THOSE OF US WHO TAKE showers are often bothered by the shower curtain's habit of moving inward, sometimes to the extent that it interferes with uninhibited lathering, splashing, rinsing and singing. Its motion can be countered in various ways. If the shower is in a bathtub, small magnets along the bottom will hold the curtain to the tub; so will simply wetting the outside of the curtain. A second, decorative curtain can be hung outside the tub, where it seems to block a flow of air that would otherwise push the working curtain inward. If the shower is in a stall rather than a tub, the only remedy I know of is to add small weights along the bottom of the curtain.

Curing the problem is easier than explaining it. Is it caused by a flow of air under the curtain and into the shower compartment, as one might expect when the shower is hot and the room air is cool? Or does the curtain move because the pressure of the water or the air in the compartment is reduced by a principle of fluid flow called the Bernoulli principle? When I investigated the matter, I discovered that neither explanation appears to be correct. The Bernoulli principle seems to have no role in the curtain's motion and the airflow under the curtain is usually outward, even during a hot shower.

I begin with what is perhaps the most popular explanation: that the curtain moves because of the principle named for the 18th-century Swiss mathematician Daniel Bernoulli The explanation has it that the water in the shower is at a pressure lower than atmospheric pressure because it is moving; the water's lower pressure reduces the air pressure in the shower compartment and so, because the air outside the curtain is at atmospheric pressure, the curtain is forced inward. Proponents of this explanation point out that the faster the water flows, the more the curtain moves in. They reason that the faster flow means more reduction in the water and air pressure within the compartment.

The Bernoulli principle involves the energy of a fluid in motion. If the flow is constrained by walls, as it is in a pipe, the energy must remain constant (provided that friction from the walls is not important). Suppose the flow passes through a section of pipe that narrows. When the water enters the narrow section, the water's speed increases; so does the energy-kinetic energy-associated with speed. The increase in the kinetic energy is at the expense of the fluid's pressure, which is a form of potential energy. The Bernoulli principle states that the exchange leaves the total energy unchanged. In a pipe the regions of faster flow have lower pressure.

The shower jet is different because it is not constrained. When the water emerges from the shower head, its pressure matches that of the air around it, which is at atmospheric pressure. As the water falls it certainly increases in speed (as do most things that fall), but the increase in kinetic energy is provided by gravity; no energy is removed from the water pressure, which continues to match atmospheric pressure. A simple application of the Bernoulli principle, then, fails to explain the curtain's motion; it also overlooks the fact that a shower is often a spray rather than a jet.

Sometimes advocates of the Bernoulli principle consider the movement imparted to the air by the jet or spray. Some of the air is entrained by the water and thus made to move downward. Since air is a fluid, might its motion be covered by the Bernoulli principle? In other words, does the air gain kinetic energy at the expense of its pressure? No, it gains kinetic energy because it is forced to move by the water.

Another popular explanation for the shower curtain's movement involves a chimneylike convection. When the shower water is hotter than the air in the room, it heats the air within the shower compartment, which rises and flows out over the curtain and into the room. Cooler air from the room should flow under the curtain and into the compartment, replacing the air lost over the curtain; the influx should blow the curtain inward. The explanation is bolstered by two observations. The hotter the shower is, the more the curtain moves inward, presumably because of stronger convection. Also, if the influx is blocked by a second, exterior curtain, the interior curtain may be stationary.

For a long time I assumed that chimneylike convection was responsible for the curtain's motion. Then, when I was leading a workshop at a hotel a few years ago, one of the teachers in the audience tested the idea. Returning to her room, she turned on just the cold water in the shower. If the heating-and-convection explanation was correct, the curtain should not move inward-but the experimenter quickly returned with the news that the curtain did move inward even in the absence of heating.

What then does account for the curtain's movement? I decided to investigate two shower arrangements. One was a large shower stall enclosed by tile walls and a glass door (except for a space above the door). The other shower was in a bathtub, bounded by three tile walls and with a single plastic curtain. In both compartments the water struck the middle of the floor. The impact region where the water hit the floor took up about half of the width of the stall and the full width of the bottom of the bathtub. I began my work with the stall shower, because the stall was roomy enough for me to explore the air circulation without having to stand under the shower.

I monitored the airflow within the compartments with a lighted candle. The flame's orientation provided a crude measure of flow direction and speed-particularly in the case of horizontal flows, which tilted the flame from the vertical. Upward flows of air lengthened the flame and downward flows shortened it. Turbulent air set the flame dancing wildly.

1t was winter, and so I was concerned that variations in the house heating might influence convection in the two bathrooms. To reduce that possibility, I closed the doors to the rooms and kept the thermostat controlling the house heat at a constant setting; after two hours the air in the rooms settled to a temperature of about 20 degrees Celsius. Running a hot or a cold shower would, of course, tend to warm or cool the bathroom, and so I worked quickly enough to prevent the room temperature from changing by more than a few degrees in the course of a trial.

In each trial I recorded the directions of the airflow on photocopied sketches of the shower compartments on which I had labeled the three walls. The "back wall" was the wall opposite the door or curtain, the "head wall" was the one with the shower head and the "foot wall" was opposite the shower head.

My candle flame proved to be surprisingly durable when I probed the air near the falling water, but of course it was often extinguished. To relight the candle I kept a second one burning in the room. Whenever my probe candle was doused by the shower stream, I reached out to hold the wet wick in the flame of the second candle; the flame evaporated the water in a series of sputters and then relighted the wick. (If you try these experiments, take care not to burn yourself or to let the unattended second candle start a fire.)

The door in the large shower stall was near the head wall. With the door open, I ran a shower with only cold water, which was at five degrees C. Although the water was painful to my bare feet (I was otherwise clothed), I managed to map the airflow throughout the compartment and in the doorway [see illustration below]. Air flowed vigorously outward along the entire width of the bottom of the opening. Along the top of the opening the air flowed outward on the foot-wall side but inward on the head-wall side. At all levels inside the stall the air circulated horizontally around the falling water, moving from the head wall along the back wall and then along the foot wall and finally escaping through the doorway.

When I held the candle near the falling water, the flame was pulled toward the water, revealing that the air was being strongly entrained. The layer of entrainment was about one centimeter thick on the head-wall side of the spray and twice as thick on the opposite side. Except near the floor, air was entrained along the entire length of the falling water. Along the floor near where the water hit, air flowed strongly away from the impact region and then either joined the horizontal circulation or escaped directly through the doorway. Since the water cooled the air within the compartment, some part of the airflow pattern I recorded was certainly due to convection.

In order to eliminate convection, I next opened the hot-water valve until the shower water was within a degree of the room temperature. (I also adjusted the cold- and hot-water valves to maintain the original flow rate.) After allowing 30 minutes for the compartment to adjust to the new water temperature, I began probing the airflow with my candle.

The horizontal circulation around the falling water was again clearly present near the floor and at intermediate heights, but now it was weak near the top of the compartment. Turbulent air flowed upward near the head wall. On the head-wall side of the falling water the entrainment of air was similar to what I had seen earlier, but on the foot-wall side the entrained air veered off toward the back wall to join in the horizontal circulation. As before, air flowed strongly outward at the bottom of the doorway, but now the inflow through the top half of the opening was weak.

The most interesting aspect of the flow pattern was along the floor of the compartment. Air that was released from entrainment flowed away from the impact region. Some of it escaped immediately through the doorway; the rest was eventually forced upward by a wall and then into the horizontal circulation around the falling water.

Next I cut off the cold water and increased the hot-water supply, again attempting to maintain the same flow rate. The water temperature rose to 51 degrees C. but then gradually dropped to 45 degrees as my water heater struggled to keep pace. The airflow within the compartment was remarkably different from that in the previous trials. Along the bottom of the doorway air flowed inward vigorously. The horizontal circulation around the falling water was missing except near the top of the compartment. Everywhere along the bottom of the compartment the candle revealed strong upward flow. Even the entrainment layers seemed to be modified: apparently the entrained air heated so rapidly that it broke free of the water and actually rose.

I moved from the shower stall to the bathtub shower. My findings in the stall had taught me that convection can greatly alter the circulation system established by entrainment. In the bathtub I therefore first brought the shower water to room temperature in order to explore what happens in the absence of convection.

The curtain moved into the shower compartment, most strongly near the falling water and near the head wall [see illustration above]. Air circulated horizontally around the falling water as it had in the previous trials. Air near the falling water was entrained, brought down to the tub bottom and then sent outward along the bottom until it was forced up by the side of the tub; where the curtain bulged inward, this upward flow sent the air out into the room. The only strong flow of air into the compartment that I detected was in the lower part of the small space between the head wall and the end of the curtain.

When I turned on only cold water, the airflow pattern changed in two respects. Air poured out through the lower part of the space between the curtain and the foot wall and air flowed into the compartment over the top of the curtain. Otherwise the flow pattern was like the cold-water pattern in the shower-stall trials.

When I turned on only hot water, most of the curtain bulged into the compartment; air flowed vigorously outward through the space provided by the bulge, except near the head wall, where it flowed inward [Figure 3]. At the bottom of the space between the end of the curtain and the head wall, air flowed into the compartment. At the foot-wall end of the curtain the flow h was chaotic but generally inward. The horizontal circulation had shifted to the top of the compartment; air in the bottom of the compartment rose turbulently.

When the trials were completed, I finally understood why a curtain moves inward when I take a shower. Both entrainment and convection are important, but entrainment is the primary factor [see Figure 4]. Entrainment removes the air that is next to the falling water, except near the bottom. On the head and foot sides, additional air flows directly toward the falling water to replace the removed air, only to be itself entrained and removed. In the region between the curtain and the falling water the replacement is slow, because the air must flow first along the curtain and then toward the water. When the shower begins, the air pressure in that region drops as a result of that slow replacement. Since the air outside the curtain is at atmospheric pressure, the curtain billows inward. Although the bottom of the curtain is near where entrained air is released, the edge is pulled in by the higher parts of the curtain. The bulge along the bottom opens an avenue for air to flow into the room. The flowis nearly always outward, regardless of the relative air and water temperatures.

If the water is at room temperature, the outward flow is air released from entrainment just below the curtain; it flows along the bottom of the compartment, upward outside the curtain and finally out into the room. If the water is colder than the room air, the outward flow is enhanced by convection as the chilled air escapes . into the room and warmer air flows over the curtain and into the compartment. The enhanced flow under the curtain may move the curtain in more than entrainment alone does.

If instead the water is hotter than the room air, there may be little release of air under the curtain because the air entrained by the falling water quickly heats up and breaks off from the fall. The bulge in the curtain does, however, expose a pool of hot water on the floor of the stall (or the bottom of the tub). The pool heats the air above it, sending the air upward against the outside of the curtain and from there out into the room. The resulting extra push on the curtain is the reason the curtain may move inward more during a hot shower than during a cooler one. To sum it up, entrainment initiates the inward movement of the curtain and convection can enhance the effect.

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