Apple #461: Shower Curtain Blow-In

Regular reader Jason went traveling recently and stayed in a few hotels.  In one of them, he experienced that annoying habit of a shower curtain liner to billow inward while the shower is running.  It blew in so much it clung to him.

I have had this happen to me, too. I've noticed it is more likely to happen if the shower curtain liner is especially light-weight and cheap.  It can be most annoyingly clingy and unpleasant, especially if you begin to wonder how many other people showering in this hotel bathroom have been stuck to this same shower curtain.


This curtain looks especially prone to billowing in.
(Photo from apartment therapy)


Regular reader Jason wanted to know why this happens, first of all because it seems to contradict what you would expect.  You would think that the water streaming out of the shower head and beating against the curtain would push the curtain away from you.  But what happens is the opposite.  "I would be interested to know," he said, "the physics behind that."

He also wanted to know why this happens so that the next time he's in a hotel room with an incorrigible shower curtain liner, he could maybe do something about it.

• As it turns out, regular reader Jason is not the only person to have been interested in the physics behind this question.

• For a long time, people have floated different theories about why this happens.  I'll list them briefly so that those of you with bar bets on this topic can settle them quickly.

• The most obvious and most-often suggested theory is basically the buoyancy theory.  Air heated by the hot water rises, allowing cooler air to rush in below, thus pushing the shower curtain liner inward.  However, when you turn on the same shower with the same curtain using cold water instead of hot, the curtain still blows inward, which means this theory also blows.

• A fancier theory proposed was that the principle is the same as that which enables airplanes to fly:  Bernoulli's principle.  In the case of airplanes, as air rushing over the top of the airplane wing speeds up, the air pressure above the wing drops in a direction perpendicular to the rushing flow of air.  The drop in air pressure is what "lifts" the wing of the airplane up.

Diagram of how the Bernoulli principle works.
(Diagram from Ted Ewert on Energetic Forum)

• Inside the shower, people said, instead of air rushing over the top of the airplane wing, it's the water spray traveling quickly toward the shower curtain.  When you turn the shower on, the velocity of the water traveling through the air makes the air pressure around it drop, thus sucking in the curtain liner.  The problem with applying that principle to this system, though, is that it doesn't account for the presence of water droplets, which act in ways very different than straight-up fluid.  And when one physicist did the math associated with this principle, it didn't result in the shower curtain's movement.  So that theory was discarded.

• A third theory said that the shower curtain moves inward because of what's called the Coanda effect. This effect says that when moving air or water hits a convex surface, the two will hug each other remarkably tightly and for a much longer time than you'd expect.  

A good demonstration of the Coanda effect in action.
(Image from The Worlds of David Darling)

• According to this theory, it's not air currents rushing in that blow the shower curtain in but the tendency of the curtain to stay attached to the water as it falls. Exactly how the curtain liner is consistently convex was not thoroughly explained, and the actual motion didn't seem to fit what this principle said would happen, but people bought it for a while because the principle had a fancy name and it was a rather imposing physicist who first suggested it.  But it turns out this theory is all wet, too.

• Finally a professor named David Schmidt at University of Massachusetts-Amherst did some pretty extensive research into this question.  He designed a computer simulation of a running shower with a shower curtain in a bathtub in a bathroom.  He divided up the model bathroom into 50,000 observable cells.  He let the simulated shower run at a fairly typical eight gallons a minute for 30 seconds.  

• As far as I understand it, he ran some other software made by Fluent Inc. that uses computational fluid dynamics to analyze what happened during that simulation.  The software looked at the droplets breaking up on surfaces, how the droplets were distorted upon impact, and the aerodynamic drag involved with each droplet.  It took 1.5 trillion calculations over the course of two weeks, but then he got the answer.

This is Dr. David P. Schmidt, who spent his Christmas break working to dispel the shower curtain mystery for us all.
(Photo from Dr. Schmidt's page at U Mass Amherst)

• It turns out that Bernoulli's principle is, in fact at work, but the reason Schmidt's calculations with it didn't turn out right initially is because it's happening in conjunction with another principle. That second principle is known as a shear-driven cavity. 

• The shear-driven cavity is a situation when a fluid is moving inside a container with three fixed walls and one moving wall.  In this case, the moving wall is the shower curtain.  I haven't found a very good explanation of how the driven cavity thing works, so let me know if I haven't explained this right. As I understand it, while the water is continually running, the droplets are also slowing down as they travel because of aerodynamic drag.  Supposedly, these two forces happening in equal and opposite directions (water flowing in one direction, being slowed in another) is what gets the air in the cavity that is your shower moving and which, in turn, moves the shower curtain.

• When we combine these two principles together, effectively, the spray of the water in the cavity with the moving wall creates a vortex.  Like the center of a hurricane or a tornado, the center of the vortex is a low pressure column.  It is this column of low pressure in the center of the vortex that pulls the shower curtain inward.  Once the water is turned off, the thing creating the low pressure column stops, and the shower curtain will hang normally again.

• (I think it's pretty cool, by the way, that there's a mini-hurricane in my shower.)

Actually, Schmidt said the water vortex is the shower is most like a dust devil, which are whirlwinds smaller than tornadoes and which can be tilted.
(Diagram of dust devils from WeatherQuestions.com)

• The low pressure in the center of the shower water vortex is a very weak force, though, which explains why curtain blow doesn't happen in every shower all the time.  Lighter weight shower curtain liners are more easily moved by the low pressure column. 

• So the solution is simple: find a way to make the shower curtain weigh more than the force of the low pressure column.  You can do this in a number of ways.

• Get a thicker or heavier shower curtain liner.

• Get a shower curtain liner with weights affixed to the bottom.

Most curtain liners are sold now with weights or, as in this photo, magnets at the bottom.
(Photo from Craft Awl)

• Reduce the water pressure coming out of the the shower head.

• Curved shower curtain rods which hold the curtain farther away from the vortex -- and from you -- are another solution.  Even if blow-in does happen, they usually keep the shower curtain liner far enough away that it won't touch you. Many of the fancier hotel chains like Hilton and Westin have installed these curved shower rods for exactly this reason.

Curved shower rod, some hotels' answer to curtain blow.  You can buy one just like the ones installed in Westin hotel bathrooms for $40.
(Photo from bookofjoe)

• If you're in a hotel room and don't want to buy a new curtain liner, to say nothing of a new shower rod, you can try these other tactics:

• Set your shampoo bottles and suchlike on or against the hem of the curtain liner to weigh it down.  

• Wet the backside of the bottom of the curtain liner so it will stick to the side of the tub.

• Turn down the force of the water spray.

By the way, if you want to see the vortex at work, hang a thin shower curtain liner and turn on your shower.  Doesn't matter if you use hot or cold water.  Now blow in some smoke (where you get the smoke is up to you).  You'll see the smoke take on that vortex shape.

Sources
The Straight Dope, Why does the shower curtain blow in despite the water pushing it out (revisited)? August 10, 2011
David Schmidt, "Why does the shower curtain move toward the water?" Scientific American, July 11, 2001
Kate Melville, Mystery Of The Shower Curtain Solved, Science-a-Go-Go, July 13, 2001
Ron Lieber, Innovations Eliminate Sticky Shower Curtains, The Wall Street Journal Online, October 11, 2004
bookofjoe, Shower curtain 'blow-in,' October 10, 2004
WiseGeek, What is the Coanda Effect?
CFD Online, Lid-driven cavity problem