from The Textbook Letter, July-August 1998

Fun in the Tub

Howard P. Lyon

Over the past few years, a half-page article called "Attack of the Shower Curtain" has been printed again and again in middle-school books published by Prentice Hall. It first appeared in the 1993 version of Motion, Forces, and Energy, one of the books in the Prentice Hall Science series. Since then it has been used in later versions of Motion, Forces, and Energy and in several successive versions of Prentice Hall Exploring Physical Science.

[Editor's note: For a review of Motion, Forces, and Energy, see "What a Display of Ignorance!" in TTL, November-December 1992. For a review of Prentice Hall Exploring Physical Science, see "Educators Should Avoid This Book Like the Plague" in TTL, September-October 1995.]

In the article, Prentice Hall's writers tell the student to imagine that he has just dragged himself out of bed, still sleepy. Then:

With your eyes only half open, you stumble into the shower. Blindly, you reach over and turn on the water. Aaaah! Suddenly your eyes pop open as the shower curtain attacks you. You push it away, but it comes right back. Instinctively, you shut off the water. To your relief, the shower curtain calms back down. You are a little confused. Could you have imagined all this? You turn the water back on and again the shower curtain moves toward you, climbing on your legs and encircling you. What is going on?

Unveiling the "correct" answer is left to the teacher. In both the teacher's edition of Motion, Forces, and Energy and the teacher's edition of Prentice Hall Exploring Physical Science, a pedagogic note alleges that the shower curtain's behavior is a manifestation of Bernoulli's principle. The teacher is supposed to convey that claim to the student, but the claim is false.

Incorrect on All Counts

Bernoulli's principle, named after the Swiss scientist and mathematician Daniel Bernoulli (1700-1782), deals with energy in a moving, incompressible fluid. It is expressed quantitatively by an equation that relates the fluid's pressure, elevation and speed. For beginners, it usually is reduced to the qualitative statement that a moving fluid's pressure decreases as the fluid's speed increases (or, as it is stated in Motion, Forces, and Energy, "The faster a fluid moves, the less pressure it exerts").

In their pedagogic note, Prentice Hall's writers tell the teacher that this concept explains a shower curtain's aggressiveness:

[The "Attack" article] helps students relate Bernoulli's principle about pressure in fluids to a real-life situation. . . . The pressure exerted by the fast-moving fluid (water inside the shower) is less than the pressure in the surrounding fluid (air outside the shower). The greater outside pressure pushes the shower curtain into the shower . . . .

That is incorrect on all counts. Prentice Hall's description of "the real-life situation" is clearly unrealistic, and the behavior of a real shower curtain doesn't comply with Prentice Hall's account. Let me develop these points in turn.

The system in question actually consists of a shower curtain and three masses of fluid -- the shower stream, the air inside the shower enclosure, and the air outside the shower enclosure. The Prentice Hall writers, however, acknowledge only two masses of fluid: a mass of fast-moving "water inside the shower" and a mass of "air outside the shower," separated by the shower curtain. In other words, they claim that the enclosure is filled entirely by moving water, and that the enclosure does not contain any air! This is obviously erroneous, so the "explanation" that the writers provide to the teacher doesn't make sense. Moreover, as we now shall see, the real explanation for the shower curtain's behavior depends directly on the fact that the enclosure does contain air.

Striking Results

In an effort to find out why shower curtains sometimes attack showerees, I observed the action of the curtain that adorns my own bathtub. The curtain had some weights on its lower edge, to keep it hanging straight, but I removed these. Then I got into the tub and ran the shower, many times, while I manipulated a variable that the Prentice Hall writers had not thought of: the temperature of the shower water. The results were striking. When the showerhead was delivering hot water, the lower part of the shower curtain moved inward and assailed me. When the showerhead was delivering warm water, the curtain moved inward again, but less aggressively. And when the showerhead was delivering cold water, the curtain didn't move at all.

I've asked about a dozen of my friends to run trials with their own shower curtains, and they all have confirmed my observations. I'll bet my goose pimples that you, too, will get results like mine if you perform your own experiments.

Clearly, the "Attack of the Shower Curtain" is a response to temperature. When the water falling from the showerhead is hot, it warms the air inside the shower enclosure and induces convection. The warmed air rises, escapes from the enclosure by flowing over the top of the curtain, and is replaced by cooler air that flows into the bottom of the enclosure. As this cooler air enters the enclosure, it pushes the lower margin of the curtain ahead of it, causing the lower part of the curtain to swing inward.

When the water falling from the showerhead is cold, these things don't happen.

Now here's the clincher. Think again about the Prentice Hall writers' claim that the "Attack of the Shower Curtain" is caused by a Bernoullian reduction in the pressure exerted by the "fast-moving fluid" in the showerstream. If that were true, the attack would continue for as long as the shower ran. During my trials, however, I found that -- even when the showerstream was piping hot -- each attack was only transitory. As the hot showerstream continued to run, the inward displacement of the curtain gradually decreased. Then, after ten minutes or so, the attack stopped and the curtain hung straight again.

Such results can't be explained by any appeal to Bernoulli's principle, but they can be explained by thermal effects. After the shower has run for ten minutes, all the air in the bathroom has been heated, and there is little difference between the temperature of the air inside the enclosure and the temperature of the air outside the enclosure. Under these conditions, convection is much milder than it was at the outset, and the flow of air into the bottom of the enclosure is so weak that it doesn't move the curtain.

When I told all this to some scientific acquaintances, one of them replied that similar observations have been published by Albert A. Bartlett in the October 1996 issue of The Physics Teacher. Sure enough! In a one-page article titled "The Curious Case of the Well-Behaved Shower Curtain," Bartlett describes how he experimented with the curtain on a shower stall in a college dormitory. He found that "When the water was cold, the curtain hung vertically downward; when the water was hot the curtain was pulled strongly inward at the bottom."

This latter behavior, he concluded, "was pretty clearly driven by thermal convection and not by Bernoulli."

Howard P. Lyon is a violinist and the father of six daughters. Since 1994, Lyon has been cataloguing some of the erroneous material that has appeared in textbooks published by Prentice Hall. (See " 'Corrective Measures' " in TTL, March-April 1996, page 10.) He also has investigated various claims that Prentice Hall has used in promoting its books. He lives and works in Erie, Pennsylvania.


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