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2019-11-12 16:08:37

It's amazing how much physics fun you can have with basic everyday stuff. Next time you’re watering the yard, stop and look at that simple spinning sprinkler. Watch the jets of water as they shoot out—why do they form those pretty arcing streams? A lot of times, a physicist’s job comes down to figuring out why the world is so beautiful.

Even more fun, once you know how something works, you can run little thought experiments by changing things up. That’s what Destin Sandlin and Steve Mould did on YouTube. Both of these guys have their own (excellent) science channels. But somehow they got to arguing about what would happen if you made a sprinkler that shot water inward, toward the center hub, instead of outward. If you took a snapshot from above, what shape would the water streams assume?

To settle the matter, Steve built just such an outside-in sprinkler, and the two got together on Destin’s Smarter Every Day channel to test it. First, though, to simplify the problem, they tried a different one that Steve had made that shot the water straight outward, away from the hub (i.e., without the angled nozzle these sprinklers usually have to produce rotational thrust).

But even on this one, their predictions were different. Destin said the water would keep moving in the direction of rotation it had when it left the tube—meaning it would go forward as well as out. Steve said it would curve back. What do you think?

Here’s what’s so interesting about this: These guys both have a solid understanding of physics, but they’re talking about two different things. Steve is focusing on the shape of the water stream—a snapshot view—and Destin isn’t quite hearing it. He’s thinking about the movement of individual particles of water. Those are very different questions!

You can watch the video and see what happens (and you should), but there is another option. What if we just model the water as a bunch of tiny balls instead of a continuous stream? Each ball will start with an initial exit velocity that depends on the rotation of the sprinkler and the speed of the water as it comes out of the tube. Then you can look at the motion of many of these water balls to see the aggregate pattern. That's what I'm going to do. It’s true that you don't really understand something until you can model it!

Squirters Pointed Outward

Let's start with the case of the water shot radially outward from the spinning sprinkler. First, we need to recognize that once a water ball leaves the tube, there are no forces acting on it. (OK, there would be gravity, but it doesn’t affect what we’re interested in, so we’ll ignore that.) With zero net force, the ball will travel with constant velocity (same speed and direction).

I’m going to model this in Python, and I’ll use just two squirter tubes to make it easier. Then I just need to pick some values for the speed of the water, the length of the tubes, the rotation rate, and the number of water balls per second. Here’s the model. You can click on the pencil icon to see the code; hit Play to run it.

As you can see, the shape of the stream bends back from the spinning tubes. So Steve was right about that. You can go into the code and try different assumptions to see how things change. What happens if you turn the conceptual faucet handle to increase the water speed?


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