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.

Insight
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 sixties by two groups of scientists: one in Massachusetts Institute of Technology (MIT), and one at the University of Sydney in Australia. Both 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).

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 property of opposite charges, and the curtain would move toward the water.
Insight
For the shower curtain, 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 Bernoulli'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 University) 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 to see how the cans move together. Further examples: The below figures show the air circulation in a prairie dog burrow. A prairie dog burrow typically has a high mound on one end and a low mound on the other. Since the wind speed increases with height above the ground (v1 > v2), the pressure is smaller at the high-mound end of the burrow. The result is a very convenient circulation of fresh air through the burrow. Courtesy: iv Courtesy: iv The Bernoulli's principle explains the lifting up of the roof when a strong wind blows across the roof of a house. The lifting force F pushes up from inside of the house against the roof. The explanation is simple. When a strong wind is blowing across the house, the air current is moving fast with speed v. The pressure over the roof is therefore less than the pressure inside, as the air inside is at rest, resulting in a net upward force on the roof. Courtesy: iv Courtesy: iv Polarization The left figure below shows the polarization of a neutral insulating object due to the approaching of a positively charged glass rod. Each atom has now become an electric dipole, in which the center, or average location, of the negative charge is separated by a slight distance from the center of the positive charge. The atom now has positive and negative poles - and we say that the material has become polarized. The negative side of the object will be attracted by the positively charged rod. The right figure shows the attractive force of a charged plastic rod on the packing "peanuts" which are made of plastic foam. Because the mass of peanuts is so small that the attractive force is capable to lift the peanuts. Courtesy: iii Courtesy: iii

Buoyancy

Small kids love to play with the rubber duck in the tub filled with water. The duck floats on water without sinking and its weight is balanced by the buoyant force of water. In this section, we will investigate the buoyant force due to the Archimedes' principle. The idea is extended to explain an iceberg floating in seawater.

How Things Work
According to the Archimedes' principle, the magnitude of the buoyant force on an object always equals the weight of the fluid displaced by the object. When you try to push a beach ball down under water. It is extremely difficult to do because of the large upward force exerted by the water on the ball. The upward force exerted by a fluid on any immersed object is called a buoyant force. To determine the magnitude of a buoyant force, imagine the volume occupied by the beach ball is a parcel of water of the same size. This volume of water is at equilibrium and its weight must be balance by a upward force, i.e. the buoyant force. And, this force is a resultant force due to the surrounding water. When this parcel is not here and is replaced by the beach ball of the same size, the same buoyant force applies on this ball. In the left figure below, as the forces on the lateral surfaces of block are horizontal, the resultant buoyant force is the net of the top and bottom forces due to the surrounding water. If the buoyant force is less than the weight of the block, it sinks down the water with acceleration, on the other hands, if the buoyant force exceeds the weight of block, it moves up and floats on the water surface. The middle figure shows an iceberg in the sea for which the ice floating above the water surface is less than 10% of the total volume. It is very unfortunate when a ship collides with an iceberg and becomes a severe accident, because the mass of iceberg in the collision is unexpected huge in size. The right figure shows a steel tanker floating on the sea. Although steel is denser than water, a tanker's bowl-like hull displaces enough water to allow it to float. Courtesy: v Courtesy: iv Courtesy: iii
Science in Depth
From the Archimedes' principle, the buoyant force depends on the volume of object submerged under the fluid. A study of the iceberg points out that about 90% of the iceberg is under water. The ratio of density of ice to water equals to the ratio of volume of ice under water to the total volume of iceberg. The buoyant force is not necessary for object floating over water, it could be about any fluids, e.g. air. Rising balloon in air is a good example about buoyant force. The density of the hot air inside the balloon is lower that of the surrounding air. The magnitude of the buoyant force on the balloon is exactly the weight of surrounding air that has the same volume as the balloon. The motion of the balloon is governed by the resultant force acting on the balloon (i.e. the net of the upward buoyant force and the weight of balloon). Courtesy: vi Courtesy: iv

Atomizers and Spray Bottles

An atomizer is a device which changes a stream of liquid into a fine spray. It is used in a perfume bottles as well as inhalers for medications. The working principle is simply the Bernoulli's principle. An atomizer has several components. A bulb, a nozzle and a tube are connected with each other. There is a vertical tube that allows the liquid to pass through the nozzle.

How Things Work

The operation of an atomizer The high-speed jet of air created by squeezing the bulb creates a low pressure at the top of the vertical tube. This causes fluid to be drawn up the tube and expelled with the air jet as a fine spray. The amount of spray that ejected from the nozzle depends on the size of the bulb. Typically, an atomizer is used to dispense something in small and controlled amounts. It serves well for cooking. Chefs prefer to dispense small amounts of ingredients, e.g. cooking oils and cover the cooking pan. It also serves patients in medical use, e.g. inhalers. The spray bottle There is another type of device which pumps fluid from a bottle, i.e. the spray bottle. This type of device works differently and it is commonly used to dispense cleaning agents and cleansing fluid. A spray bottle has a spring-connected trigger lever which provides strokes to the pump. The downstroke has the piston pushing in and the upstroke has the piston moving back. The barrel is narrow such that the fluid comes out through it and reaches the nozzle. Inside the pump, there is a cylinder which has its volume decreases when the piston is moving in. The fluid inside the pump is forced out of the barrel. The trigger lever returns to its initial state when the elastic spring restores its length. The volume of the cylinder increases and the pressure of it drops rapidly. The pressure difference between the pump and the reservoir sucks the fluid into the pump. These two strokes of the piston constitute the pump cycle. To ensure the flow is in only one direction. The spray-bottle head has two one-way valves. The one in the barrel has a tiny rubber ball that rests in the barrel and blocks the barrel until the fluid is forcing out (figure 1). The next valve is located between the pump and the vertical tube connecting the reservoir. It blocks the vertical tube at all times except when the trigger lever is moving back (figure 3). Notice that this valve is kept closing the tube when the fluid is emitting out through the nozzle (figure 2). The design is to ensure no fluid flowing back to the reservoir. However, when the trigger lever returns the volume of the cylinder increases and thus a decreasing pressure inside it. The fluid in the reservoir moves up the tube by sucking and the flow opens this valve. The cylinder is filled until the valve closes again.

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