Physics

# The Physics of a Toilet

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A toilet has three main parts: a bowl, a tank, and a siphon.

Four principles of physics suffice to explain how it works: potential energy, pressure, the siphon effect and buoyancy.

The bowl supports the seat and receives the "deposit" from the user.

The tank is mounted on the bowl and holds the water used to clean it out. There's a hole in the bottom of the tank that's normally closed by a stopper called the "flapper." Turning the handle pulls a chain that lifts the flapper, causing the tank water to drain into the bowl. From there it runs through the siphon and into the house plumbing, carrying the contents of the bowl with it.

The siphon is a fairly wide channel shaped like an upside-down letter J that connects the bowl to a waste pipe in the floor. Its shape forces water leaving the bowl to flow uphill for awhile before finally running down the drain. This creates a trap which keeps water in the bowl between flushes.

The tank and bowl refill after every flush like this. A high-pressure water supply line runs into the tank. Its opening is controlled by a "float valve" which has a lighter-than-water part - the "float" - that floats in the tank. Whenever the float drops below high-water mark, the valve opens, allowing water into the tank. When the float is at high-water-mark, the valve is closed, stopping flow. So after every flush, the float valve lets just enough water back into the tank to fill it again.

Potential energy is energy caused by a substance's position or condition, rather than its motion. A book on a shelf has potential energy relative to the floor. If you push it off the shelf, this potential energy converts to kinetic energy (energy of motion) as it falls.

When the book hits the floor, its kinetic energy dissipates into heat, sound and wind.

On the floor, the book is as low as it can go - at "ground" level with zero potential.

Put it back on the shelf, and it regains the same amount of potential energy it had before.

Lifting it up takes work. Your muscles provide the kinetic energy required for this work - which equals the amount of potential energy gained by raising it. This illustrates the Law of Conservation of Energy, which states: Energy cannot be created or destroyed - only changed from one form to another. (This law holds in everyday life, but not in nuclear physics, where energy and mass are interchangeable.)

In other words: When we drop things, we convert potential to kinetic energy. When we pick things up, we convert kinetic energy to potential energy. So lifting stuff up is a way to store energy for later use.

When the tank refills after every flush, potential energy is stored in the water due to its position above the bowl. When flushed, its potential energy turns kinetic as it drops from the tank through the bowl and on down.

So lifting water to a tank on the second floor from a pipe down in the ground takes work. Where does the energy for this work come?

From the water company. Water moves up the pipes because it's under pressure. It's under pressure because the water company constantly pumps more water into the pipes under pressure. (The water company gets the energy for this from the power company, which likely gets it by burning oil or gas or nuclear fission.)

When high and low pressure substances comes into contact, stuff moves from high to low pressure and continues moving as long as pressure differences coexist within a system. When pressure equalizes, movement stops.

Think of a balloon. The air inside is higher pressure than that outside. But it doesn't go anywhere because it's trapped inside. If we stick a hole in it, however, high-pressure air inside rushes out to meet low-pressure air outside, and the balloon bursts.

Water in supply pipes acts the same. When valves are closed, the water has nowhere to go. When a valve opens, high-pressure water in the pipe contacts low-pressure room air, and moves out into the air. Water leaving the pipe creates a low-pressure zone behind itself that is instantly filled by more high-pressure water moving up from farther down the pipe; and so on down the line. Water runs whenever the valve is open, because the water company keeps pumping enough water back into the pipes to keep the pressure high. When the valve closes, the flow stops.

Now we need to look at how flushing works.

When the toilet is flushed, two gallons of water drop from tank to bowl with enough speed and force to clean it out. If we poured two gallons in slowly, however, the toilet wouldn't work. Water would trickle down the drain, but the "deposit" would stay in the bowl.

Why is this so? The answer lies in the siphon effect.

Fill a bucket with water. Place it on the kitchen counter. Submerge a length of tubing in it until it's completely full of water. Make sure all air bubbles are gone. Pinch one end of the tube shut. Lift it out of the bucket without dripping any water from it. Keep the other end of the tube inside the bucket. Make sure there are no kinks in the line. Place the pinched end of the tube in the sink, below the bottom of the bucket. Un-pinch the tube.

Water will flow from the tube. The whole bucket will empty eventually if you keep the tube open.

That's the siphon effect.

Potential energy (and Hydrogen bonds) can to explain it.

Without the tube setup, water in the bucket has zero potential. It's at ground level with nowhere to go.

With the water-filled tube in place, however, there's now a clear path to a lower level - an open channel full of water leading from the bucket to a point below the bottom of the bucket. The water now has somewhere to go. It has potential energy relative to a ground level somewhere down the sink drain. So down it goes.

Siphons seem unnatural because water leaving the bucket moves uphill all by itself for a while, before falling down the drain. This can be explained, however, by the fact that more water flows down the other side of the tube than flows uphill, so the average or majority of the water is a net downhill mover - which is natural. (The water acts all together like one continuous system because of "Hydrogen bonding" - but that's chemistry!)

The siphon effect works only if the channel is completely full of water and empty of air. Air in the tube prevents the formation of the continuous channel of water all the way down the tube which the siphon effect requires.

When two gallons of water drop into a toilet bowl all at once, the siphon below the bowl backs up, filling up with water all the way down. So the water in the bowl and channel act together as described above. A siphon effect is created which causes the contents of the bowl to get sucked down the drain with the tank water.

There's no siphon effect when you pour water into the bowl slowly because then air remains in the siphon. There's not enough water flowing to completely push all the air out of the siphon. So there's no continuous channel of water from the bowl to the bottom of the siphon, and so there's no siphon effect.

And that's why you need to dump a couple of gallons in the bowl all at once to flush a toilet. (You could dump it from a bucket - it doesn't have to come from the tank.)

Just one more principle to touch on.

Recall the float valve. Why do some things float while others sink?

The reason is the Archimedes principle, named after the ancient Greek scientist who jumped out of his bathtub shouting "Eureka!" after discovering it.

The Archimedes Principle states: Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

Called the buoyant force or buoyancy, this force tends to push things up, towards the surface.

The other force acting on any object submerged in, or floating on, a fluid is gravity - its weight - which tends to push it down.

The total force on the object equals the sum of the buoyant force plus gravity.

If the object is denser than water - if it weighs more than the same volume of water would - then its weight is greater than the buoyant force, and the object sinks.

If it's less dense than water, then the buoyant force is greater than its weight, and it floats.

Hope you enjoyed your physics lesson. Stay tuned for the next installment of "The Physics of Everyday Life."

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