You know I like to point out where you can spot hydrodynamics concepts in your everyday lives (at least if your everyday lives include strolls along rivers and generally a lot of water)
A while back we went to Geesthacht. We were hoping for more ice on the Elbe river, but sadly there was none. But! In Geesthacht they have a weir, combined with locks. They keep water back to bring the level of the Elbe upstream of Geesthacht up to 4 m above sea level for shipping purposes. But then they obviously need a lock to get ships up and down this sill. But the coolest thing is the weir:
Do you see the three different states the fluid in the picture above is in?
Looking from right to left (i.e. with the direction of the flow), we first see normal flowing water. You can see that there are waves and ripples going in all directions. Then, the middle part of the picture, all disturbances on the water surface are clearly oriented right-to-left. That is because here the water is shooting (meaning flowing faster than waves can propagate), and all disturbances get deformed by the flow rather than spread by themselves. And then on the very left, we have a submerged hydraulic jump (which we cannot see, because, as the name says, it is submerged) and above massively turbulent water.
Weir on Elbe river near Geesthacht
I just love the look of it!
Watch the video below to see the whole thing in motion.
Looking at a creek on a Sunday stroll, and seeing lots and lots of concepts from hydrodynamics class.
For example below, you see waves radiating from each of the ducks. And you see interference of waves from all those ducks.
What happens if the ducks bring their waves closer?
At some point, all those waves from the ducks are going to hit the weir in the picture below.
And there, they are going to somehow react to the flow field caused by the changes in topography.
And you can spot so many different phenomena: Standing waves, hydraulic jumps, and lots more!
Watch the movie below to see the whole thing even better!
Btw, you might remember this spot, I have talked about standing waves from right there before. Interestingly, the wave pattern in the other post looks really different, probably due to different water levels or changes in topography (maybe someone threw in rocks or they did some construction work on the weir?). But it is still just as fascinating as last time :-)
And for those of you who like to see a “making of”:
Hydraulic jumps, especially submerged ones, are a very theoretical concept for many students, one that occurs in a lab experiment if they are lucky, but more likely only seems to exists in videos, drawings, and text books. But we can observe them all the time if we know what we are looking for! They don’t only occur in hard-to-see places like the Denmark Strait (for you oceanographers) or inside some big plant, mixing in one chemical or another (for you engineers), they are everywhere!
So. Submerged hydraulic jumps. You don’t think about them for years and years, then one day a friend (Hi, Sindre!) asks about them and the next day you come across this:
A tiny waterfall in Schleswig
A tiny waterfall that not only shows a beautiful submerged hydraulic jump, but provides extra entertainment in the form of two empty bottles caught up in the return flow above the submerged hydraulic jump:
Litter caught up in the return flow above a submerged hydraulic jump
You should watch the video, it is really entertaining!
So what is going on here? Below a sketch: Water from the reservoir (A) flows down over a sill. It actually doesn’t flow, but it shoots (B), meaning that it flows faster than waves can propagate. Any wave in the flow that would normally propagate in all directions now cannot propagate upstream any more and is just flushed downstream. At (C), the flow has slowed down enough again that wave speed is the same as flow speed, we are at the hydraulic jump. In this case it is submerged – meaning that it occurs below the water’s surface. We can also think of non-submerged hydraulic jumps – see for example here. But what also happens with submerged hydraulic jumps is that the water jet shooting down the slope is so fast that it entrains water from outside the jet and pulls it down with it. This water has to come from somewhere, so we get a return flow (D). And this is exactly where the bottles are caught: In the flow that goes back towards the jet shooting down the slope.
Sketch of the submerged hydraulic jump. A: reservoir. B: water shooting down the slope. C: hydraulic jump. D: turbulent return flow.
When the bottles come too close to the jet, they get pulled under water and then “jump” because they are too buoyant to actually sink. They might jump away a little from the jet, but as you see in the movie, the return flow reaches out quite a bit from where the jet enters the water, trapping the bottles.
This is actually what makes man-made waterfalls so dangerous: You saw in the movie that the return flow pattern is very similar over the whole width of the “waterfall”. So anything trapped in there will have a really hard time getting out. If either the sill or the slope were a little more irregular, it might break up the symmetry and allow things (and animals or people) to get out more easily. Of course, in this case the drop isn’t very high, but imagine a larger weir. Not fun to get caught in the return flow there!
Talking to my Norwegian friends about these things and especially using movies from my reality to illustrate concepts always makes me want to apologize for how tiny our waterfalls are, how in the middle of a city everything is, how much litter there is everywhere, how regulated even the tiniest streams around here are. But then I realize that it is actually really cool that even in the middle of the city we can spot all this. You don’t need the wide open, pristine nature to get yourself – and your students! – excited about oceanographic phenomena!
Last week I went to beautiful Lüneburg with a group of climate scientists to continue working on a very exciting project I’ve been involved in over the last year or so (see “scales in the climate system” funded by CliSAP here). I so enjoyed being with a group of people who talk about converging solutions of discretized differential equations over dinner! I have really spent way too little time with people like that ever since I left oceanographic research and went for instructional design. So it was great to discover that I haven’t lost that side of my life but that I can still happily talk about climate models and eddy covariance measurements!
Waterfalls in Lüneburg
But the “continuity” in the title of this post is actually referring to something else which I saw during a break we took. In the picture above you see the river going through Lüneburg, which is clearly going downhill, just like every good river should. You also see a couple of fronts, so clearly something is going on there. Watch:
I find it super fascinating. Where does the water that comes down the wide waterfall go to if the sea grass (hey, I’m not a biologist! You know, the green stuff in the river!) is going towards the waterfall, too? Is there a vertical circulation involved? But then where does the water actually sink? Yet it doesn’t really look like it could all go in the current along the front. What is going on there?
Isn’t it weird how I always look for continuity? :-)
Another neat experiment in the collection I’ve recently been talking about is measuring pressure at different points on a wing profile. It’s not terribly surprising that – as long as the wing is oriented in the correct way in the flow – pressure is high below the wing and low above it. Kinda the whole point of having a wing profile. Yet, it’s nice to actually measure it.
Measuring pressure at different points on a wing profile
And yes – next time I set up that manometer I’m gonna make sure that it’s a little easier to get a good reading!
Another one of those awesome hydrodynamics toys: A Pitot tube!
This is what it looks like:
Pitot tube. The tip pointing downward in this picture would point right into the flow.
What you can’t see here is the little hole at the tip of the tube that is pointing downwards in the picture. What the Pitot tube measures is the pressure difference between that hole (the stagnation pressure since it’s the stagnation point) and the vents some 3.5 cm above (the static pressure), from which you can calculate the dynamic pressure, hence air speed of a plane (if the Pitot tube was mounted on said plane) or, in our case, the speed of air flow from a fan relative to a stationary Pitot tube.
Again, I’m sadly too lazy to calculate anything, but you can take the measurements from the movie below and do it yourself if you so desire! :-)
On Monday I posted about playing with Venturi tubes. Guess what: We are going to play more today! Because today the Venturi tubes are connected to a “proper” manometer:
Venturi tube connected to manometer
Now, if I wasn’t so lazy this would be a great opportunity to get good readings of the pressure differences caused by different flow rates. However, I’ll just let the images speak for themselves. Enjoy!
A Venturi tube is one of the things one hears about in hydrodynamics class all the time, but one never gets to see them for real. And even though I just said on Friday that the thing that I found most fascinating in the aerodynamics collection I got to borrow recently was to see how the flow reversed downstream of a paddle I might have to take that back, because the hands-down most exciting thing was to play with a Venturi tube!
So what is all the fuss about? This is what a Venturi tube looks like:
Venturi tube in the no-flow state
Basically, it is a tube, open at both ends, that gets thinner in the middle and wider again. All the rest you see in the picture is props: The mouth of the fan in the top right, and then three U-tubes filled with dyed water below the Venturi tube.
The Venturi tube is so famous because it nicely demonstrates the Venturi effect, namely the reduction in pressure that occurs when a flow is accelerated. In the case of the Venturi tube, the flow is accelerated in the thin section of the tube, where – for continuity reasons – it has to go faster than in the wider sections. So what happens when we turn on the fan?
Venturi tube. Pressure decreases in the thin section of the tube, visible by the red water being “sucked up” in the middle U-tube
Yep! The levels in the three U-tubes change. And most importantly, the pressure for the middle U-tube drops, as demonstrated by the red water being “sucked up” on the side of the U-tube that is connected to the Venturi tube.
One of the things that fascinated me most when playing with the huge fan we used to look at the flow downstream of a paddle was how the flow direction reverses.
Unfortunately (alas, it was to be expected) we didn’t really see this on the paper towel stream line test I did the other day.
But here is another way to visualize it: using a propeller!
Propeller in air flow
Depending on the direction the air flows at the propeller, its direction changes. So as we move it towards and away from the paddle, when the flow direction changes, so does the direction of rotation of the propeller, too.