Supermoon 2015

Nikon D700  1600mm
Mid-Autumn Festival @Hong Kong 2015

From Vacuum Pump to Flush Toilet

I learned vacuum pumps 28 years ago in the Material Science course. At atmospheric pressure and mild vacuums, molecules interact with each other and push on their neighbouring molecules in what is known as viscous flow. For UHV (Ultra-High Vacuum) applications, about 10⁻⁷ pascal (10⁻⁹ mbar, ~10⁻⁹ torr), requires multiple vacuum pumps in series and/or parallel working together. Categorised by technologies, there are broadly three types of pumps:

1. PULL/拉 Displacement pumps for low vacuums (e.g. piston pump), 
2. PUSH/推 Momentum transfer pumps in conjunction with one or two positive displacement pumps to achieve high vacuums, 
3. Entrapment pumps used in the final stage to reach ultrahigh vacuums.

In daily life, we move unwanted thing away by push and pull. When we do it, momentum of the object change. In a momentum transfer pump, gas molecules are accelerated from the vacuum side to the exhaust side. But the pumping action is only possible below pressures of about 0.1 kPa or 1 mbar (1 bar ~= atmospheric pressure on Earth at sea level). This regime is generally called high vacuum (because the distance between the molecules increases, the molecules interact with the walls of the chamber more often than with the other molecules. So molecular pumping becomes more effective than displacement pumping).

The two main types of molecular pumps are the diffusion pump and the turbomolecular pump. Both types of pumps blow out gas molecules that diffuse into the pump by imparting momentum to the gas molecules. During the operation, a base pressure will be reached when leakage, outgassing, and back streaming equal the pump speed.

Turbomolecular Pump

Diffusion Pump

Flush Toilet

What can we tell if applying the knowledge of pumps to the flush toilet? First, both are on moving floating (air/water) things (dusts and particles/“things”) from one place to another place. Second, the chambers are very different. For the vacuum systems, pumps are mounted to the exhaust of the sealed close chambers. But for flush toilet, the chamber is the open bowl. Third, since there is no moving part, the flush toilet is similar to the diffusion pump system.

Consider the design of the flush toilet, “things” are flushed through the pipe by the water jet from the tank (conventional: 10L/flush, modern low flush toilet: ~5L/flush) with the help of siphon of the S-shaped trapway.

In fluid dynamics, Bernoulli's principle states that for an ideal fluid with no viscosity and heat flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. This is equivalent to, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant.

Apply Bernoulli’s equation to the siphon:

we can determine,

1. Velocity of the siphon v_c is driven solely by the height difference between the surface of the upper reservoir and the drain point. That means, the sucking force is directly proportional to the total weight of water inside the filled tube! 
2. Maximum height of the intermediate h_b high point occurs when it is so high that the pressure at the intermediate high point is zero; this will cause the liquid to form bubbles and if the bubbles enlarge to fill the pipe then the siphon will "break". The value is about 10m for water. 

What is the volume of water to start the siphon inside the bowl? The amount is small. You can see it from the video at below. Also note that the waterways in the siphon toilets are designed with slightly smaller diameters than a non-siphoning toilet, so that the waterway will naturally fill up with water, each time it is flushed, thus creating the siphon action.

Conclusion

1. You see a large flow of water running down the bowl carry away the “things”. But it is not the complete story, siphon of the S-shaped trapway (inverted “U”) is the main mechanism of sucking.
2. Running water from the tank acts like a diffusion pump. It is in serial connection with a displacement pump in which now is the siphon action.
3. Because the amount of water to start the siphon is small. So siphon happen quickly after the start of water flow. The following water running from the tank until stop is the current carrying the “things” along the pipe.
4. The followings will either “kill” or slow down the siphon at the beginning:

• blocked trapway, 
• pipe leakage (below normal water level), 
• frozen pipe (empty trapway), 
• back streaming (imbalance of water pressure).

Take Home Lessons

1. Make a clean flush before using the toilet (put down the cover may increase the downward force).
2. After using the toilet, before trigger the flush, gently pour some water into the bowl (may consider using hot water in winter).  
3. Uses toilet tissue not facial tissue. Toilet tissue is designed to decompose in septic tanks because its fibres is shorter. Compaction of toilet paper in drain lines, such as in a clog, prevents fibre dispersion and largely halts the breakdown process.
4. Don’t rush Wait a few seconds before trigger the flush may help softening the tissue in water.