Chapter 2     Toilet Science

The toilet is wet and moist, with water in and out through pipes and sewers. Sometimes, you have puzzled experience there, especially, in the hand basin, toilet bowl and shower curtain, etc. In this chapter, the hidden science will be revealed and you will have a better understanding on them.

The Swirling of Water in a Basin

A common observation that the water in a basin (bathtub or toilet bowl) goes down the drain in specific directions: counter-clockwise or clockwise. One can also find both counterclockwise and clockwise flowing drains in both hemispheres. The over-addicted physics teacher may even said that it is the result of the Coriolis effect. Don't believe them! There is one technicality: although water will tend to swirl in the basin as it nears the drain, the effect is so incredibly slight that the swirling direction you observed is not Coriolis effect but instead the geometric structure of the basin and the outlet. Surely, the physics teachers are not that crazy to have such arguments, but they wrongly emphasize such effect and reluctantly apply them to the basin (bathtub or toilet bowl). In a rigorous experiment, not using hand basin this time, the more precise conclusions are: counter-clockwise in the Northern Hemisphere and clockwise in the Southern.

How Things Work
  • What is Coriolis effect?
    We know that all points on the Earth have the same rotational (angular) velocity, w (they go around 360o per day). Also, places at different latitudes have different linear speeds. A point near the Equator may go around a thousand miles in an hour, while one near the North Pole could be moving only a few dozen miles in an hour.
    When an object moves to the Equator from the North Pole and is not firmly connected to the ground (air, long-range missile, etc), then it maintains its initial speed as it moves (an extra left component in speed, if it is initially a distance apart from the North pole) . This is just an application of Newton's First Law. An object moving left continues going left at that speed (both direction and magnitude remain the same) until something exerts a force on it to change its velocity. Objects traveling towards the Equator from the North Pole will eventually be going more slowly than the ground beneath them and will seem to be forced right. The following figures show the Coroilis effect.

  • Similarly, objects launched to the North from the Equator retain the right component of velocity due to its sitting at the Equator before. But if it travels far enough away from the Equator, it will no longer be going right at the same speed as the ground beneath them. The result is that an object traveling away from the Equator will eventually be heading right faster than the ground below it and will seem to be moved right by some mysterious "force".
  • Go back to our discussion in the swirl of water in an "ideal" basin and drainage (see the experiments described below in "Science in Depth"). The above Coriolis effect leads to a right deflection on every moving water element in the Northern Hemisphere. As a result, a vortex is formed, as shown in the drainage (the shadow region) in the figure. The blue arrows show the direction of the flowing water.

Apparently, objects stay on the ground travel the same speed as the ground. As a result, there is no Coriolis effect. For example, a stationary object on the Earth does not exhibit such effect, because the object velocity relative to the Earth is zero.

Science in Depth
  • To prove that the effect does occurs, experiments were actually done in the sixities by two groups of scientiests: one in Massachusetts Institure of Technology (MIT), and one at the University of Sydney in Australia. Boths groups used a tank six feet in diameter, filled to a depth of six inches with water. The drain was three-eighths of an inch across, set in the middle of the tank, flush with the bottom. Both groups allowed the water to sit for 18 to 24 hours after filling. Their plugs were being pulled out from below, leaving the stilled surface of the water undisturbed. These experiments confirmed what everyone had expected - the water does flow down the drain in different directions in the Northern and Southern Hemispheres.
  • Here shows an illustration to the Coriolis deflection on a moving ball in a rotating merry-go-round. Note that the deflection is to the left of the moving ball. Do you know why?

The Flush in a Toilet Bowl

The bowl of a flush toilet is a porcelain (pottery made of a special white clay) vessel with a built-in siphon, usually visible (sometimes hidden in some toilet bowls) as a curved pipe protruding from the back. In most toilets, the bowl has been molded so that the water released from the tank enters the rim and it drains out through the holes in the rim. Normally, the bowl contains a small amount of water which is enough to form an air trap inside the siphon pipe, preventing foul air escaping from the sewer.

When the toilet is used, liquid flows slowly through the siphon pipe as waste matter is added, but the flow volume is too small to fill the siphon. To flush the toilet, the user activates the water tank which pours a large quantity of water quickly into the bowl. This creates a flow large enough to fill the siphon pipe, causing the bowl to empty rapidly due to the weight of liquid in the pipe. The flow stops when the liquid level in the bowl drops below the first bend of the siphon, allowing air to enter which breaks the column of liquid. In this section, we are not interested in the refill mechanism in the tank but instead the siphon in the toilet bowl. The crucial mechanism is called the bowl siphon which is shown in the following animation (Credit: Marshall Brain's How Stuff Works).

How Things Work
The flushing mechanism is summaried in the following points.
  • Since all of the water in the tank enters the bowl in about three seconds, it is enough to fill and activate the siphon effect, and all of the water and waste in the bowl is sucked out. The figure below shows the structure of the toilet bowl (Credit: Selected Lectures in Toiletology 101). Inside the rim is a number of holes so that water leaves the rim and enters the bowl after flushing. An inverted U-pipe is attached to the back of the bowl and it works like a siphon pipe.

  • When flushing the toilet, all of the water in the tank (around 2 gallons, that is 7.6 liters) is dumped into the bowl in about three seconds. A good portion of the water flows down to a larger hole at the bottom of the bowl. This hole is known as the siphon jet. Water rises in the bowl and flows over the dam, but no siphon or flushing action has yet started. As more water enters the bowl, the volume and velocity of water flowing over the dam also increases, creating a curtain of water through the passageway, creating a partial vacuum -- the start of siphonic action. The curtain of water also prevents air from entering the passageway through the outlet.

  • As incoming water continues to accelerate, more of the air in the down leg of the passageway is displaced, as shown in the figure below.

  • When the passageway is filled, a good flush or siphon action is created. Everything in the bowl is sucked out through the passageway.

  • As soon as the level of the water in the bowl drops to the level where air is again introduced into the passageway, the siphon is broken.

  • When deep seal of water is not restored with refill water, sewer gas will enter. The below figure shows the foul gas coming up from the sewer.

Science in Depth
  • What is a siphonic action?

    • As mentioned before, a siphon is an inverted U-pipe that can transfers water from a higher reservoir to a lower reservoir by lifting that water upward from the higher reservoir and then lowering it into the lower reservoir. As a demonstration on siphonic action, please click the right movie (Credit: Department of Physics, The Wake Forest University) to see how siphon pipe works.

    • In fact, the water is simply seeking its level, just as it would if you connected the two reservoirs with a pipe at their bottoms. In that case, the water in the higher reservoir would flow out of it and into the lower reservoir, propelled by the higher water pressure at the bottom of the higher reservoir. In the case of a siphon, it's still the higher water pressure in the higher reservoir that causes the water to flow toward the lower reservoir, but in the siphon the water must temporarily flow above the water levels in either reservoir on its way to the lower reservoir. The process is initiated by your first suck on the open end of the pipe to the lower reservior. However, the water is able to rise upward a short distance with the help of air pressure, which provides the temporary push needed to lift the water up and over to the lower reservoir. At the top of the siphon, there is a partial vacuum--a region of space with a pressure that's less than atmospheric pressure. The same kind of partial vacuum exists in a drinking straw when you suck on it and is what allows atmospheric pressure to push the beverage up toward your mouth.

  • The siphoic action can be explained in terms of energy.

    • We know that the higher water is, the more gravitational potential energy it has. Water, like a ball at height, accelerates in whatever direction reduces its total potential energy. Consider the case, you connect two containers which are at different levels, one higher than another, with a straight pipe. As long as the water goes only downhill through the pipe, the situation is simple. However, replacing the straight pipe by an inverted U-pipe, the flow starts upward before it bends downward. The mystery lies in the fact that water has more than one type of potential energy. In addition to gravitational potential energy, water has potential energy associated with its pressure.

    • High-pressure water has more potential energy than low-pressure water, which explains why water tends to accelerate from high pressure toward low pressure-from high potential energy to low potential energy-even in the absence of gravity. Clearly, the pressure of water in a sealed pipe decreases with altitude. Because of this pressure effect, the total potential energy (gravitational plus pressure) of water in a closed pipe doesn't change, even as that water rises a short distance upward inside the pipe! Undoubtedly, the gravitational potential energy of the water is increasing as the water rises, but its pressure potential energy is decreasing by an equal amount.

    • In a siphonic U-pipe, the weight of water in descending portion of the pipe actually decreases the pressure inside the rising portion of the pipe. As a result of this extra pressure drop, water in the high container can reduce its total potential energy by accelerating toward and then through the pipe. Water begins flowing through the pipe, even though it has to go upward for a short time during that passage.

    • Practically, the failure of the siphon effect occurs when the water is about 30 feet (10 meters) above the higher container. You can't use a siphon to lift water higher than 30 feet because above that height, an empty region will develop at the top of the pipe and stop the siphon process.

Shower Curtain

When you are having a shower, the curtain sneak up and slap you on the leg. Do you have such experience? You might explain it by knowing that the hot air rises. The hot water in a shower warms the air, especially the air bounded by the curtain, the cold air then rushes in and fills the space caused by the escape of hot rising air in the bottom. The curtain moves inward and slap your leg. Perhaps, it is a reasonable answer. Surely, you will reject it when you do have the same experience while having a cold shower.

How Things Work
There are two possible answers that explain the phenomenon.
  • The Bernoulli's principle
    The falling water is carrying along some entrained air, making an air current near the inside surface of the curtain. According to the Bernoulli's principle, the faster a gas/fluid moves across a surface, the lower its pressure against that surface. Since there is no speeding airstream on the outside of the curtain, the air pressure on the outside is higher and the curtain moves inward.
  • The induced electrostatic charge
    When water streams out a narrow opening such as the hole in a showerhead, it can pick up a static electric charge. Electrons can also be scraped off - or onto - the water by the showerhead, depending on what it is made of. But if the water's molecules are to pick up, say, a negative charge on their way out of the showerhead by picking up some negative electrons, those extra electrons would repel some electrons from the surface of the shower curtain, because similar charges repel each other. That would leave the curtain's surface with a deficiency of negative charge, and its inherent positive charges would dominate. The negative water and the positive curtain would then attract each other, as is the propertry of opposite charges, and the curtain would move toward the water.

  • The forces so generated due to the above processes are very weak. They are only sufficient to pull light, thin curtains inward. Typically, heavy plastic curtains don't have this problem. Also, if someone has poor water pressure or a poorly atomizing showerhead, they may not see the curtain suck in. The easiest way to keep the curtain from slapping your leg is to sew weights in the bottom. Or, if you have a metal tub, magnets can hold the curtain in place.
  • A daily example about electrostatic charge. Have you ever opened a carton packed with those styrene foam packing peanuts, especially when some of them are broken into small fragments? Just try sticking to your hands as you try to brush them away. It's because of induced electrostatic charges.

Science in Depth
Bernoulli's effect is the result of conservation of energy. As a simple illustration, consider a running fluid through a horizontal pipe which has a narrow constriction on the flow path. The fluid moves faster on the narrow constriction, but at the same time we find a lowering of fluid pressure there. In general, a flowing fluid can be considered having energies due to two parts, namely, the potential energy and the kinetic energy (the third term in the following equation). The former is static in sense, while the latter is dynamic as it relates to the velocity of fluid. The potential energy includes two components, the gravitational potential energy (second term in the following equation) due to its altitude and the pressure energy (the first term in the following equation) due to the pressure the fluid experiences. Specifically, the gravitational potential is considered when the fluid is running through an inclined pipe.

The equation above is the well-known Bernoull's equation, it states clearly that the total energy per unit volume in a flowing fluid is a constant. The Bernoulli's effect is widely applied in aerospace engineering, for example the design of airfoil.
A simple illustration can be done by blowing a stream of air on the top of a strip of paper just below your lower lip. The paper rises as the result of a lower pressure occurs above the strip of paper while blowing on it with a stream of air. Click the right movie (Credit: Department of Physics, The Wake Forest Univeristy) to see how the paper rises.

The second illustration is performed by using two empty aluminum drink cans on a bed of drinking straws over a smooth table. Strongly blow air between the cans which are 3 cm apart. The cans move together. It is again the result of the Bernoulli's effect - lowering the pressure at the place where the fluid flows faster. Click the right movie (Credit:The MCA Millchrest Academy) to see how the cans move together.


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