozzle posted of his home made fountain that demonstrates several of these properties (feel free to skip ahead, the night shots at the end are especially cool). Original forum post HERE

Laminar Maths:
If you’re in to math and the equations that govern when a stream is laminar than this is the section for you. I find it super cool how this works so lets dig in!

In an engineering fluid dynamics class (study of moving liquids, a really fun course) you learn about the Reynolds number which will tell you if a fluid’s flow is laminar, transitional, or turbulent. Here is the equation from Wikipedia:

AHHHHHH!!!1!1!! Maths! *Deep Breath* This equation is actually super simple so hold on and keep reading.

AHHHHHH!!!1!1!! Maths! *Deep Breath* This equation is actually super simple so hold on and keep reading.

Hold on, we’ll kick that scary equation in the teeth. Lets start by focusing on the first variation of the equation listed.

Re = (p*v*D)/u

Two of those are actually constants. p is the density of water which we can google (1000Kg / m^3) and u is the dynamic viscosity of our fluid (water is 0.000404 at room temperature). So putting those back in and simplifying we get this:

Re = (2.475×10^6)*v*D

That’s not so bad. v is the velocity of our fluid in the pipe in meters per second and D is the internal diameter of our pipe in meters which should be pretty easy to calculate. Once we have our Reynold’s Number (Re) we can see if the flow will be laminar. An Re value below 2300 means that the flow is Laminar. An Re value between 2300 and 4000 is Transitional and an Re value above 4000 is Turbulent. All this means that we need to adjust our water velocity and pipe diameter to get an Re below 2300 for our fountain. That’s all the math!

How the math works in real life:
So now that we have the math (or trust me if you didn’t read it) we can interpret it. This is what it all boils down to in real life:

The faster the velocity of the fluid and the bigger the pipe, the more turbulent the flow will be.

Or inversely:

The slower the fluid and the smaller the pipe the more laminar the flow will be.

So to put this in to the real world lets tackle one problem at a time and start with velocity. We need a certain minimum amount of volume flow to achieve the fountain size we want. For instance, the pump I used in the pictures above is rated at 500 gph (gallons per hour) which gave me the nice big water arch you see. The problem shows up now in that the velocity is found by dividing the flow rate by the cross sectional area of the pipe which is a function of pipe diameter as well! So we need a bigger diameter to slow the velocity down but a smaller diameter to get a low reynolds number…… Crap.

But what if I told you we could have a separate diameter to use for velocity and the diameter in the Reynold’s equation? The trick is to take a large pipe (8 inch PVC here) and pack it full of small pipes (drinking straws). This way you get to use the large diameter of the PVC  for the velocity part and the small individual diameters of the drinking straws for the Reynold’s diameter. Bingo! We can now achieve laminar flow!

Inside my laminar fountain are nearly 2000 drinking straws to give a small diameter to the water flowing through while keep the slow velocity of a big 8 inch outer pipe.

Inside my laminar fountain are nearly 2000 drinking straws to give a small diameter to the water flowing through while keep the slow velocity of a big 8 inch outer pipe.

Theory crafting complete!
That’s it for the what a laminar fountain is. Stay tuned for some more posts talking about my first laminar fountain and how I am hoping to use my 3D Printer to start a new cycle of designs!

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Lego PF Hacking – Wiring the Arduino

PowerFunctions_Logo

Lego Power Functions Hacking Guide –  Part 4 – Wiring the Arduino
Part 1 – Introduction
Part 2 – Equipment
Part 3 – Wire Hacking
Part 4 – Wiring the Arduino
Part 5 – Programming (coming soon)

The saga continues! Bust out the breadboard because its time to make use of those Power Functions wires we just defiled with our wire cutters.

Breadboard Schematic

Breadboard layout for connecting our lego motor and battery box

Breadboard layout for connecting our lego motor and Arduino to our motor driver

The above picture shows roughly what our breadboard will look like after we connect our Arduino and Lego parts to our DRV8833 motor driver. I included the reference schematic from Pololu in the upper right hand corner so you can see which pins we are connecting too. If you missed the link from the equipment post you can find the Pololu product page HERE

Layout Description and Explanation
I’ll provide a quick overview before I move on to a detailed list of our connections. The central focus of our circuit is the DRV8833 motor driver in the middle of the breadboard. It is what converts our low power signals from the Arduino to the high power outputs that a motor needs to run. Two lines are used from the Arduino to drive the motor (essentially one for each direction) and the Lego motor is tied to the corresponding motor output. The Arduino power is used for the logic side of the driver and the lego battery box is used to power the motor side.

Detailed Connection List:
1) Arduino Power
The 5V and Gnd from the Arduino are wired to the upper power rails of the bread board. This power rail is now the “Logic Power” for our circuit. Logic ground is tied in to the motor driver ground pin. (When two separate power supplies are used, as is often the case with motor applications, the grounds of the power supplies need to be tied together for them to interact. The motor driver does this for us)

2) Arduino Control Signals
To drive a motor you need two control signals. Each control signal ties to one of the motor wires (C1 and C2 in our case). For our control signal connections we need Arduino pins that are capable of PWM output so we can control motor speed. For this circuit I chose pins 6 and 9, both are PWM enabled. These lines will tie in to our AIN1 and AIN2 pins on the motor driver. (The motor driver can control two motors, we’re only using one so we will use the ‘A’ pins)

3) Motor Power
Motors require a higher amount of power than control circuits can handle so its good to use a separate motor power supply to drive them. In our case we are going to use the standard lego battery box and one of our hacked Power Functions wires we made in the previous PF Hacking post. Attach the Lego block end to the battery box. The hacked end we will connect to the breadboards lower power rail. Tie the 9V line to the red rail and the Gnd line to the black rail. The C1 and C2 wires are not used and can be taped off with electrical tape. BE CAREFUL THAT C1 and C2 DO NOT TOUCH. They will short out if power is turned on and they are touching. This is why either electrical tape or simply cutting them off is important. (PHOTO COMING SOON)

4) Lego Motor
Time to use that last hacked wire. Attach the lego block end of the wire to the lego block connector of your motor. At the other end, attach wire C1 to AOUT1 on the driver and wire C2 to AOUT2. Use electrical tape on the unwired 9V and Gnd lines from our hacked cable.
(PHOTO COMING SOON)

5) Capacitors (optional)
With motor applications its always helpful to add capacitors to the the power rails to help protect against spikes and dips that can occur when a motor is first started. Standard 10uF capacitors work great. These are optional but helpful and recommended.

Putting it all together

When you are done you should have something that looks a lot like the picture below. Once that is done its time to move on to the final steps of programming our Arduino! Stay tuned for the final post in the Lego Power Functions Hacking series where we get it all running and moving!

(Photo and Video of final circuit coming soon)

3D Printer – It lives!

Mini Kossel printing a trilobite head

Mini Kossel printing a trilobite head

The 3D Printer is up, running, and calibrated! My wife and I have been having a blast with it so far and its been running non-stop the last two weekends. Its been quite a learning experience figuring out how to calibrate it precisely. Delta style printers like the Mini Kossel are really robust and fast but due to the trigonometry required to converted x,y,z coordinates to tower movements the calibration can be a bit tricky. There is a fantastic blog post HERE that walks you through step by step how to calibrate your printer.

Now for a little show and tell. Here are a few of the things we’ve been able to print so far and a video showing the printer at work!

A few of the things we've printed

A few of the things we’ve printed

More to come as we keep printing and learning about building our own 3D Models!